Hello everyone, welcome. I'm Rod Kumar. I am the president and editor-in-chief of DevEx coming to you from my home like so many others who are joining call and want to thank all of you for joining us from all over the world. We're streaming live on YouTube right now and we're going to have a discussion on what to me is one of the most important topics in the world, one that is really not getting enough attention today and that's the nexus between conflict and the pandemic. If you look at a map of the pandemic of where the COVID-19 cases are around the world you will see that there are about 4.3 million cases or so and they are spread largely in advanced economies and a lot of the news as a result is about what's happening in places like New York or London or northern Italy. Understandably what epidemiologists will tell you what they've told us at DevEx is the case counts are rising in many fragile countries and many conflict ridden and the situation in many of those places will get worse as time goes on. We hope it doesn't but there is a likelihood that this pandemic will reach many many other parts of the world where today it may not be as prevalent and the big question is what do we do about that? What's going to happen and what can the international community do to prepare and reduce human suffering and make sure countries that are making progress don't backslide and we have got an exceptional group of people to get us into this conversation today. A conversation that's brought to us by the US Institute of Peace and the World Bank Group and I'm really delighted to be asked to moderate the session today and I really want to call out all of you who are joining us from around the world. We've had a huge response to this topic to please show us exactly what you think we ought to be talking about. Ask us questions, provide comments in the stream. We'll try to get to as much of it as we possibly can. I want to mention who here is with us today. We've got Nancy Lindborg, the President and CEO of the US Institute of Peace. Mr. Axel von Trottenberg who is the Managing Director of Operations at the World Bank Group. We have Lamis Aliariani who is Head of Monitoring and Evaluation for the Yemen Social Fund for Development. Lowcock who is the UN's Humanitarian Chief and Minister Samuel Tway who is the Minister of Finance and Development Planning in the Republic of Liberia. Really an exceptional group. Thank you all for making time to talk about this today. I'm just going to ask each of our participants to kind of go through and give us a couple of minutes of their take on this topic and I want to start with Nancy who as I mentioned is the President and CEO of the Institute of Peace but she really led the US Government's humanitarian efforts and humanitarian chief at USAID for a number of years she was involved in many crises that happened during her time there and at USIP has put together a task force on fragility global extremism and has really advanced the new US policy on this topic. So Nancy I'd love to hear your take on the situation now on this nexus between conflict and the pandemic and how you see it. Thank you so much Raj and let me add my welcome to everybody. Thank you for joining us this morning and as you said Raj a perfect group of panelists to talk about what we're seeing has been devastating for advanced economies and we're now looking at the specter of pandemic taking hold of more fragile countries. USIP works extensively on the world with a focus on fragile states and as we know 1.8 billion people live in those countries where poverty is concentrated. Conflict is more prevalent. It helps affected societies and most of all beat mistrust between citizens and governments and all of which make them far less resilient at the society level at the country level to the battering ram of this pandemic. I led the USA task force on the Ebola response in 2014 where I worked with ArcLocac and we saw how that disease ravaged through three West African countries that were just emerging from conflict and I'm pleased to also have with us here today the minister of finance from Liberia who has some observations but that effort left me three indelible impressions which I believe hold true today as well and the first is that when facing the pandemic number one citizen trust in government is paramount. There needs to be clear and factual information that helps people understand and believe the critical life-saving messages that are given, behavior changes that can mean life. This is as important as the health interventions. The second is security is hope but security forces can be either an enormous help or a blunt instrument that exacerbates mistrust. I'm going to turn my video off to understand it's shaky so I'm going to Arc, excuse me. We saw in 2014 when the government tried to enforce a lockdown in Monrovia that erupted into riots and we're seeing that it's happening now. We're heavy-handed police responses to those who are stuck after curfew in places like Kenya are greeted with repressive heavy-handed responses and the third is that international cooperation is essential. The world came together to contain the Ebola crisis in 2014 worked together with a common strategy with coordinated efforts that brought together contributions from around the world. That outbreak in 2014 never became a pandemic and I am constantly reminded that all the public health officials said at that time that we were very lucky and what they feared most was a lethal airborne disease which is what we have now and as terrible as this has been as a disease in the more developed world we're looking at a multi-dimensional devastation in more fragile countries political security economic and health consequences as Raj said all intertwining to have really devastating effects and I know our colleagues on the panel will talk in detail about how the pandemic is damaging these fragile countries where we risk losing precious development gains and it took two and a half decades for 700 million plus people to lift themselves out of poverty and COVID-19 could push half billion back into poverty in a fraction of that time with the lack of remittances, interrupted supply chains, shuttered economies, weak health systems all of this contributing to even greater poverty and more fragility and conflict so I want to end with like all crises there are opportunities to seize and what I really hope we can talk more about now and as you were mentioning Raj there's been this remarkable convergence of ideas over the last several years on how to more effectively address fragility fueled by the growing evidence that without more inclusive legitimate governments our development investments are less likely to result in sustained gains we will be less successful in combating this pandemic and less successful in recovering if we don't take these strategies under advisement for our many wonderful new strategies including the world's bank congratulation axle I look forward to hearing more about that and importantly the US passed in December the global fragility act and the act directs the US to work in fragile states in cooperation with the international community to support locally led strategies that integrate political security and development efforts and reinforce mechanisms for accountability and transparency and inclusivity with the goal of strengthening state society relations and in short strengthening the core government functions without which we cannot recover we can't sustain our gains so the global needs before us are absolutely enormous and the opportunity is to divert these in a way that can have longer term more effective impact at a time we need it more than ever thanks Raj thank you Nancy I think you laid out a great framework to get the conversation started um you know and as you say for a long time you've been beating the drum on this issue of prevention and resilience and now here we are facing something that many experts predicted but until it's face staring you in the face a globe a truly global pandemic is shocking and it's highlighting all the inequalities in the world and many of the countries we're talking about just don't have the resources themselves and they're turning organizations like the world bank group and I want to ask you Axel what you're doing at the world bank group many of these fragile countries that don't have the domestic resources they can't they can't address this challenge entirely on their own what are you doing what's your fragility strategy look like at the bank well thank you and uh good morning and good afternoon or good evening to everybody's pleasure that we have this discussion and let me also thank the organizer for taking the initiative this is uh important and and it is important for two main reasons first of all everybody in most countries is busy with themselves and so uh people are looking at what one can do at home uh but uh what we need to keep in mind is that unfortunately the fragile countries are going to be the most effective because they are fragile have weak structures and when our new strategy was always emphasized we need to understand the drivers of fragility I think the driver of conflict is well understood it increases fragility and I think we should be worried about that the second concern is is the lack of focus on the countries that in in a case of acute uh crisis in the world um these countries need voice they need to be heard they need to be also seen that they are uh struggling and sometimes I think we captured this well first that poverty and extreme poverty will increase with this as a consequence of this crisis and unfortunately the concentration of poverty and extreme poverty is most in the fragile countries so it's a fair assumption that this will increase secondly these countries are the weakest with health infrastructures I sometimes mention that if you are in a OECD country you have 300 people per doctor in some of the fragile kids you have 70 000 people for one doctor and that shows uh you know the enormous challenge these countries have and why we need to see how we can help there so what is in general with this type of crisis is we got to be uh fast we have to be uh action oriented and we need to provide massive support and this cannot be like little trickle support and the crumbs that are left are for for the fragile states so this is our challenge our collective challenge and uh that means that we need to look that everybody needs to see what they can do not only for the fragile mind you also for the low income and what will the bank do in the very short term we have said we would um mobilize a lot of health emergency packages we are now at 60 countries that we have uh approved packages for and we will do another 20 in the next couple of weeks we are with debt restructurings uh approaching the 100th country mark probably this week or next week so uh we are so that basically countries can buy the PPEs the the medical equipment etc and we need to continue on this uh this will be important done always in coordination with the national authorities with the UN with the rat cross whoever is engaged in this but the main thing is to help on this at the same time short term is not enough and we have said we will do over 15 months period uh about 160 billion of which two thirds will be coming from IDA and IVRD in the case of IDA the the the ambition is to have well over 50 billion dollars committed over 15 months period and uh if if IDA 18 is any measure it's about 20 to 25 percent going to the fragile state so over a 15 months period my sentence is a fair assumption that something in the order of of 10 12 billion dollars is going to be destined to uh a fragile countries but it is clear what our concern is that we may do some front loading for IDA and provide more resources but what is after that period once we have we will need more money and it is we meaning the international community needs more resources for fragile countries for the low income countries they will be affected