Apologies for starting late today. We've had a flurry of activity.  So there's a lot of action going on without imminent speakers that have joined us. Today I'm joining you from Canberra, the land of the Ngunnawal and Nambri people for our Australian audience who join us from different parts of the country. I would like to acknowledge the land of the first Australians who you meet with us on. Pay my respects to elders past and present, as well as the emerging elders, some of whom we work alongside at ANU. Thank you for joining us today for the fourth big picture series panel discussion. And I'd like to particularly extend a welcome to the many audience members who are joining us from across Oceania. During the 2020 bushfires, people from across the Pacific committed defence, force, personnel and funds. Prime Minister Morrison acknowledged the loving response from our Pacific family. Now the oceanic region faces a new set of challenges. While many Pacific Island countries have managed to close their borders to keep out COVID-19 cases, all countries are facing a growing economic crisis in part due to the lack of tourism. Many countries are severely impacted by tropical cyclone Harold. These challenges prompt the question, what does our shared regional future look like in a post COVID-19 world? Does it involve some of the following? Inclusion in the Trans-Pacific bubble as a pathway to economic recovery. Greater recognition of the ongoing impacts to the region caused by climate change. Longer term and more flexible seasonal worker program opportunities. These and other important regional issues are going to frame our discussions today. I'm James Batley from the ANU's Department of Pacific Affairs. And before we get underway, it's my pleasure to introduce our distinguished panel to you all this morning. First, I'm delighted to welcome from Samoa, the Honourable Fiamme Naomi Matafa, Deputy Prime Minister and Minister for Natural Resources and Environment. Great to have you with us, Deputy Prime Minister. From Fiji, I'm delighted that we've got my old friend, the Honourable Ayaz Sayed Kayum, Attorney General and Minister for Economy, Civil Service and Communications. And I believe also the Minister responsible for climate change. From Australia, we're also delighted to have the Honourable Alex Hawke who's had to step out just briefly because Parliament's sitting and there's a division. He will be with us momentarily. Alex Hawke, as I'm sure you know, is the Minister for International Development and the Pacific, as well as being the Assistant Defence Minister. So it's great that you could all join us this morning, a very warm welcome to you all. And I'd like to start our discussion this morning by asking our Pacific guests if they could describe to us briefly the effect that COVID-19 or I suppose the COVID-19 response and lockdown has had on your country. How has that impact been felt in your economy, in your society? And good morning again to everyone joining this session. I think some was experience of COVID-19 is very much the shared experience globally with the impact of the lockdown and how that has affected our economies. But perhaps in addressing the COVID challenge, we have had to have a look at our capacities within our health systems. And I think that is the priority. Although we are COVID free, the weaknesses in our health infrastructure is such that we have to ensure that we do prepare in case COVID does arrive in Samoa. But secondly, also how we can prevent it, especially since there is no cure so far. So just following on James with repairing is having to then coordinate our responses, not only internally with our health infrastructure, but also with the regional and international communities to assist us, especially with supplies. Now, we had the measles outbreak in Samoa and we were very fortunate with the international personnel that was able to come to Samoa. But I think the COVID experience is such and we're seeing it internationally. It is going to be very difficult to expect to have international personnel, this to countries. So essentially the supplies have been around, the coordination has been around supplies. This has been through the Pacific humanitarian pathways and also of course, the bigger tower agreement within the region and this essentially is more, the political cover to the coordination and the work that's being carried out. And also to ensure that if there are blockages in terms of those humanitarian pathways, that that particular provision at a regional level can assist that those pathways are clear and running. Just on the economy, of course, our governments in the region, we've all had to respond in different ways. The sizes of our economies and our capacities, of course, dictate what we are able to do. With our government, essentially our stimulus has been around utility subsidies, business loan subsidies for our private sector, some capital injection through the development bank for particular sectors, agriculture, infrastructure, fisheries and so forth. Ensuring that the public sector employment is intact and filling vacancies so that people have a wage. And also, you know, contracting and this has to do with government spending. I think one of the things that I do need to just speak briefly too. And I think the experience will be different in the different economies within our region is the whole concept of social security. Now, with larger economies, you have more capacity to offer formal social security provisions, wage subsidies and so forth for smaller economies like our own.  And you will find now with job loss that people are returning to the land and we're fortunate in that we are able to do that. Our size enables us to do that more easily. But nevertheless, I think we have a shared experience of our populations in the urban areas, you know, where there is complete dependence on wage for livelihoods. So there has been some efforts from the government for wage subsidies and so forth. But I think we need a little bit more bigger to look after that particular sector. So I think I might just stop there. I note we have a three-minute allocation, but that's just a brief response to that question, James. Thank you so much, Deputy Prime Minister. Attorney General, how's the situation in Fiji? What's the impact been there? Well, thank you for that. And also, hello to all the other panelists. You know, we had 18 cases, positive case of COVID-19. They were all essentially brought in from overseas. We had a couple of people come from Australia, New Zealand and also from India. And then, of course, then they transmitted that. We managed to bring it all under control and we now no longer have anybody in the positive case of COVID-19. So, you know, the knowledge we need is COVID-free. But so far, we'd like to give people questions and say we don't have any positive cases in Fiji. As seen by the New Zealand experience just a couple of days ago, while they educated themselves COVID-free, there are now two cases, apparently, who have not been telling the public or the quality, which essentially demonstrates how fluid the situation is and how it still needs to be physically cautious about it. We, of course, you know, we carry out large-scale fever testing throughout the country and also, I think, that's what helped to stop any local transmission. And we also took very stringent controls in respect to border controls, you know, in terms of stopping flights, in terms of lockdowns in specific areas and a lot of those lockdowns were in the first place. The sewer was in a lockdown. And then, parts of the labour room was in a lockdown.  