disproportionately and there has to be international solidarity my concern is that there will be nice words but enough not enough support we need to ensure the real support and it is not only for yet for for health it is for human capital for giving them a chance at least that they don't fall back into greater fragility and unfortunately conflict that is the real risk so that is what our common challenge has to be and we have to pull together and we have to put our fingers on this therefore i'm happy to join this uh conversation because there will be urgency to act it will need to be uh seen that here unfortunately countries are disproportionately affected we stand ready to do whatever it takes we'll need to do that together nobody alone can solve it so we need to work with the UN system with the private bilaterals the NGO community and of course with the people in the countries themselves to see how we can best support them but that commitment is there from the bank my sense is it will not be enough that we do front loading of IDA and after that front loading we don't have enough resources we will need more and that we need to engage the international community with let me stop here thank you very much for that message axon we will be absolutely getting back to this theme of financing and global solidarity what does it really look like but i want to bring lemmas into the discussion because lemmas you um you have been with the social fund for development in yemen for more than 20 years now and your country has gone through a lot during that period um and is really in a state of active conflict right now and there's been just dramatic human suffering there for quite a long time and now you lay on top of that this COVID-19 pandemic so i'd love to just get your take on how you see this from that perspective from how you're seeing it in yemen and what you think we should all be keeping in mind when it comes to to countries that are suffering really that are in the most vulnerable situation during this pandemic thank you thank you raj thank you for having me on i would like to start with a common statement that that is being heard now in yemen death from coronavirus fiction is possible but death from hunger is certain yemen has as you said yemen has been in at a war for the past five years posing the largest humanitarian crisis in the world with 80 percent of the population in need of humanitarian assistance now it is facing the COVID-19 pandemic it is the most uncertain time in the life of yemen as of yesterday 65 cases have been officially reported with many more unaccounted may lead you to lack of testing just to give you an example for a population of 30 million in yemen only above slightly above 800 coronavirus tested tests has been uh have been conducted in one day in adan south of yemen more than 60 deaths were reported with no mention of their causes except for breathing problem hospitals are unprepared and under equipped health workers lack personal protective equipment and proper training it has been reported that some hospitals have denied access to several suspected cases due to fear of spread of infection it is estimated that 60 million of the yemenis will be infected with go with COVID-19 this is 55 of the population with only available in the country 700 seven ICU beds and 500 ventilators yemenis are at risk of not being able to access medical services they need but also yemenis are more exposed to COVID-19 as more than 18 million yemenis are food insecure and malnourished impacting their health and affecting their immune systems 20 million lack of reliable access to clean water to practice frequent hand washing and hygiene such factors in addition to the ongoing conflict displacement and limited social protection leaves yemenis leave millions of yemenis more at risk to the to pandemics yemen has experienced waves of color but this pandemic is like no other as it associated with loss of livelihoods food prices have increased remittances reduced and international aid is being cut to note that remittances are vital source for yemenis survival at some businesses were forced to close down such as woman hairdressers wedding halls adding to the economic strains and cutting vital source of income to many small businesses yemeni fair hungers like many other poor nations more than contracting coronavirus we fare for our lives but we have to go out and make a living authorities are asking us to stay home but they don't provide us with food rations this is from an interview on a local TV with this grim picture however there is hope in public and community actions there has been an ongoing efforts since march for confronting the outbreak of the virus from various players and i would like to focus on community actions youth these initiatives were formed in adan to clean streets from flood and sewage waste youth initiatives formed in san'a for community education and providing economic support to embellished families in rural areas with the support of social fund for development which is the largest national institution for social protection and development communities are mobilized to take initiatives including locally producing masks for their community members and youth providing awareness messages to their communities SFD also with the support of its donors has been transferring cash into the hand of venerable households along with other along with along with suitable awareness the ongoing projects that we have currently is close to 50 000 households and currently we are preparing to target additional 50 households with cash transfer for nutrition delivering at the same times health and nutrition messages and to educate family how to prevent uh how to how to take preventive measures i think i have to stop here and um back to you thank you so much love is it was an excellent review and i really appreciate you bring to the table the idea of these first and second order effects of the pandemic right there's a health crisis first but obviously it could be access to food or access to basic livelihoods that might be the thing that hurts people the most in fact we saw that experience in West Africa in countries like Liberia during the Ebola crisis where it wasn't just Ebola itself it was the second and third order effects that that really hurt people in fact i was going to go to our minister he's he's got it up for a second so i'm going to go to you mark the humanitarian chief mark locock you know we the message from Axel he said we need fast action oriented and massive support how do you judge the global community on those three factors at this point mark well hello everybody thank you good to be with you all so the starting point for me is we have an exceptional situation right we have we have basically a one one in a century situation on the pandemic and when you're in an exceptional situation what you need is extraordinary measures and lots of nation states have taken extraordinary measures but my concern is that we're not really stacking up to the scale and the speed we need this is a little bit too much business as usual when it comes to international cooperation so we really need exponentially to increase the level of f on on um collaboration i'm hearing um the story that lamis told us now about more people getting the disease every day from dozens of countries um most of them aren't being tested but they're still dying of COVID-19 but what i'm hearing to an even greater degree is the economic side of this story i think the disease is three to six months away probably from peaking in many countries but the economic calamity is with us right now and the combination of the global contraction and the lockdown measures lots of nation states have put in place is leading to a prospect we see of a doubling this year of people starving who will not survive and let they simply won't survive unless they get assistance to purchase or acquire food we're seeing a big spike in other disease related problems and our projection is that um as axl alluded to we're going to see an increasing global poverty that the proportion of people living in the most extreme poverty for the first time this year for 30 years is going to go up and not by a little bit potentially potentially by quite a lot so that's the challenge that is ahead of us and the question is how do we organize a a better response so the humanitarian system that i coordinate the UN agencies the red cross the NGOs is basically the responder of last resort for those places where governments can't or won't won't act and you know the humanitarian system at the moment reaches 100 million people a year including millions of people in Yemen and saves millions of lives a year and we have a you know we have an extraordinary seven billion dollar appeal out at the moment to do more of that in multiple places and so far you know we've trained two million health workers we have got testing kits and diagnostics and so on to 125 countries we've replaced the disappearing commercial airliners across more than 30 african countries with a UN air service to get supplies and aid workers in and out but that's the beginning we need a big scale up but because the humanitarian system is just the responder of last resort what we need to do is reduce the rate at which populations are falling into that category where they won't survive unless the humanitarian agencies help them and that's where i think the agenda axel set out is so so crucial i think that the rich world which has invested eight trillion dollars in protecting the global economy needs to invest about one percent of that in protecting so 90 billion dollars or so in protecting the world's poorest um 10 percent of the population so they don't fall into that live or die humanitarian category and i my own view is about two-thirds of that could be financed through the IFIs it was smart for the world in 2008-09 to um recapitalize the IFIs but we need to do a whole bunch more now and in particular on the fund side um and we need to make money more affordable for these fragile countries the easiest way to do that is a big sdr allocation but we need to do some things on the um subsidy side for members for borrowers accessing um fund emergency resources as well on the bank side i think it's the kinds of things that axel has been talking about across all the multilateral development banks actually but supercharged so i would be i would personally more aggressive on the front loading partly because i think the price is cheaper if you act earlier you try and contain the problems within the next one or two years to avoid a 10-year problem but i but i also think that um the price of the money is going to be a problem for some countries we need to find a way to be more generous on the um the debts debt payment suspension side i think that just as every rich country has had to rethink its fiscal rules we're going to need to have a much more um a different approach to fiscal space and and debt sustainability in these poorest countries to recognize there needs some more i think the um what the bank did in the last capital increase are starting very gently to introduce some differential pricing i think we have to do more of that i really like the stuff i know axel is trying to do to hoover up unused funds in trust funds that the shareholders have put into the bank and haven't been used um in the way they thought might be used over the last 10 or 15 years or so a lot of that can be unlocked that doesn't cost the providers of those trust funds any money because they've they've committed to it or provided it already but it can be unlocked for different purposes and my core point really raj is the smartest strategy is a big fast aggressive strategy to minimize the scale of the problem and its duration and we're not going to get that on a business as usual mindset we need something extraordinary thanks for that message mark and i we can maybe gun truth it right now with minister twaya um you know you're in Liberia a country that's gone through a lot as well in the last 20 years you've had civil conflict you've had the Ebola crisis seven or six or seven years ago now what are you seeing in terms of mark's health action here for global solidarity and for an aggressive response are you getting the response you would like to see in terms of debt suspension and cancellation in terms of financial flows from the international institutions the ifis as mark described you're muted let me ask you to unmute oh you're so sorry okay we hear you now all right i'm muted okay good so again thanks for the invite um i think this is an extraordinary opportunity um the Liberia's response has been all of society the government with full involvement of international development partnership and so the get go out say the coordination across the multilateral the bilateral the donor community space has been massive uh they've all come together and this is coming on the heel of Ebola obviously they were all here and they were quite some amazing lessons that we've learned and they wanted to see how we get ahead on this uh so from the get go the president launched a preparedness plan Liberia was around the first country uh in this on this in the continent i believe that began quarantine arrivals from highly infected european and asian countries okay so long before people told this thing serious quarantine started pretty much uh i think early february uh with that because of Ebola all right but we are at a different stage now today i think we have around two hundred twelve cases uh about 20 deaths and so the first thing we need to say the impact of COVID-19 is not going to be health in fragile countries and countries with fragile situations the impact is going to be non-health and so it's uh it's the private impact it's impact on on governance systems it's impact on resilience on health strengthening it's it's those kinds of impact on an impact on on conflicts propensities because of weakened fiscal spaces this is where i think uh the situation will be so we're not going to see the number of deaths we're seeing in america and in europe uh even those models are predicted that millions of africans will die i think those models are dead they made the same predictions with Ebola i think what has to happen that some of my colleagues have said is is we just need to develop a new paradigm a new framework of of COVID and and inculcate the key risk to fragile countries some of which i was mentioned for example our growth will be negative this year and this is coming out of a very difficult macroeconomic reform we've had to undertake in the last two years and that came out of a difficult experience with Ebola and so it's like is there any limit to the number of crises like the area can go through you know unnerved departure exerted serious macroeconomic impact because we're internalizing a lot of the internal flows resource flows into our macroeconomic framework this was not sustainable when the UN peacekeeping troops leave obviously the macro took a big hit we had to deal with that two years ago inflation went as high as 30 percent inflation is down to around 20 percent but that high inflation has exacted a toll on the poor and the vulnerable it had to deal with lost income over the last two years now we're dealing with economic difficulties getting through revenue losses slowed down in business because of COVID all right total revenue loss in the current budget here is around 10 percent of GDP and we're projecting that in the new budget here we may get there depending on the on the severity of depending on this i'm sorry you know this is some of the advantages of working from home depending on the severity of the of the the COVID response the COVID situation so the key challenge for for the private sector I'd particularly like to recommend document here the informal undocumented private sector the market willing the petty traders those people who have to walk their ways daily to survive are paying a huge price in order for us to get ahead of this disease so in a lot of countries they've been locked down we've had a state of emergency here we're preparing for a lockdown but they've lost significant impact already coming out of high inflation down the losing income I think the response has to particularly address these people I'm emphasizing this point because since they're not part of the former system who often tend to overlook that in budget systems in planning and so there's a need there's a there's always a tendency to just allocate a small amount of that we're resisting that temptation in our engagement with the IMF and saying the vulnerable households the these vulnerable people have to be taken care of because they're paying a price for us to get ahead of the disease so that's a key thing we risk substantial risk to a household agricultural households who will experience delay in planting or may not be able to plant the ministry of entire of agriculture has put together a corona response plan for food security and we're working with that there's going to be risk to governance in all of these countries Liberia has come with an IMF supported program in the last two years incredible amazing macroeconomic reforms this risk being derailed but as a government as an administration we're not going to allow that happen so a lot of the things is happening in COVID response is going through the national budget process or through an off-budget framework that is that is a fully internalized and rationalized along with our development partners we are aligning all of the support whether it's World Bank as IMF as a USAID is Swedish government German government all of these are support are going to target key areas the key thing we want to emphasize here is that for Miibola what we've learned is that we did not really prepare for the next epidemic in Liberia the president has instructed that we don't make that mistake in COVID and so there is a need that resources flowing into the country will strike a delicate balance between dealing with the emergency phase today and preparing the health system for example or economic system for the next for the next crisis there will be the next crisis no matter what it will be epidemic when epidemic whatever sort there will be one coming up will we be prepared and all of the stakeholders have agreed and it seems like after Ebola we still are not prepared in Liberia so we're quite we're trying to incorporate these lessons so the point is as economic situations intensify our difficulties intensify in in fragile countries social tension will likely rise okay and they manifest themselves in different forms land disputes for example in some kind in Liberia here we've had a very difficult land situation and we've been able to work on that but some of these gains could be eroded if economic situations have become very difficult all right Miibola may also complicate some problem the corona may come complicated cross border situations here in the West African manor river basin you know we're in a hard zone where a lot of countries are going to elections and gaining their elections in their constitutional questions in Cote d'Ivoire and so I mean we're preparing knowing that nothing nothing bad is going to happen in these countries but the expectation is that if there are refugee situations for example and you have to deal with COVID at the same time that is another dimension and so we have to we have to incorporate that in all of that I think so many earlier speakers mentioned the debt situation COVID induced economic weaknesses with aggravated Africa's debt vulnerabilities as Minister of Finance this is the biggest headache I'm dealing with Liberia is moderate debt distress but we have a huge stockpile of concessional borrowing in the last 12 years that are using up substantial space so that the space needed to expand the economy and to include concessional loans are now limited now coming out of COVID when we want to make that big jump it seems like it's going to be difficult and this is the this is the situation that many countries are going to be dealing with so the conversation around debt forgiveness around debt I mean I don't want to say a new hippie ground but some kind of smart thing coming out of COVID knowing the difficult situation fragile countries are going to be in has to be the order of the day and and I think we're bringing that conversation to the World Bank and I hope we can you know you can press that case to the World Bank that we need to look at these countries so right now we're working with the bank here the the World Bank here to look at creative ways in which we can analyze the full spectrum of the country's debt so that coming out of COVID we can we can have financing projects to really have impact okay I've made these comments a lot of time at spring meetings and it does seem that we talk about debt issues but the portfolio selection problem in loans whether concessional loans or non-concessionary is a problem for Africa because it does seem that a lot of these monies go to agriculture and we don't see the impact now if we're spending 200 million dollars in agriculture we don't see the impact when prices hit and we're food insecure that's a problem so we're going to a meaner and a smarter strategy to select a portfolio of projects and finance things that will have serious economic dividend for the country the key message is is that in all of this our experience is that look we need to strengthen the health system and not just worry about the the emergency we're learning from Ebola that the focus on emergency can come at the cost and we don't want to repeat that mistake it's very important for inclusion of all stakeholders so the government has launched an all of society all of a government approach to this and we've invited members of political opposition as well into the response president set up a committee on food distribution to vulnerable households and opposition political parties are all a part of this this is in the spirit of of of engaging a new paradigm coming out of COVID I think and so in short um don't forget about transparency and governance and I think we're looking at that let's turn this up this crisis countries have to turn this crisis into an opportunity to showcase that their systems can work that the macro systems can rebound that the uh that your planning systems are adapted to crisis and I think we're trying to do some of that and ensuring that all spending is going on budget but we are fully accounting for resources the president has ordered that a full dashboard of all fundings received be made publicly available and we're about to release that it will show funding souls disbursement levels and and and economic impact what impact all of that is going to be on the dashboard and this is our attempt to be fully transparent and to change the paradigm coming out of out of it so we can we can learn some real things coming out of this crisis that it well it is a it is an economic crisis in as much as the health crisis in vulnerable countries like Liberia in fragile countries it is more than economic and it is a health crisis we need to strengthen our health system to deal with the next uh system and next crisis and we need to strengthen our economic systems coming out of it thank you thank you very much minister you and the others have put on the table a lot I think a couple of key themes emerge for me one is this issue of what is the global international response look like you know what what is the financial response and the other is the idea that it's the non-health issues that might hit fragile countries the most everything from food insecurity to livelihoods to maybe social disruption you know if you if you have extended periods where people can't get access to food and to basic services so you know I wonder there's a lot a lot of direction we can go with this we've got a lot of questions coming in from our audience our live audience around the world and obviously limited time but I think maybe we can