That has an impact, of course, on government revenue. The border's closing, of course, means that a much bigger, you know, nearly 40% of our GDP directly is dependent on tourism.  In anticipation of it, when we first set the first case, we realized what were the implications in these ramifications of it. So we put in place the supplementary parts that we had to reconfigure our budget and we had what we call a COVID-19 budget response, which meant we reduced our expenditure but also became a lot more realistic in respect of the revenue streams. So, I mean, going forward, of course, our financial year begins on the 1st of August, so we prepare for another financial year. And, you know, the shutting down of the borders and hopefully now the opening of borders which leads us onto the second question can, you know, offer some ray of hope regarding that it has enormous impact. We expect our economy to contract by at least 21%. Initially, we thought it would be about 4% because, you know, the tourism sector is simply not open and because of the fact that many in-signal sectors depend upon the tourism sector. But it's not just tourism per se, I mean, we obviously have a fairly healthy government industry. So when New Zealand and Auckland and Sydney are locked down, there's obviously less demand for the dynamics. We predominantly supply to Australia and New Zealand. So there's less retail sales, less demand. So, you know, they're working to be sent home. I know it's probably only one or two days a week and reduced hours. So that's the impact of it. I mean, I think in respect of the positioning of Fiji, it needs to be the testing. We have them with Australia in respect of, you know, testing of COVID-19, Fiji's number of COVID-19 tests per confirmed case is about 214.7, just a few percentage points less than Australia and New Zealand. And also, of course, in respect of the Fiji's average daily COVID-19 testing positivity rate, one of the most reliable measures of whether government is testing enough is the game, about half a percent right up there with Australia and New Zealand. So I think in that space, we're doing well. Of course, as the Deputy Prime Minister of Samoa did highlight, you know, it made us focus a lot more on our health system in terms of anticipation. Should there be an outbreak? What are the emergencies we have in place with the reconfiguration of our budget? Of course, they had to allocate a lot more money to the Ministry of Health, you know, basically procuring equipment, et cetera, and the registration of an outbreak. I think going forward now, of course, we are more, you know, attuned to opening up the borders. We hope that the Prime Minister in the next few days will make some announcements in respect of the lockdowns domestically and perhaps some movement, you know, internationally. What are some of the protocols we want to put in place so we can start opening up borders? You know, it's interesting because during all of this, we also had a cyclone, you know, a cyclone harrow. So a majority of the bulk of these sort of winds actually went through the maritime areas down the southern and eastern parts of Fiji, Kandago and Laos. And so to be able to, you know, bring emergency supplies, take emergency supplies and all the other sort of relief efforts, we had to in the meantime, ensure that none of the COVID-19, you know, possible cases would actually transmit to the maritime areas. And thankfully, by the grace of God, none of that happened. But of course, it means a greater sort of, you know, awareness in respect of your logistics and also in terms of costs, obviously the increase of your costs is a lot more freely in the large scale.  So we have a superannuation fund that relax all the, you know, schemes. Government is then topping up in respect of that. And we have to ensure that there is sustainability in all of this. Thanks very much. If I could just follow up, just on this question of international borders with both of you, obviously a lot of talk about the trans-Tasman travel bubble, but also the possibility of including Pacific Island countries into a broader travel bubble. How important, how much of a priority is that for your governments? And what's your sense of how close we might be to achieving that? James, I mean, for some more, our key entry points, New Zealand, Australia, CG and American Samoa. So of course, we're very much keeping an eye on what's happening in those four points of entry. We've opened up with American Samoa because they're COVID free. We do, of course, appreciate and Minister Tayed Kayum has talked about, especially with tourism. And I mean, many of us are in that same position. And of course, when you talk about tourism, you're necessarily talking about travel and opening up. I think our approach would be a cautious one, although we do recognize that in opening up, we start with our neighborhood, so to speak. And I think that there are good signs of countries coming out of the COVID infection. So we've started, we're bringing back Samoans from New Zealand. We've had three flights so far. We're negotiating with passage through New Zealand from Australia or Possibility Direct and so forth.  I mean, it's very critical that that link also opens up. But in brief, we're a bit more cautious. How about Fiji? Yeah, I mean, I think we're working on some papers at the moment. And as I said, we all will be able to make some announcements very soon regarding that. But I think it's a matter of general principle. You would assume that when you have countries that have got, for example, testing facilities domestically and there is a lot of transparency with respect to the numbers, the statistics. And there is third party validation. And if countries are then declared to be COVID free, I think then travel becomes a lot more easier and I think it can be facilitated a lot more easier. So, for example, in New Zealand is that contributes about 17 or 18% towards our tourism or libraries. If they are COVID free and Fiji's COVID free, then you would think that certain protocols in place, you could allow some travel, as opposed to perhaps, at this point in time, that Australia and New Zealand are talking about a trans-Tasman bubble. There are various, of course, nuances within Australia itself with different states, different approaches. And perhaps that may be delaying the trans-Tasman bubble. I'm not sure about that. I just read an article, I think this morning or last night about the Australian Prime Minister making some announcements. No, no, sorry, I want to be a Minister of Kingdom, I think, saying that it may be somewhat delaying. So, the different kind of, you know, noises in respect of that. But we obviously are very keen with various protocols being developed. As the Honourable Dean of Samoa did talk about, you know, within the Pacific itself, there could be a mechanism through which we have various protocols developed within the Pacific Island countries. We could, you know, be of some sort of an inter-Pacific hub between the Pacific Island countries because there's a lot of trade that takes place between the Pacific Island countries. There's also the movement of people and, of course, different agencies are based in the different Pacific Island countries. For example, the foreign fisheries agency in place of Samoa. If the people from Samoa would travel to BG and other Pacific Island countries, so there'd be various protocols developed and perhaps that can be facilitated. But I think the word, of course, you know, they do say that the most predictable thing about COVID-19 is its unpredictability. And I think, you know, that's why everybody's been very cautious about it. And somebody needs to take the first, I suppose, not believe, but perhaps first step to be able to, you know, open up these corridors. And that we quite keen to explore those. Wonderful. Thank you for that. I note that Minister Hawke has joined us. So I wonder, Minister, if you could perhaps speak to the kind of commitments that Australia's made to the region recently in relation to COVID-19, given its special status to our family, as our family. But also, we've just heard from the Pacific leaders the importance of thinking around the mooted trans-Tasman travel bubble. So if you perhaps could touch on that as well, that would be helpful. These are very important topics. I think we all understand the difficulty of the pandemic and what's happened. I just want to commend everybody in the region for the very strong and swift action we've taken. I mean, the Pacific has really set a standard for the world in the sense that, you know, we've got it under control. We've got it managed, whether it's New Zealand, Fiji, Australia, Samoa, we're doing a great job together. And our efforts have very much been directed at working together with the region to make sure we get as prepared as we can be for whenever the health impacts do reach us. And we will have them reach us sometime when we need to be as prepared as we can be. So our efforts have been focused on that. I'll just briefly touch on some of the things we've been doing in partnership with the countries in the region. And then I'm very happy to go to travel bubbles all of the important topics. Our prime minister's made it clear from the very beginning, treating this as a pandemic in advance of the World Health Organization's recommendation that we wanted to take it very seriously because it was not just going to be a health crisis, but a twin crisis and the second crisis is the economic crisis. And I think now we have the health crisis under management and on this watch, and of course, the economic crisis is the one that we'll have to be dealing with. And regionally, you know, that's just as severe as anywhere else. And we're very focused on that. So you've seen the Australian government reprioritizing our budgets in partnership with countries where wherever we've had money that now can't be spent because we're unable to travel, programs are unable to go ahead. We've been very quick to say how much is that money we want to spend in a way that will make a difference to the health system of ordinary people in the Pacific and also support governments in, you know, the great challenges are getting ready. And we've seen very advanced countries in the world be completely unprepared and struggle to catch up and be ready. So every country in the whole world has a very significant challenge. So that money, I think, has been well spent and reprioritized to support health systems. And we'll continue to do that. And obviously, as we get the right drugs, the right vaccines, the right health equipment, we'll be working with countries to make sure as much of that can reach all the systems in the Pacific as quickly as possible. So then partnerships for recovery is the flagship program that Maris Payne, our foreign minister and myself, announced as well in partnerships for recovery is about tackling what is going to happen next for everyone in our region. And we're working closely with countries right now on the details of our country plans. And we're working on our regional plans to take account of what has happened and how we can best spend money in a way that enhances recovery, that puts a floor under the difficult economic conditions that are now a semi-permanent state for the region and the world. And that means less travel, it means less availability of capital and capital markets. And that's why I think Australia's also put a premium on Indian international forums. Our prime minister has spoken out very strongly in favor of receiving more assistance from international financial institutions, getting it quicker, and being considered in all the policy considerations of multilateral banks, United Nations for vehicles, and I myself have been participating in a group of international development minister calls regularly of countries all around the world, drawing attention to the Pacific region and saying we need to really focus our efforts on helping all parts of the world. So there's a lot of work to do there. And I know countries in the region have been using their voice as well. And I think regionally we'll continue to use our voice through the Pacific Islands Forum and other counterparts to make sure we're getting attention on what is gonna be quite a serious economic situation coming up. So I look forward to all the ways we can work together through this. We're very conscious of the fact that as a Pacific family, we're disconnected now and some of the very strong measures we've all taken have actually worked to separate us, separate us physically, but also to separate us economically and we respect the calls that we're hearing from people to start the work, the policy work on how do we reconnect in a way that is safe, that can enable economic development to continue. In Australia, we're working on some of the flagship programs that we've got. So the Pacific Labor Scheme and Seasonal Workers Program we've changed the conditions so that people who are here can stay for another year if they wanna keep working. We've changed the conditions so that people here can be moved to different jobs if we have tourism problems the same as every country in the region that can be moved to other sectors. And we're looking at a way to make sure we can keep bringing people here throughout this crisis now. We're working on that right now so that the Pacific Labor Scheme and the Seasonal Workers Program can continue and the opportunities are there. They're gonna, we need more numbers. We won't have the same amount of backpackers and food students and people coming from anywhere else in the world. So we do see a big opportunity for the Pacific to come in greater numbers to Australia and work and remit money and obviously get skills and go back home as well. So we're working on that part. And then very importantly, going to your point, Siobhan, about the Trans-Tasman bubble, that work is well advanced. We're in constant dialogue with New Zealand on a daily basis at the moment. That is progressing well. Every country has their challenges with COVID at the moment and disruptions. The Prime Minister said we're gonna get this bubble up, please. And so I think I got a partner countries have. And some countries out there, I understand don't want to reconnect with Australia at this time. And we're very cognisant of the fact that we have, we're gonna have a low level of COVID cases for some time to come. We haven't pursued elimination and we're not gonna be able to achieve elimination. So we have to think hard about the conditions and get the policy right. But it's relatively fast in governmental approach. And I know my colleagues here will understand what I'm saying in terms of governmental approach. We should be able to have the Trans-Tasman bubble of running in the very near future and then start to add on those countries that really would like to. VG has obviously been very vocal and very committed to this. We're ready to do so. I'm obviously at pace as well. Any more questions? I think if you want to discuss I was a little bit late. I apologize