go to you Axel first because the world bank's been brought up a couple of times here and on this first theme of the money on the financing we've got this challenge where the international system's been set up with a humanitarian approach when there's an emergency or a crisis and yet a lot of what sounds like is required are more infrastructure investments you know we're talking about food insecurity we're talking about health systems are we going to be able to bridge that gap and get to what mark is talking about in terms of an aggressive and meat response to kind of murder take the the ethos of the humanitarian world and bring it to the long-term development world do you think that's going to be possible right now well you know that differentiation between development humanitarian fragility that has been breaking and I think that is a clear recognition that we can no longer think in this type of paradigm I think also certainly our new strategy emphasizes this this was a world of maybe 20 years ago where we had so nicely well the world bank only provides in post-conflict situation support well that is is not the reality and I think that has evolved so I think that bridge we have crossed I think where it is more important is that hey I I do think that in in most crises we need to be faster than and basically that's what we are responding to and they I fully agree what mark is saying look if you want to make a difference you do it now you don't do it in five years from now and so that means you will need as an institution make mechanisms more flexible fast tracks procedures you know at the end of March we did within two weeks 25 countries for health packages that is of course normally never possible because it takes you nine 10 12 months to prepare I think we should be learning from that I think that we can do a lot of things differently but in the time of crisis is even more so but this is not enough only to to to prepare the packages we have also to help how the implementation is I'm actually worried also that we may be very successful to to to organize the money but at the end of the day that doesn't matter as long as we don't make a difference on the ground ie that's implemented and there are structural weaknesses in these countries and so here we need to to see how we can work across the spectrum to make sure that these things are being implanted started with the health emergency at the same time we need this longer term commitment and here we are I think between a rock and a hard place because the donor community is busy with itself and they will be saying well why don't you burn first some of your money and then come back the problem is we need assurances that we have the money certainly in either we don't commit on the basis of of empty promises and as you know a full well we have the world is full of conferences with announcements and pledges that sounds nice and in case of doubt you add another zero to it and then what is the reality often it doesn't follow I think we need to to get to a realistic business that we basically say look this is absolutely necessary and therefore I'm I'm I'm thinking that particularly for the French I'll say it is it is it's the right thing to do for the countries but it is also the smart thing for the the world because if we can avoid another conflict that investment is worthwhile and so I I believe that we need to do that we need to push very hard this is also a moment for the multilateral community from whether you're sitting at the UN or in a multilateral development bank you got to show what the difference is and that multilateralism can be key in in helping this country so it is a huge challenge but we need to push ourselves very hard yeah in some ways a crisis like this is naturally leads to a sense of isolationism right sort of multilateralism because you look at your own community and you say I've got problems in my own country and I think some of that narrative is in a lot of the donor countries and you've seen big announcements huge fiscal stimulus in countries like the United States but nothing at that scale nothing that would match that level of ambition for fragile countries and as we've heard from many of you if we don't make those investments now things could get much worse bill could get much bigger I wonder maybe I can get you into this discussion Nancy and then anybody else who wants to jump in on this theme you know Actle is talking about not just getting the money but also how do we spend it so far debt relief has been the main way we're going forward and many ways because it's the quickest it's the easiest thing to do we're going to suspend debt payments but of course a lot of fragile countries may not be in a position to even spend that money effectively given everything you've learned Nancy about about how we could finance in fragile countries what are some of the things you'd like to see the international community do with a big step up in financing for these these situations great thanks rod that I think is a is a huge important question and I fully fully agree with everyone's points on the multi-dimensionality of this crisis and as Mark said the need to be fast big and aggressive but as important as how much money and how much financing we're able to put together it's what do you do with it and you know I think there have there's been enormous progress in the in the recent years on bridging that humanitarian development divide that that Mark and Axel both spoke spoke about and it's been really important for having faster action for being able to understand how those things knit together where I think we still have the challenge is understanding how all of that needs to be lodged in the political and security countries and minister Tuya spoke about this about the need to have you know the greater legitimacy and transparency and some of that can be addressed through the way that you structure the financing or you know compact approaches that you take that are locally led where you have leadership at the at the country level that is fully committed to the kind of include more inclusive approaches and Liberia was an early leader of the initiative known as G7 plus or the New Deal for fragile states which was which was a initiative led by countries that call themselves owned the label of more fragile going forward as you know as Axel said you know most most of the more developed economies are very focused on themselves right now so it will be a big struggle to get them to focus on how important it is that we consider this a global crisis and that the health of everyone depends on the health of everyone you know you can't have the virus you know still percolating around in some of these other countries and coming back to a resurgence so you know this is as Mark said an unprecedented generational moment it is uh the kind that a kind of moment that we have rarely to seize for a reset button to really think differently about how we apply the funds that we must raise to address this challenge yeah in some ways it is an opportunity as we've heard I mean this is such a unusual unprecedented circumstance that maybe we can get donor countries to really change the way they think and to think big for once and so I wonder Mark you think you want to jump in on this on this conversation what do you see as the potential to to really start thinking big I know you've just released as you and I discussed earlier this week a new a new request for your COVID response in the UN system of 6.7 billion dollars you called for 90 billion dollars to be unlocked for low and middle income countries what do you think is possible in this moment what do you want to see I think the 90 billion is affordable frankly means 1% of the global stimulus and the question is who can play what role and I think you know all of the international systems need to play a role I wanted to come in on the previous question you put about well if you have money how do you ensure it gets to people who need it now the good news on that is the world has got scores of examples even in the most difficult countries of channeling resources through social protection systems normally in the form of cash so you can relieve people's immediate suffering the bang had a terrific example of this in Somalia a country which has very little by the way of government but was able to channel resources using text messages basically and virtually every country in the world you can do that in now so this immediate starvation threat and disease killer disease threat can be largely dealt with through social protection systems but that but then what you need is investments to get the economy going again and these crucial investments that Nancy was talking about about social capital institutions you know conflicts instability have causes they have causes and you have to address the causes not just the symptoms so you need a multi multi-pronged approach but that crucial short-run social protection thing is doable we we know how to do it if we can unlock the finance now why should the why should the rich world want to do this the the argument I'm I believe about this is that this is a this is not primarily an argument you have to win in terms of human generosity and empathy this is about self-interest it's not just the virus that will travel around the world forever until we deal with it everywhere there are other consequences of instability in 2015 a million Syrians walked to Europe because they didn't they survived where they were and other global public bands emerge from instability and unrest so I think we need to find a way to help politicians and policymakers and decision makers in the this world elevate their thinking for one percent of their headspace to think about that longer term agenda in their own interest as well you're absolutely right these issues are senator twine let me just mention for example remittances you know if you see remittances going down it might lead to more need to migrate you know even in countries that don't experience conflict and many of you have mentioned that poverty rates are going to be expanding at historical levels you know reversing a historic trend that could lead to more migration so you could see many layered effects from this if you don't get ahead of it if others want to jump in on these themes we've brought up so far let me see if you want to add to the discussion just I want to add that now Yemen is experiencing cutting of aid and reduction of aid it's irony that Yemenis now are in need more than any other time and particularly on part of Yemen in the northern areas for the majority of the people are residing so it might be for some political reasons but people don't understand why like for example world food program is very vital to the life of Yemenis distributed food now they are announcing that they are going to cut aid because their donor country are not providing any more so this is a very very very difficult for Yemenis even ourselves when we turn to our donors to to find a way to raise funding for to confront COVID-19 we have like we are not we are receiving a lot of sympathies but except like it's true that we have coming now 100 million from the World Bank that is being will go to approve in July for the social fund for development and also there has been a response a rapid response for Yemen through the World Bank 26 million point six through the WHO but it's not enough usually in the country and ongoing conflict so it's a lot of what is going on in Yemen that people are suffering but this crisis is is is causing more suffering and also if we can see that the conflict still continue we were hoping that a truth will be reached but actually it is being increasing it is ongoing and it's being increasing we've we've touched a lot of the questions that are coming in but there's one for you minister Tway I think that maybe you can help us address which is about jobs you know we're talking about a lot of countries yours as well that have rising populations a lot of