about that. But so over to you, Siobhan. The next question I want to move on to is thinking around climate change impacts in the region. So we know recently discussing the impacts of COVID-19 and tropical cyclone Harold. Dame Meg Chaylor, the secretary general of the Pacific Island Forum has said, and I quote, COVID has shown us our vulnerabilities but climate change remains the single greatest threat. And this sentiment echoes previous statements by the Pacific Island Forum leaders that climate change remains the single, the greatest security threat in the region. So the question then is how do Australia and the Pacific create a shared future with attention to the growing climate change impacts on Pacific countries? And I wonder if I could open up to you, Attorney General, knowing that you also have carriage as the of the climate change portfolio in Fiji. A lot of people have, you know, there's been a bit of discourse regarding climate change vis-à-vis COVID-19. And there's also a huge, bigger focus on COVID-19, generally speaking, and we've got articles coming out every two hours on the internet and some experts writing on COVID-19. And it may appear that climate change has taken effect, but it cannot and should not. This was obviously highlighted to us with Harold in the midst of the COVID-19 cases that we did have. You know, just to highlight it, since 1993, sea levels in Fiji actually have risen by about six millimeters per year, which is about double the global average. Just in the past few days, our PM has gone to about three different villages where they've put up new seawalls and these things all cost money. But obviously it's highly symbolic of the fact that climate change is very much here. This is supposed to be our dry season. It's been raining every day in Suvo for the past umpteen weeks. Reality of the matter is that the climate change is a reality. And we cannot actually lift our foot off the pedal. And the fact of the matter is that in response to COVID-19, there may be an urge by a lot of people for economic growth to perhaps drop the dial on climate change. That is our concern. We cannot do that. We need to continue to focus on the next COP. As you know, that's been deferred in Glasgow still, but to next year. Fiji, for example, and is very much a great advocate with respect of the UNIFCCC process. But of course at the same time, apart from that UNIFCCC process, the Paris Agreement process, you know, daily basis, the fact of the matter is that it's a reality. The fact of the matter is that you need to build resilience in our infrastructure. It does cost money. Of course, now with COVID-19, with the revenues are drying up. We, in fact, left in the economy, but we cannot actually let the guard down on climate change. We cannot compromise, for example, environmental standards that we've had people say to us, why don't you drop the guard on environmental standards? And because you know, we have a pandemic on. Last week, Fiji signed up with the UK Initiative of 30x30, which is getting 30% of your EZ area into the ocean area into reserve marine protected areas. Now, we're very much keen on that because the reality of the matter is that, you know, the sea of the ocean, the mangroves have much greater carbon sequestration rate. We need to be able to protect the marine environment. There's a enormous impact in respect of the livelihoods of people who live off the sea. So we need to engage in the protection of ocean areas, protection of reefs. So tourists come to Fiji because they love smoking. They like the, you know, pristine environment.  Because if you don't have the environment, you don't protect, you know, or stop the acidification. And obviously, there's a much greater impact on the overall economic productivity and output of the country. So in short, I mean, I realize we don't have that much time. I think the reality is that we need to be able to collaborate across the board. We cannot, like I said, look at the foot of the paddle regarding climate change. We need to see the Pacific Ocean with it. Fiji is looking at various options. There's no way that we issue the first green bond from the emerging country. We're now looking at a blue bond, perhaps, laid on downstream because not a good time to go out into the market, I suppose, at this point in time. But it most definitely do all the groundwork for that. And, you know, I have to also acknowledge the fact that we have been working with our development partners. Australia included in some of the areas regarding the oceans. And we hope to further those engagements. We had just last but not least, we're in the process of the second round of public consultation on climate change bill. And we are fine-tuning that which will also lead to a lot better ways of, you know, central carbon trading and between the, you know, great source of revenue, but also in terms of the overall impact of reducing carbon thrust growth. I wonder, Deputy Prime Minister, would you like to add anything from a Samoan perspective? You know, in asking the question about Australia and the Pacific, the shared future, you know, you are talking about that collective. So perhaps I can take more a regional approach or a regional angle to the discussion. So this is not new. We're all members of the Pacific Forum. And, you know, we have platforms and vehicles by which we carry our message. I don't think anyone will disagree that within the context of COVID-19, that somehow the climate change issue will take a back seat. In fact, it should give us more impetus to put it more to the future. Oh, for now and the future, because, you know, we're talking about pandemics, but the impact and effect of climate change impacts us in all aspects of our lives, including health as well.  It might be a reframing, but I think the picture is still the same in terms of our lives and how we want to continue with that. So just coming back on the theme of our regional approaches, of course, the forum has the Blue Pacific Continent 2050. And more pertinently to climate change, we have the Kainaki 2 declaration. And I think the point I want to make there is that the Pacific has advocated very strongly that climate change become part and parcel of the whole security discussion. So I think we've been at the forefront of that and we should keep it up. But primarily, I think, moving forward, we should not lose momentum in terms of the Pacific advocacy in the area of climate change. And I think it's very important for Australia as a member of the Pacific Forum that it comes in strongly. And as one of our larger members with the Pacific and the message, you know, to ensure the 1.5 objective that we've been advocating for, that we raise the global ambition with regards to emissions. You know, COVID now talking about being disconnected, we're not able to have the COP and we were very much anticipating that this next COP we could conclude on the rulebook for the Paris Agreement. And I think all of us have been anticipating this. And although it might be delayed, I don't think the momentum, and I know that through the UNFCCC processes that there are still ongoing negotiations to forward that work, I think also, you know, through the climate change processes that gives us opportunities also to find new partners, not only to address climate change, but also, you know, the economic benefits that could fall through from those arrangements. I just want to speak briefly about the Pacific Resilience Facility. You know, financing is one issue, and I'm sure my colleague from Fiji is a lot more knowledgeable about the financing on climate change. But why I wanted to make mention of the Pacific Resilience Facility is that, you know, it brings that financing component into a more usable way of not only accessing, but also working through the financing that are made available. You know, it's targeted, it's contextualized for the Pacific context.  So, you know, I think we should persist with the development of the Pacific Resilience Facility concept, especially also for simplifying the processes. I mean, a lot of us, you know, there are capacities in our respective agencies and governments to be able to work through those. So I think having that concerted attention on developing this particular financing facility will serve us very well. I think just on climate change and where the priorities are for the Pacific, most of us are still on renewable energies. And I think in that, we have opportunities also to develop new industries for ourselves. So moving from the electricity sector and to transport both land and maritime, but I think we might also be looking in that link between energy and waste. I think those are opportunities available to us in the Pacific. Now, you know, we're talking about the Pacific with the stewards of the largest ocean in the world. You know, there are other groupings. You know, we're here at the Indo-Pacific. That's still a bit of a mystery to us, but nevertheless, you know, we have these configuration and circles set over that. And I think, you know, as a Pacific, also, you know, pooling our knowledge, and this is where I think Australia, with its particular reach, the minister was referring to some consultations he's been having with other international ministers. I mean, you know, these are all windows that can be made available to our neighborhood, so to speak, or our Pacific family through the participation of some of our members in all these different forums. So just coming back in terms of the Pacific Ocean, of course, we have Asia. And then, you know, there's a whole other area with the South America, Latin American continent.  But there are opportunities there, I think, for us to make new partnerships in that direction. So the next question is one that we've received a number of questions around, which is a very important regional issue that's been creating a lot of media coverage over the last week in the region. And it's the significant governance issues that are being raised at the University of the South Pacific. Obviously, the University of the South Pacific is an extremely important regional institution. It's one that has trained a large number of Pacific leaders. So I would like to say, how can we move forward in addressing these concerns? You know, this is an institution that is highly valued throughout the region. It has served us for, you know, 50 years. Many of the graduates of USD, you know, have come to serve their countries, have, you know, been leaders in their respective countries. On the current governance issues, I'd just like to say that the council is holding a special meeting tomorrow. And I think that's where the matters should sit.  So the council has not been able to meet physically. The meeting, there was a meeting due in May. But now I think, you know, through, you know, the technologies available to us will be holding that meeting tomorrow. And hopefully council will play its role as the governing body of the university to bring some resolution to the issues that are in the forefront. The province of university plays a very important role. It's given, you know, a source of many leaders in the Pacific. The Lodala campus here, it's always the largest campus out of all the campuses. It's true across the Netherlands, you know, campuses, you know, for example, in Samoa and not to embrace other Pacific Island countries. And, you know, obviously, good governance is very important. Transference is very important for the future. And I think that these are the issues that need to be resolved by the council. And the council is meeting tomorrow. And hopefully, you know, that's what the council will do. Regarding the future of the university, I think it's critically important that the council works our way forward. That we don't have those kind of issues that have arisen in the past a year or so. Because you need this university. Everybody needs this university. PG has two other universities. We have our national university. We have also a private university. But the USP still plays a pivotal role. I mean, it has, for example, a number of schools and faculties that don't necessarily exist in the other two universities. They don't necessarily have the experience of depth and expertise. So the University of South Africa is a very good role. And the only way for universities to survive is obviously to ensure that it's, you know, based on good governance structures. So I'll hand over to James now. Thanks, Siobhan. We have heard back from Alex Hawke's office that, again, there's another division in parliament. I guess this is an occupational hazard of holding a meeting during a sitting week of parliament. But one of the things that Alex Hawke mentioned in his earlier remarks was the Labor Mobility Schemes, the seasonal worker program and the Pacific Labor Scheme. And he seemed to suggest that there would be increased flexibility introduced into these schemes. I just wanted to ask our Pacific guests how important these schemes are in terms of your own economies and your own societies. And are there particular things that you are looking for from Australia or New Zealand for that matter in terms of increased access, increased flexibility, particularly once we move beyond the immediate COVID phase that we're in? I was quite encouraged by your minister's remarks with regards to the RSE, especially in the current conditions. I think it's very comforting the approach that Australia has taken to people who are there now. And because of the lockdown, I'm not able to return. I'm very pleased that they are able to be redistributed to perhaps other sectors and that the work is available. I think the point still needs to be underscored, that the scheme is a two-way work. It meets our needs, but it also meets the particular labor needs of Australia and New Zealand. But I think one of the things that have come out of the current situation is the protection for RSE workers in the situation like we're in now and what would be the protocols. And like anything else, unless it happens, we don't really know. So perhaps this is an important thing. Australia seems to have responded very quickly. I think New Zealand is slightly different, so we're working through those. But I think from our perspective at the moment, we should be perhaps defining exactly the status of these kinds of workers. We talk about essential workers in this period. And so the categorization and the protocols and protections I think is an area we do need to look at. Of course, the scheme has changed over time. There's flexibility. There are different optionings depending on the skill level and what is wanted. And I think that serves the interest of sending and receiving parties. It does play a very significant function for the economies of the sending countries. I know that myself from Samu. I had gone to an event last year where every year with the returning parties, the sending villages have an event to welcome them. But the reporting from that was quite incredible. And for this particular district with perhaps 30,000 population or so, they were having an injection close to 8 million Tala, our dollars, into that community. And