youth populations people looking for jobs under normal circumstances then you go to lockdown you go to you know economic recession you talk about the macro economic situation how negative it looks how do you think about the job market and how to create jobs for young people coming out of this pandemic that's the most important question here we have to remember that the economic challenges we face today are COVID induced they're not part of the normal business economic cycle the word we start from dropping toward recession before COVID it can make slowdown there is a natural slowdown recession and repression in economies countries have challenges that they're dealing with Liberia for example is an underversified commodity dependent country we have that structural deficit we've now being able to to domesticate the source of production historically you know so we relied on inflows large externals and investments but these have not translated into the domestic economy so you have a disruption like COVID and the thing I want to agree with is that this needs a paradigm shift it's 75 years since we've established a multilateral institution the reason we established them was World War II that was an epic all watershed moment COVID-19 is showing us even we're hearing that the great economic recession of 2008 economic impact we're seeing COVID is even worse than we saw from 2008 so what this begs is for an imaginative rethinking of the nexus between humanitarian vision development and the private sector somewhere along the line we've left the private sector in all of this development work the private sector is supposed to take on the life of its own market fundamentals the competition that exists incentives are there this does not work in private countries this does not work several years of economic history are still stored in Africa these things don't work you have to catalyze the private sector how are you going to catalyze the private sector governments have to play a big role but how can governments play a big role when governments themselves are physically constrained and I want to bring this important element here when you look at the destruction of countries countries don't have the room to move in the private sector the way they would like to the significant electricity infrastructure gap the significant roads only seven per six or seven percent of the roads in Liberia now how will agriculture prosperity happen we're making investments in agriculture and don't make the kind of investment in infrastructure to release that binding constrained roads of power and then move on to agriculture we it's all mean it's a model I think COVID is begging us to rethink job creation in agriculture for example this is where you can put a lot of young people to work technology but countries need the space and I can tell you in Liberia the fiscal space is extremely extraordinarily tight okay so that so that it limits the ability of the government to move on in these directions so I think it looks for for a lot of resources flowing in the part of multiple agencies that's a great point minister and that paradigm shift might even apply to the basic model of development I mean so many of the fragile countries have had a model of development that relies on exporting commodities natural resources which are being hit really hard in a crisis like this tourism which is hit hard in a crisis like this bringing on light manufacturing cheap labor kind of oriented manufacturing where the trends it looks like are going to be a lot of developed countries wanting to bring manufacturing back on shore so there's huge headwinds that that really argue for this kind of a major response we are running out of time I'm told we can go a couple of more minutes and we've got a number of questions that have come in so I wonder maybe Axel you could give us another thought you know you've got a global fragility strategy how does that interact with your pandemic response your COVID-19 strategy so this is actually one of the topics that they are going to be discussed also with the board because basically we need to think of COVID at the same time we should not lose sight of our longer-term goals in general for developing countries for fragile states even more so so I think that we have of course a risk that we are now getting into the short fixing of some of the problems and forgetting the longer-term development needs these development needs actually have become larger and more urgent so I think that also as a development organization that cares about the long-term we should not throw that out we should basically embed the response of COVID-19 with the longer-term needs we should not compromise that we just say we are now looking for the next couple of months we need to have this longer-term perspective particularly now that poverty levels will increase and unfortunately also extreme poverty it's more urgent than ever and therefore I think we need to integrate that I think that's not easy but I think we need we need to really think about this how to do this now the other thing is and I was in February I visited I had already questions how when we are scaling up our engagement in the Salah and in the Lake Chat or the Horn of Africa how are we going to think strategically about this because there will be considerable resources and I think this is now highlighted even more how we combine it with COVID and then making the case for actually continued large flows there so this is something that that will affect us I think that you know we need to to to adapt but at the same time our focus and then the interesting thing sometimes the boards are while your country strategies are no longer so relevant I actually back to disagree the the core of our strategy is poverty reduction and that has become even more relevant than ever so it's more urgent so the part what we are seeing is we should not forget if you look at the SDGs we're off track and we even worse off track today so that means we need as a matter of urgency at least to defend the achievements that are key and so that it doesn't get worse and ultimately get back on track and we need not to have a short-term strategy of a band-aid approach where you do a little and you leave the long-term challenges unmet that's unacceptable you know we're running out of time I really appreciate that great message so I'm going to just ask Nancy to maybe give us a closing thought um this is an event you and your team have organized at USIP so I'd love to hear your your take in the conversation so far and leave us with some parting thoughts please thank you and you know everybody made the important crucial point I wanted to add one example um Axel mentioned the Horn of Africa and you know to to just underscore what minister Tuyah said about the the convergence of the political social economic needs and the paradigm should then need minister Tuyah you you talked about humanitarian development and the private sector and you know the political dynamics absolutely need to be a part of that Ethiopian both undergoing historic transitions right now um and they for a region that is food insecure in the times very fragile the set with all of these dynamics that everyone has talked about so the opportunity right now is to really move in with the kind of support that take into account the political regional dynamics and I know the bank is working with some of the members of the states in the Horn and the EU to place some regional strategies and we really need to look at what are the greater political dynamics that enable these strategies take hold with both the immediate and the longer term events uh results both Axel and Marco have talked about so my overall I think the common theme that's emerged from everybody's comments is that a lot of people around the world are rising to the occasion as was talked about it at the individual at the community level um we're seeing institutions strain uh to do things differently in the face of this just extraordinary unprecedented global crisis and we need to we need to keep the pressure on to make sure that we do things as differently as with and seize all these opportunities so that this is a manner of reset and we're able to break out of a lot of the old patterns and systems that are not serving us well and put in place some of the best ideas that we have already developed but haven't yet put into place and so Raj thank you very much and appreciation for everybody and all the work they're doing who've joined us this morning I'm sure everybody feels the same way it's been great to see all of you and especially to hear all your voices on this issue unfortunately not getting enough attention people are looking at the crisis as it exists today and not where it's heading and we know where it's heading it's it's clearly going to have a huge impact on many of the most vulnerable people in the world so thank you all of you for the work you're all doing every day on these issues and for highlighting for urgency and need to focus on those who are most vulnerable and the need to think big I'm hoping we take that out of discussion and thanks to all of you for joining the conversation from all over the world from wherever you are thanks the World Bank Group and USIP it's been a pleasure to be part of this today thank you


All right. So there is a first problem of the current assignment is posted on the finished exam for the final problem. That will be posted later today. I don't know. And we are having an exam coming up. And it will cover through the material on the Symbol Hermann Gospel, which we will finish today. And you have the second assignment done as well. And I've gotten some feedback, but I'll wait to hear more as I ask the last lecture what your preference is for a take-home exam for an exam of the sort we had for the first exam. A take-home exam has the advantage of much less time pressure, but it'll be a little bit of a more challenging exam. So there are trade-offs. So get your feedback on that. Just send me some email. Very good. So last time we talked about uncertainty relations related to the Symbol Hermann Gospel. So if we look at the position and momentum of the particle in the Symbol Hermann Gospel, then in the number basis, that is the energy island states, the mean position and the mean momentum is here. And they, of course, have, though, fluctuations in those values that is to say, if we were to measure the position of momentum, we wouldn't necessarily get a definite value. We could get some random value about that mean with fluctuations given by the variances, or we want the RMS as the fluctuation. Given that we calculated just looking at base using the operator algebra and the position momentum variances in the energy level is equal to n plus 1 half, something we could have just seen just looking at what we know, of course, the energy eigenvalue is n plus 1 half h bar omega. And there's equal amounts in this. So we could just read it off just from the energy eigenvalues. And so in the ground state, in these dimensionless units, the uncertainty is in the RMS, it's 1 over root 2. So we have 1 over root 2 in dimensionless units of delta x and delta p in the dimensionless units. If we put the units back in, then as we saw, as we know, that those are, that's a minimum uncertainty state. That's to say delta x times delta p is the minimum value allowed by the uncertainty principle. And we saw that also from the fact that in position of momentum space, the wave function was a Gaussian, a Gaussian with delta x being the minimum of delta x if we have a Fourier transform, a limited Gaussian post, it's a minimum uncertainty. I'm going to come back to this in a moment. I want to, I really meant to say this first, so let's talk about this. There's another kind of uncertainty relationship, one that we've not always talked about, but should be. And that's number of phase uncertainty. So if I just, this is a terrible picture, let me try. You get the picture. These are circles. Sorry. Classically, we can think about different sets of canonical coordinates. We have x and p. That's a set of conjugate variables. We also have what are called shin angle variables. If you've ever taken an advanced course in dynamics, you'll learn about those things. They're really just, in the case of a harmonic oscillator, they are the polar coordinates of phase space. So I have an amplitude and a phase. Those are conjugate variables in classical mechanics, just like x and p. And in the context of the harmonic oscillator, we know that we call these things the quadratures of the oscillator. And this is the amplitude and the phase of the oscillator. Now, of course, when we go to the quantum description, then what we said is that this classical amplitude became the annihilation operator, the lower operator, which has, is a non-hermitian operator. It has a hermitian part and an anti-hermitian part. Now, we could try, and it was a natural thing to do, to think about not a decomposition of this operator in terms of its sort of real and imaginary parts, its hermitian and anti-hermitian parts, but in terms of a polar decomposition, which we studied at the beginning of the semester. It's just an exercise and operator algebra. And so we could think about this. It would be natural to think that this could be written as some kind of amplitude and phase. And an amplitude loosely is the square root A, of course, here is the square root of alpha star alpha. And so you might think, well, this is the square root of A dagger A times some e to the i phi operator, the natural thing to do. Actually, it's not quite. I mean, if you were to do the polar decomposition, of course, there's a right and a left unitary as we studied in that homework assignment. So we could write in the polar decomposition, we would say that this is equal to some unitary times the square root. If this is upright on the left, if we're going to write this A dagger A, then I write it right on the left. And this would be unitary. And a unitary, we know, is of the form e to the i times our hermitian operator, which we would call the phase operator. The problem is that this doesn't work. And in infinite dimensions, things are just different about linear operators. There is no polar decomposition of A in this way. There is no hermitian operator that does this, that allows us to make this operative composition. So this is in truth. So there does not exist a phase operator. We cannot write a canonical set of coordinates quantum mechanically that are the equivalent exactly of amplitude and phase. However, well, that doesn't mean that in some sense, amplitude and phase are not conjugate variables quantum mechanically in the same way that position would have to be. There is a generalization. So what we showed last time was the following that I can decompose A. This is true. That there is an operator. I'll call e to the i with a big hat over the whole thing without putting the hat over the phi, because this is not the exponentiation of a hermitian operator, times the square root of the non-operative. And a dagger, I wrote e to the i phi as an operator that does the lowering. The problem is that this is not unitary. It looks unitary. It looks unitary because a unitary operator takes an orthogonal basis to an orthogonal basis. But the fact that this starts at n equals 1 and doesn't go to n equals minus infinity is why this is not unitary. And you could see that. You can just try, if you look at the commutator of this with this, what it equals is this. And since this doesn't commute with its adjoint, it's not a normal operator. Normal operators commute with their adjoints. This doesn't. So it's not unitary. It has no, it's not a unitary operator. And the reason it's not is because this is, if you look back at this picture, it's this, what goes on here. We can't displace beyond this point. We get to the minimum point, and we're stuck. There's kind of singularity that would be all right. There is an approximate sense in which these guys are conjugated. What we can say is that approximately, just like x. There's a very sophisticated mathematics in which we can kind of derive this based on the theory of POVX, which I'm not going to describe in great detail, but just give you a little flavor for it. And that's the following. We can define phase states, states of definite phase. These states were defined to be states which are the equal superposition of all the number of states. So in some sense, this is conjugated in the same way that when we had a position eigenstate, a position eigenstate is a superposition of all the momenta states with equal weight. An momentum eigenstate is a superposition of all the position eigenstates with equal weight. X and P are conjugated. Number and phase are conjugated. The problem with these states is that they're matter of volume. But just look at that. But look at this for two different guys. So this is equal to the sum of 0 to infinity of minus i and minus n prime. Sorry, part of me. And you can find minus i. Is there a minus or a plus there? Should I get that wrong? This is a problem. So that's not a delta function. It would be a delta function if this was from minus infinity to infinity. But it's not a delta. So these are not orthogonal states. They're not the eigenstates of our permission operator. However, what is true is that these states, you can check this, form a resolution of the identity, which means that they form an over-complete basis in the same way that X and P do. Now, since this is a resolution of the identity, this is a PODM. That is to say, I can look at this as an integral over this guy of positive operators. They're not orthogonal projectors. It's not a projected measurement, because these guys are not orthogonal for different files. But that's OK. We learned that not every measurement is an orthogonal projective measurement. We could do measurements that are associated with non orthogonal positive operators, which would say, now I ask you, what would be the probability of finding, or probability density, a finding 5? Yeah. So this is this. That's what we learned sometime in the beginning of the semester when we had Bayley-Faradu. That's the Born rule with PODM, rather than projectors. And of course, if this was a mixed state, we could say this is this, because that's how you find expectation values in the other mixed states. This is the probability. And so there, in principle, exists a measurement. It's not a measurement on a permission observable. But we learned that not every measurement of quantum mechanics is a measurement on a permission observable. So it's perfectly fine to talk about phase and quantum mechanics in the same way, even though there is no phase operator. There is a measurement we can try to rid up. Now it's not easy, and we don't know how to do it necessarily easily in the lab. But it's a perfectly good thing to think about. And that would be equal to, in this case, if it's a pure state, that's equal to this probability distribution is 1 over 2 pi. Sorry. 1 over 2 pi, the phase states, the sum over n equal 0 to infinity. And it follows from this the fact that this probability distribution is like this, that we get from this we can derive for states. So this is that number and phase are conjugated. That is to say, this is approximately true. I wrote a quarter of your last time, and I meant to have it. So let's go back now to dynamics. So nothing we talked about last time was the dynamical evolution of the system for the simple harmonic oscillator. The fundamental object is the time evolution operator. And that has this simple form. We typically ignore this overall phase. It affects nothing. So we typically just write it like that. And what we showed last time, and it's very easy to show, is that the Heisenberg equations of motion for the quantum operators are exactly the classical differential equations. This is exactly the same thing. And the solution is exactly the same as we have in classical dynamics. So one thing we see here, and again, this goes to this number phase uncertainty relation, is that n, the number operator, is the generator of translations in phase. That's to say, classically, what would happen is this thing would just go around, translate in phase. So that's why n is conjugated to phase. And phase generates translations in n. It's conjugated to n. All right. So this seems to indicate that everything about the simple harmonic oscillator is in some sense classical, because the equations of motion are the same. There's subtleties involved there. For example, if I was in a stationary state with some energy eigenvalue n, then the mean position momentum are for all times 0. And that's not classical. So the stationary states aren't really representing the classical evolution, even though we talked about the WKB approximation and the fact that at high n, we see something about the wave function building up near the turning points in the same way that we would expect for a classical oscillator to be. So there are aspects of the classical dynamics that say something about the stationary states. But stationary states don't capture classical evolution. In fact, we kind of know that from the number phase uncertainty principle. n has a definite, I mean, an eigenstate of the number oscillator as a definite n. So it has a completely uncertain phase. In some sense, a stationary state is a state that's in some sense equally distributed around the whole circle with a completely uncertain phase. It has a definite energy, which means it's on this circle. But we don't know where the phase is. Its phase is completely uncertain. So now we come to really the subject of today's lecture, which is, so, we want to ask ourselves, is there some state of the quantum system that in some way we would call quadrilateral? That's to say, it has features that we expect from the classical dynamics. So what would we expect from a quadrilateral? So we seek a quantum state such that the expectation value, say, of x and p, written either in the Schrodinger picture or the Heidegger picture, I don't care, follow the classical trajectory. We might also want not only that the mean value, but what we would like if this is really as close as possible to classical, we would also kind of like it to be the case that the fluctuations in x and p at all times are minimal. That's to say, we want something that's as close as possible as a point in phase space that goes around like this with the minimal possible uncertainty in it. That we would call a quasi-classical state. A state such as the wave packet in the center of the wave packet moves around in phase space along the classical trajectory and the uncertainty is minimal. That we would call a quasi-classical state. Does such a state exist? How would we find it? We can guess. Let's unquantize. What do I mean by that? Well, we quantized by saying the classical amplitude alpha, which we had mistaken, when to a quantum operator. We seek a state that in some sense, its x value is the classical x and its p value is the classical p. We seek a simultaneous eigenfunction of x and p. Now we can't do that because that violates the uncertainty principle. We can't find a state that has both a definite position and a definite momentum. But we want to find a state that is as close as possible to a state that has a definite x and a definite p. Let's look for a state which is an eigenstate of A. If it was an eigenstate of A, it would have an x and a p. So let's look for a state that is an eigenstate of A with eigenvalue alpha. That, in some sense, would have both an x and a p. This is written, this is the x plus i p hat on this state. Is this? Now, there's no guarantee that such a state exists. Why don't I know? Why can't I just say, of course, every operator has eigenvectors, doesn't it? It's not a revision. In fact, it's not only not a revision. It's not normal. A and A dagger don't communicate. Their commutator is one. And we know that the only operators that are guaranteed to have a complete set