that's enormous. And of course, the impacts will be felt if the situation changes with the situations that we are now with the COVID. But we like it. I think it's worth looking at and to see how we can improve the scheme as we move forward. I think that the ministers say that these workers that can be allowed to stay there as long as it's obviously much appreciated. That does make a lot of sense, too. We will have some workers, for example, that have specific labor schemes, who have been engaged, for example, in resort work. We had some in the cable beats resort, some in the Hamming Island. They were working there in the hotels there. But then we'll move to aged care to facilities where they will obviously continue to work and some went to meatworks, where they said so quite also. I think that ability and the level of flexibility I think is very much appreciated. And of course, going forward, Fiji is very keen to ensure that we work with the various protocols and provide employment opportunities. For our people, as the minister highlighted from some of that, they also benefit from the temporary emergencies. I think there's an opportunity also to not just focus on the agricultural sector, not just on the civil work program, but on the specific labor scheme. There were, I think, some who went to places other than the East and Seaboard of Australia and some talk about what they're going to call the territory and perhaps even Western Australia. Of course, we've got some of the results to involve the Queensland. I think there's opportunity to do that. We had unfortunately some people who were supposed to leave and had resigned from the existing work. They're going to Australia, but of course with the travel restrictions, they could not. So we had to deal with that situation. But I think our assessment is that there will be a demand in Australia for a lot of these people to come in once a year, but for example, the agricultural sector opening up and also the hospitality sector. And given the fact that there has been a downturn in the hospitality sector in Fiji, there may be more immediate opportunities for our company to look after the sector in Australia. So really important for them to talk to me. If we're coming towards the end now, and if I could just put a final question to both of you and I understand there are still divisions ongoing in the Australian Parliament. So we may not see Minister Hawke again, but all of our speakers this morning have talked about the impact of COVID on borders and around the region and indeed on the regional, the pattern of regional meetings and of course the looks like the Pacific Islands Forum, the leaders meeting this year itself will be delayed. But so I guess what I wanted to ask you was that what's your sense of what this whole COVID crisis has meant for the region? We've got a really good sense from you of what it's meant for your countries. But has it, it's been a challenge for the regional organisations and where do you think the region and regional organisations will be placed as we come out of this situation in coming years? I think, James, just take this session as an example. It's definitely a new way of work for the different agencies, but like anything else, we need to adapt. So I understand there has been mixed experience in terms of using the new technologies, but I think if this is the thing that is available to us, then it's very important that we do make the investment to ensure that these platforms can avail us the opportunity to keep those connections. Having said that, it's quite interesting. The whole COVID thing, I think it's given us all, and this has been the global experience, I think. And I think for smaller countries, it's given us some opportunity to reflect also. I mean, in economic terms, when the connections are cut, then first and foremost, you're looking internally. How do you keep that internal economy turning over? And that just depends on the different circumstances, but it may not be such a bad thing for us to be reflecting and working with what we can control, perhaps reprioritising, because I think that in any event where we're challenged, everything is there, but perhaps it's the prioritising that we need to reflect on. If I could take a leap out of what the audience at the end said. I think the regional organisations obviously will continue to exist. The platform to use for engagement obviously will change upon technological engagement. And of course, there is in itself a need there to beef up the technological capacities in different countries. Some months that we've talked about certain countries not necessarily having the right bandwidth to be able to have such confidence. So that in itself is an issue that needs to be addressed, and of course, our development partners can work. And the regional organisations will have a pivotal role in perhaps spreading the use of the technology in building the local capacities. I think also the regional organisations need to have some more, we require them to play a more nuanced approach in respect of how they deal with the different countries, because I think what the pandemic has also highlighted is the different positions or different capacities that individual countries within the region have. What, for example, one may be about technology, the other may not be. Now, this we need to assess vis-à-vis the SDGs too. When we have the SDGs go by 2030, the reality of the matter is that when the pandemic has a huge strain on the revenue ability to build capacities to meet the goal of the SDG by 2030, it is again limited. So I think the regional organisations to maintain its relevance for the individual countries to be able to obviously leverage off the regional organisations, it needs to be understanding a more nuanced approach about the individual countries situation and tailor-making for those individual countries. Of course, there are certain areas where you need to have a one-size-fits-all for all the Pacific Island countries. But I think in order for the individual regional organisations, again, it's also a lesson for the local partners, when they do use the regional organisations, they need to highlight to them and they want the programmes to be actually delivering the right outcome. They need to be able to talk or relate to them about what do they want and how the individual countries are dealing with different situations and build those capacities individually. Because the reality of the matter is, for example, using Fiji as an example, a lot of people are saying, well, you should not have to depend so much on tourism. Because of the fact that you depend so much on tourism, this is why maybe it's a huge hit with respect to government revenues and tax revenue. So, yes, it's true. We were in fact, for example, in the tourism sector, our past number of years, our goal has been to, as a mantra, to spread our risk within the tourism sector, and that is not to depend so heavily on Australia and New Zealand, in terms of the percentage of the arrival. So, of course, we want to grow the numbers. We need to look at other source markets. You know, whether it's more growing the North market, the Europeans, the Chinese, the Indian to the emerging markets. And of course, therefore, the connectivity needs to be a lot wider. So, we fly directly to Singapore, Japan, San Francisco, LA, et cetera, Hong Kong. So, that's one aspect of it. So, what can I develop in partners and regional organizations doing, for example, to build capacities in creating new employment opportunities? That, I think, is pretty important. I mean, one of the areas that we are looking at is because we've got a very young population, because we're at a very high level of penetration of technology, whether it's feasible, et cetera, and smartphones. We have over 600,000 smartphones in the population, 900,000 people, for 70% of the population below the age of 40. So, perhaps we need to look at things like coding, building capacities in our university. So, you know, our students, our youth, can actually go and learn coding and you can provide services now, remotely to San Francisco, the vendors can actually come and see the products here, the people who develop the products for them and then fly back directly. So, those are the things that you need to look at. So, what can the regional organisations do to build these capacities to go and develop the partner's language? Shavon, I'll hand back to you now to close up. Yeah, look, thank you for what's been such an insightful and thoughtful conversation today. We've covered such a wide range of issues and it's been really wonderful to hear first hand around your opinions, but also perspectives of directly from the leadership around how COVID-19 has been impacting your countries.


So, today we will just discuss this quiz because I have taken a cursory look through all your answer books and I have not yet marked them, I have not graded them but I thought I would do this so that you get some idea of what this whole thing is all about and in the process we will be able to all make some side remarks, some peripheral remarks as well. So, we will go through this very slowly. The first question said the density operator of an isolated system in thermal equilibrium is delta of H minus E. So, in the micro canonical ensemble or an isolated system in thermal equilibrium the idea was rho equilibrium was delta of E minus H and the question is this true or false where E is the total energy of the system. Since it is an isolated system the energy is a constant, E is a constant and certainly you are on the energy shell which is what this thing is all about with some finite resolution. So, this is the density operator at least formally, formally it is so. Interesting question side remark that one can make is we know in a classical system which has got many constants of the motion for instance if this is a system with central forces present and no external force on a system of particles the total angular momentum of the system is constant. The total linear momentum of the system is also constant. So, strictly speaking you have access only to those micro states where not only is this true not only is the total energy fixed but also this is constant a constant of the motion and this quantity is also a constant of the motion. These are also called Galilean constants of the motion. So, the question you should ask is why do we focus on just the energy? Why should not we say that it is the intersection of the energy surface with the surface on which this is constant and that is constant. So, really it is only those micro states that are accessible and not all micro states on the energy shell. Do you see the point here? What would you say is the answer and yet if you look at every book on statistical mechanics in the micro canonical ensemble it is just the energy shell that people worry about. How come they are not worried about the other constants of motion?  So, you have this big phase space and on this phase space if you fix an E there is a sub space of it on this E is constant on this surface on this hyper surface. But you must also look at the intersection of this with the surface on which capital P is constant capital M L is constant and so on but you never do that you only talk about the energy hyper surface. So, what do you think is a reason for that? There are not too many such constants of the motion basically there are just 10 Galilean constants of the motion for an arbitrary set of particles interacting by two body central forces unless there are special symmetries in the problem. The point is the answer is that when you do statistical mechanics you are talking about a system with a given state of motion. So, you are already saying the state of motion is given to you such as capital P equal to 0 for instance you are in a state where in a system or in a frame where the total momentum is 0. So, the state of motion is already prescribed to you implicitly or tacitly which is why you do not worry about the other constants of the motion. All that you worry about is the total energy because you can increase or decrease the energy by opening up the system and letting it interact with the environment. So this is true but you should also be aware that the conditions under which this is so. The next question was each Cartesian component of the velocity of a Brownian particle obeys the famous Langevin equation in one dimension which is V dot plus gamma V equal to 1 over m 8 of t where this 8 of t is a 0 mean stationary Gaussian white noise the usual white noise we have been dealing with although I have not said so explicitly it is also a Markov process we have not talked about that in detail at the moment but you have a stationary Gaussian delta correlated Markov process that is what this noise is and the proposition is that the velocity V of t is a stationary Gaussian random process is this true or false it is true. The Gaussianity property is transmitted it has driving V so this is the driven this is the driving force and this is the driven variable the output variable and the Gaussian nature of the probability distributions of eta goes over into those of V as well. As for stationarity this one we saw is stationary it is very much stationary if you did not have the noise then you had a runaway solution for the mean square velocity and then that was not stationary at all so this stationarity is certainly true the presence of this ensures that you do have this stationarity. If you did not have noise but you just had a process for instance in an abstract way you have a process Xi dot equal to eta of t so I give you a random process Xi whose derivative is Gaussian white noise or Xi is the integral of Gaussian white noise it is called the Wiener process and the Brownian particle satisfies such an equation here. This process is not stationary because what happens now is that Xi square Xi of t minus Xi of 0 whole square this average given this thing here is proportional to t whereas we know that if you must have a process that is stationary we know that it is mean mean square mean cubed all moments and so on must be at least independent of time moreover the 2 point correlation must be a function only of the time difference the 3 point correlation must be a function of 2 time differences and so on that is violated if you did not have this friction term so this introduces regularity into the system it by the way makes the V process also Gaussian makes it also stationary process as well as a Markov process. Continuation of that is that V of 0 V of t correlation is a decaying exponential function of t we know that is true because we know that V of 0 V of t this quantity we discovered was k Boltzmann t over n that is the t equal to 0 value and it is multiplied by an exponential gamma modulus t so the correlation drops off on both sides so indeed it is a decaying function exponential function of mod t continued the displacement of the particle X of t minus X of 0 is a stationary random process so the proposition is that this quantity this random variable integral from 0 to t dt prime V of t prime this is said supposed to be a