of eigenvectors are normal operators. And those are the permission operators and the unitary operators. But this is neither permission nor unitary. So we don't know that such a thing exists. In fact, there are no, I will show that thing to you in a moment. But we might have asked for this. And in fact, there are no eigenvectors of A dagger. They don't exist. There are in mathematics. There are eigenvectors, A, but not of A dagger. So I'm going to look for those states in a moment. Well, if such a state exists, if a set of states exist here, what would their properties be? We'll move in a moment what those states are. But why are these states for quasi-classical states? Let's see if they have the properties that I asked of them. What is the expected value of the position? Well, by definition, I said alpha for quasi-classical states is an eigenvector of the annihilation of the group with eigenvalue alpha. So how am I going to evaluate that? Anybody have a suggestion? Do you form the creation of an ally? Sure we can. But there's no, you know, a larger point, see, but let's do it. So this acts on this and gives me alpha. But this acting on that, I don't know. However, yes, but oh, excellent. I can act it to the left, because this is true. So this is alpha plus alpha star root 2, which is acting what we have classically. This is root 2 times the real part of alpha, which is x. The x, if we wrote alpha as root 2 x plus i b. And similarly, in the case you now use the imaginary part, which is b. That's what we expect. And if I wanted to look at this as a function of time, I could do it in the Heisenberg fiction. That's the expected value of position as a function of time. That's how you do it. And we just solve that. This is equal to the expected value of x 0 cos omega t plus b 0 sine omega t. This is the classical trajectory. The mean value of positional momentum as a function of time follows the classical trajectory. The mean value of this wave packet follows the classical trajectory. In some sense, that's always true, because the Heisenberg equation is a motion. It's just that these guys have in the post of the stationary state where these were 0, the mean value at 0 was 0. And then for the mean value at 0, it was always 0. These guys can have any value you like. What about their uncertainty? So let's look at the uncertainty in x, the variance. Well, once again, to do this, we write this in terms of a and a dagger. But we have to ensure that all the a's are on the right and all the a daggers are on the left. Because we know how a dagger acts on this and we know how a acts on that, but we don't know it the other way around. So let's do it. What have we got here? We've got to normally order it, which means put all the a's to the right and all the a daggers to the left. How am I going to do it? Use the computation. Use the commutator. So this thing is equal to a dagger a plus the commutator, which is more. So what do I got here? This acts on this twice as alpha squared. This acts on this twice as alpha star squared. And then I got twice alpha star alpha plus 1.  And this is just x squared, the mean value of x squared. That's what we just found. So what is this? What is it in here? A half. Exactly. And what is it? What's the minimum value? A half. In fact, the only reason this came about was because of the commutator. If there wasn't a commutator, there would be no quantum uncertainty, right? We would just come back to itself. And similarly, delta p squared, you could do the same thing as a half. It's a minimum certainty state. Delta x, delta p is a half. So indeed, this state has exactly the property that we want. It is a state which has its mean value localized at the classical point in phase space and has a uncertainty, which is the minimum uncertainty product, the equal amounts of uncertainty in x and p. And as a function of time, what happens? This thing moves around. Just like the classical trajectory, it's got a little look. It's technically known as the uncertainty bubble. And it just moves around at angular velocity only. These are the quasi-classical states. By the way, these states were examined and brought to the fore most in detail in quantum optics by Orich Lauer in the 1960s. And in the context of quantum optics, and now they're almost always simply called the coherent states, the term coherent is kind of technical. It has to do with up-co-coherence. It's not important why they're called coherent states, but they are typically called coherent states. So they're quasi-classical states for the harmonic oscillation. Yes, sir? So the only superposition of member states that's unaffected by the Lorentz operator, does that have to be an infinite? Like how important is that to have an infinite number of states? So we're going to look at that in a moment. It has a normalizable state. It is a well-defined state. It has probability amplitude over all number states. But it falls off very rapidly. So it's localized in number. We'll talk about that in a moment. The state that is a complete equal superposition of all number states is the phase state. So the phase state you could think about is this state, a state which is localized at a given in faith that has a completely indefinite number. It goes off to infinity. It's localized and has a perfectly well-defined phase, but a completely uncertain number. Completely uncertain energy. It has a definite time, but a completely uncertain energy. This is the time energy that's certain to you. But that always does this a lot nicer than that. Yeah, OK. Now, do you think states exist? There's no guarantee they do. But thank you, and let me show you how. We already know of one state, a state which is an eigenstate of the annihilation of energy. Can you even tell me a state that's an eigenstate of the annihilation of energy? It's beside that. But there's a general state. There's one you've seen, a ray on the state. The ground state, excellent. What if it goes to zero? It's eigenvalue is zero, huh? Exactly. So a acting on this is zero times that, right? That's zero. So this is an eigenvalue. This state is a coherent state. The ground state is a quasi-classical state. It's a state whose mean value is zero. So in this case, alpha equals zero. That is to say, x equals to e is zero. That's the ground state. That's a state that would be, classically, it would be the origin of space space. That would be the state that would do nothing. Quantumly, it's a state which is a uncertainty bubble around the origin. So this is the quasi-classical version of the state that just has no position, no amendment. It's at the bottom of the world. Classically, it would just be at the bottom of the world. Normally, it has its kind of fluctuating. Now, of course, that's a little bit of a confusing picture because it's really a stationary state. But let me just ask you the following question. Suppose I have x and p. And suppose that I have a probability distribution of initial complex amplitudes, initial x and p, that is either mutually symmetric. What would happen? Well, the whole thing would go around at omega t. And it would be stationary. I couldn't tell the difference. So if I had a classical distribution that's to say, I'm not going to tell you what x and p are. I'm going to prepare with my little ball p-hammer and pull it. But I'm not going to tell you what it is.  Well, then at any time, what you would see would be completely stationary. You wouldn't tell the difference. It would all go around. So this is actually equivalent to a classical distribution of possible x and p's that are as a mutually symmetric around the origin. That's a stationary state, classically. OK, so that's one. We're done. We've got none of that. We've just got one of these five console states. How can I make another? Here's the trick. So we call that d. And with the dimensions in there, that was equal to either the i over h for x of p hat minus p x. No, that's what the squeezing operator is. The squeezing operator had a dagger squares and a net square. This was the displacement operator. Remember, we have that either the minus sign p or p x hat minus p hat. Remember that we had that either the i x p hat is a translation in position. That is to say momentum generates translation in position. And e to the plus i p x hat is a translation in momentum. That is to say the position operator translates in momentum. This operator has both. This operator had the following, well, I could write this also in dimensionless units. Characters, momentum characters, the position x hat now have capital p capital x minus capital x. And what is the product of the characteristic position times the characteristic momentum? h r. x times p is h r. This is why not putting the 2s makes this pretty. Otherwise, we'd have a 2 there. And this had the property we showed in homework that this had the property that if you did the unitary transformation on x, it translated into x. And if you did the unitary transformation on p, it translated into p. Or dimensionlessly, it does the same thing. So now I ask you. Let's write it in terms of dimensionless stuff. What is this? k. This is equal to x plus ip, a plus alpha, right?  So you have x plus ip, that's alpha. So this is equal to a plus alpha. It translates in phase space. This is a phase space translation. It takes something and translates it by the complex amplitude alpha. So in fact, we can express the displacement operator in terms of the complex amplitude instead of the real number x rs. d and p, if we write that out again, that's equal to i alpha minus alpha star over root 2 times i, that's p, a plus a dagger over root 2. That's x minus alpha plus alpha star over root 2. That's x, a minus a dagger over i root 2. That's p. That's just rewriting the thing. And a little bit of algebra not much shows that this is a dagger plus alpha star over root minus. That's another way of writing the phase space displacement operator. We often write it as p as a function of alpha. So why is this useful? Well, suppose I take the ground state. Let's come back over here and take this ground state, which is a minimum uncertainty state. It has uncertainty and x of p, which are the minimum. And displace it by some alpha. If I do that, is it an eigenstate of the annihilation operator with eigenvalue alpha? If it was, that would be great, because that would just be my state localized at that point with that minimum uncertainty. So let's do it. Let's consider the phase space displacement operator on the ground state. Consider. What is if I apply, I claim that this is equal to alpha. That's to say, this is an eigenstate of the annihilation operator with eigenvalue alpha. How do we prove that? Any suggestions? Yeah, it's a good one, apply the annihilation operator. Let's just do it. So let's take this and apply it to the displacement ground state. We know about the displacement operator and what do we know about it? We know this. So what are we going to do? We can't just apply the data, because that's not the identity. I mean, if we had an equation on both sides, so we can't just willingly apply the operator to life. But what do we know? It's unitary. Yeah, exactly. We know it's unitary. So I can apply the dagger. That's cool. I can do that. That's the identity. And now what is this? That's that. It displaces it by alpha. This then is equal to d on alpha, a plus alpha, right? This is a constant. It comes out. And what about this? Zero. Voila. The displaced ground states are quasi-classical states. So we all start rotating around the origin? Exactly. So if at time equal to zero, I take my particle on the spring and I pull it, and I give it a push or a pull or whatever, or I take my hammer, then I give it an x and a p and let it go. And then it goes, right? What it means, of course, is that the wave packet goes up. The wave packet, which was the Gaussian at the origin, is now a Gaussian here, and it goes to the turning point, and then it turns around. And it was a classic Gaussian. Now, we can see that kind of wave packet picture. We showed this sort of in the Heisenberg picture. Let's look at it in the Schrodinger picture. Let's say, let's look at the time evolution of the wave function given an initial condition that at time t equals zero, the state is this. That's it going to get around. So let's say at time t equals zero, the state is a covariant state. See, the Hamiltonian is a simple harmonic oscillator Hamiltonian, and I wanted to know what is the state at a later time. How am I going to do it? Any suggestions? You did a problem like this in homework with the squeeze state, apply the time evolution operator, right? So this guy is the time evolution operator on that, right? And for the simple harmonic oscillator, now I guess it's going to raise to just here, wasn't it? That is the minus i omega t n hat. Any suggestions?  The times the acting on the ground state. That's cool. Well, this is the exponentiation of something, right? Can I just put a db dagger on the left side? Yeah. I couldn't do that. Yeah, I could do that. But I think it will be easier. What you said suggests even is it's a fine solution, but it's easier to put this in here. Let me just call this u, and I'm going to stick in a u dagger. Now, u dagger acting on the vacuum is what? It should be u dagger u. It should be, yep, that would be better. So what's u acting on the vacuum? What do I do? Yeah, it doesn't do anything to it. It's a stationary state. So this is equal to u t d in an alpha u dagger. Now here's the trick. We have d over there. So I'm going to write it out. e to the alpha a dagger minus alpha star a. Within the exponent, right? u e to the a u dagger is equal to e to the u a dagger. So this is equal to e to the alpha u a dagger minus alpha star. It does. So we've got to be a little bit careful here, but you're absolutely right. What do we know? What did we know from time evolution? A dagger to a dagger e to the i omega t. So we know from the time evolution of that trick, right? But we got the u and the u dagger on the wrong spot. What's the sign? What's the sign? Because you know that u dagger of t is equal to u of minus t. So this is e to the plus i omega t a. And this is e to the minus i a dagger. And so what we see here is that this is equal to e to the alpha minus i omega t a dagger minus acting on it. The ground state. And what's that? What is this operator? Well, it's not the squeeze operator. It's this operator. It's the displacement operator. But it's d at a function at alpha t, which is just, in other words, the time evolution just makes, still an eigenstate of the annihilation operator. But with the new eigenvalue corresponding to the time evolved classical phasor, that is to say this thing is just a classical phase. So as I was saying, this coherent state just is a new coherent state, which whose mean value follows the classical trajectory. Beautiful. I love it. So now let's come to the question of number and phase uncertainty that a coherent state cannot be an eigenstate of the number operator because it has a well-defined phase. A state with a well-defined phase cannot have a well-defined number. What about the number? So is this an eigenstate? If I look at the number operator on this, it's not an eigenstate, right? Because that's a dagger a acting on that, which is alpha a dagger on that, which is not an eigenstate. So alpha is not an eigenstate of the number operator. What is the mean value? This acts on this alpha, this acts on this alpha star. It's what you expect. It's the classical amplitude squared. So the mean number is alpha squared. But what is the fluctuation in the number? It's not an eigenstate of the number operator. It has fluctuations around the mean. It has uncertainty in the number. I don't know what is the uncertainty in it. That's the expected value of a squared minus the mean value squared. How am I going to evaluate this? What would be a dagger a times a dagger a? That's what it is. Now what? This is alpha squared. That's fine. That's this times squared. That's a dagger a on the outside. The alpha squared turns on the outside. Well, I can't do that, right? I have to be careful because I can't. No, you can look on the right and then on the left. Sure. Then do one minus a dagger a. Sure. So that's the key. The key here is to always normally order it. Commute these things so that, right? This over here is a dagger a plus one. So this is equal to a dagger squared a squared alpha plus one times that, which is... And this is alpha squared squared. And this is alpha squared. And then just alpha squared. Exactly. Which is equal to the mean value of n squared. And then that's n. Sorry. Thank you. All right. So the point here, what we see is that for a coherence state, we don't have the eigenstate of number. There's number fluctuation. The mean value of n is equal to alpha squared. The uncertainty in n is equal to the square root. Because the square root is equal. So given this fact, do you know of a probability distribution whose fluctuations, this is correct, whose fluctuations are equal to the square root of the mean? Plus one. Plus one. This is corresponding to a plus one distribution. So how do we see that? That this is plus one. We want to find the probability distribution in the number. I want to know the probability distribution of having a certain number of excitations of my oscillator. How do I find that? Well, what is it by definition? This is... I have... I wonder what is the probability to find the particle at the level n given that it's in a coherence state? I just want to get to one more. So I want to know what is the expansion of the coherence state in the number basis? What's the probability of having that? So let's look at those amplitudes. Well, that's going to be complicated. Because the way we define alpha, alpha is the displacement operator acting on the vacuum, right? That's how we...  Now here's a trick. Remember, we have this is equal to... We can separate these guys when any of the commutes make their commutes. Right? And that is the case here. So the displacement operator using this rule is e to the minus 1 half alpha squared e to the alpha a dagger e to the minus alpha star. So with that said, the coherence state is equal to e to the minus alpha squared e to the alpha a dagger e to the minus alpha star a. Now what? Well, a acting on this gives me zero. So every term in this will be e to the zero. So that's one. This I can use in Fridays with Taylor series. You know that when you apply the creation operator or the raising operator n times, you get the nth eigenvalue. I can say this n over the square root of n factorial. And that is that. So this is equal to the sum n equals zero to infinity alpha to the n over the square root of n factorial e to the minus alpha squared. And this is... So what is the probability distribution? It's the square of that. The probability of seeing n and citations is the square of that amplitude, which equals alpha squared to the power n e to the minus alpha squared over n factorial. Alpha squared is the mean n. This is equal to e to the minus the average n average n to the power n over n factorial. Do you recognize that probability distribution? That's a Poisson distribution. So for a coherent state, we don't have a definite number. We have number fluctuations. The number fluctuations go like the square root of the mean. That's Poissonian. Those fluctuations relative to the mean become smaller and smaller as the mean gets bigger and bigger, it becomes more and more classical. But nonetheless, they're always there. There's always... What about the phase? Let's just conclude with the phase. Now that's complicated because we have to calculate this thing. So if I put that in over here, that's equal to the sum and equals zero to infinity. Then I have this distribution over here. I have e to the minus alpha squared over two over two the square root of n factorial alpha e to the minus i5 to the power n. Now, what we can say though is that this sum is going to have these very rapid oscillations except where the phase of this cancels the phase of that. As I say, if I wrote alpha at some phase at zero, then this sum is going to be very big. When the phase is away from this phase, this is going to have lots of oscillations and those terms will tend to cancel. So we kind of expect this probability distribution to be peaked around a phase of alpha. In fact, it is. And if I were to draw this picture here, say here's my coherent state, it has a mean n. It has this uncertainty bubble has a width square root of two. Then I ask you, what is the width in phase? Now, it's going to depend, the width in phase is going to depend on n, right? The bigger it is, it's way out there in the same, it's going to be much smaller. So what is the uncertainty? Just geometrically. Roo two, square root of n. Mean value of n. So that tells me that for a coherent state of fluctuations in phase, my uncertainty phase are equal to a half the mean value of squared. But that's equal to a half times the uncertainty of n. So this is a minimal uncertainty wave packet. That's the same graph story. That's to say delta n, I know those factors are two here. Maybe it's twice, I should call phase twice that. But the point here is that this is, you know, of order. It's a minimal uncertainty packet. So the quasi-classical states are toward states and thinking about the fact that in the harmonic oscillator we can create wave packets that go just like the classical trajectories. And they are way, they are important particularly in thinking about quantum fields. Because if I wanted to think about the state of a field which is an oscillator, the field states which are classical like, classical fields are coherent states. The state of the quantum magnetic field that comes out of a radio antenna or out of a laser beam is described by a coherent state. So that concludes our discussion on the simple harmonic oscillator. We'll have some problems on that.


Purdue's Jaden Ivy is one of the highest ceilings in the 2022 NBA draft. While there are great similarities between Ivy and John Moran, it's unfair to Ivy to compare him to somebody who is currently dominating the league with the Memphis Grizzlies. One of the best things about Ivy is cheetah-like speed in the open court. At the NBA level, he'll play with more space and be able to showcase that philosophy mostly because he won't be playing with lane-clogging big men like he did at Purdue with Zack Eadie and Trayvion Williams. Ivy is also special at getting to the free throw line. Last season as a sophomore in 11 games, he got to the line eight or more times. He also made significant strides in terms of his offensive efficiency as a sophomore compared to as a freshman. Again, Jaden Ivy, one of the highest ceilings in the 2022 NBA draft.


Here are my favorite ways to get through flashcards quicker.  And so one of my favorite ways to make sure you're still chugging along through all the content is use a concept called stacking. Basically means that if you look at a flashcard and there's multiple things there that you just haven't mastered all of it, focus on every time that you seek the card of saying, what is the next thing that I need to learn or test myself? So if your flashcard has three points or three bullet points, using the concept of stacking, instead of saying, I'm gonna try to memorize all of it at once, you can instead say, I'm gonna master the first bullet point. And when I see it again, you just have to test yourself on whatever you learned. Once you do that, stack and add the next component of that flashcard until you master it. This is a great way of making sure that you're moving through your cards and all the material is getting equal love, but also the cards that give you the most difficulty are getting the most repetitions possible during that study session. If you enjoy that tip and you want more study tips just like this one to help you on your journey, make sure you hit that like, follow and subscribe for more content just like this one.