stationary random process or more generally if you wrote t naught here this is t naught this is a stationary random process but surely this thing is a function of both t naught and t there is no guarantee that is a function of t minus t naught at all definitely not and it is in general not a stationary process in fact it is the integral of the velocities the displacement and we know it linearly increases with time so it is definitely not a stationary random process. Next again for all positive t the mean square displacement is given by X square is 2 dt so the proposition is that in this case X of t minus X of 0 whole square the question is is this equal to 2 dt 2 or false it is false it is only 2 in the diffusion limit right large how large greater than gamma inverse the time scale in the problem we know that the exact result here is this so if I call that capital X X of t X square of t we know this is of the form k Boltzmann t over m gamma twice and inside you have m gamma squared gamma t minus 1 plus e to the minus this is for t greater than equal to t. So only for gamma t much much bigger than 1 does it go to the diffusion limit that is the diffusion regime so that was straight forward enough. Next we have the velocity of a Brownian particle of mass m and charge q in an applied uniform magnetic field the Langevain equation is given and the statement is the different Cartesian components of v are also uncorrelated to each other for t greater than equal to 0 is this true or false it is false because they get tied up with each other due to the magnetic field which mixes up components in fact we computed this you notice that the v should have been a bold face in the dot so the equation is v dot plus gamma v this quantity here was equal to the cyclotron frequency v cross the direction of the magnetic field plus 1 over m a vector valued noise a vector valued noise white noise in this case we know what the velocity correlation does we know that v i of 0 v j of t by the way the fact that it is in the magnetic field does not change the stationarity property the velocity is still a stationary random process in fact it is still diffusive just with the modified diffusion constant so this quantity is k B t over m that will appear and then e to the minus gamma t for t greater than 0 and then if you recall there is this portion which comes from this part comes from solving the problem in the magnetic plus or minus I do not remember I think minus epsilon i j k n k sin whatever it is it is not proportional to delta i j so it is clear that there are cross correlations here entirely because of the magnetic field then for the same problem in the magnetic field the mean square displacement is a formula given for it and the statement is whether the displacement r of t minus r of 0 whole square this is just the dot product with itself whether this thing here is 2 k Boltzmann t over m gamma times phi gamma square plus omega c square over gamma square plus the question is whether this is true or false recall that what is happening here this is x square plus y square plus a square if you like if you feel this along the z direction then the x and y portions get inhibited they get attenuated by the z displacement remains as before so this still remains 2 k Boltzmann t over m gamma gamma but inside you have times t and then you have the same thing and then 1 plus gamma square over gamma square plus omega c square from the displacement in the y direction or x direction plus 1 in the y direction so that gives you this in the diffusion limit once again in the diffusion limit so all that is happened is that the diffusion has been inhibited somewhat if you did not have magnetic field omega c is 0 then this cancels out and gives you 3 3 2s are 6 and you indeed have r square goes like 6 d t because 2 d t is a portion between x square y square and z square on the other hand when gamma is small or negligible compared to omega c and this becomes very very large then you still have diffusion but you would not have any motion in the x y direction at all that means where this displacement will actually tend to 0 and it will diverge only along the z direction and therefore it goes to 2 k t over m gamma t so you should check this you should check these limits always just to make sure that you get the right answer the correct physical answer again continuing the same problem given that the initial velocity is v 0 the statement is the conditional average velocity v of t conditioned upon the initial condition v 0 is a vector processing around the direction of the magnetic field with angular frequency omega c cyclotron frequency while its magnitude decreases with time like e to the minus gamma t true or false this is true the statement is true you solve the problem exactly this is precisely what you would expect and what you get so the mean value v of t we want the mean value of this thing but suppose you did not have any noise at all you did not have any thermal noise at all just had a magnetic field switched on and then you have a magnetic field in this direction n and then initial velocity of this particle v 0 like this now what is this going to do the magnetic field does not give any energy to this particle all it does is to change the direction of v 0 so it starts processing around and what is the formula for it it is a rotation formula rotates by the amount omega c t in time t so this is equal to clearly it must be equal to e to the m omega c t on v 0 if you did not have any friction before you took any average this is all that would happen this is the rotation matrix remember that m i j in three dimensions this is actually once you write the generator of rotations in three dimensions so what has been written is j dot n i times j dot n is equal to this precisely what it is in three dimensions I have used here for the three generators of rotations you have used those three by three generators the representation the original representation of rotations by 3 by 3 orthogonal matrices when you do that you end up with this answer here this is the matrix and then the angle through which you rotate is omega c t you exponentiate it you end up with the finite rotation so it is this fellow here you have to exponentiate this on and this is a function of course of t as well as omega naught and since we know that in this case we know that if you square if you cube this matrix you get minus the same matrix we have already seen that so this is equal to i plus m sin omega c t plus m squared 1 minus cos omega c t this guy acting on v naught and you can write this down explicitly so what is it going to be proportional to there will be a portion along n there will be a portion along v naught and a portion proportional to v naught cross n the portion along the original vector itself along v naught v v naught itself the portion along n would involve v naught dot n times unit vector n and then the perpendicular portion will be v naught cross n with a sin omega c t multiplying so this is some finite some vector which you can compute if you took this average out here after putting in the noise what happens what happens to this guy all that happens is as it is going around it is being hit buffeted and it is making the average go to 0 so all that happens is this is equal to e to the minus gamma t times that that is the only effect of the magnetic field so this is all that happens you still have a diffusion in the velocity space you still have a mean which is going to 0 a variance which is increasing from the initial delta function it increases till it hits the equilibrium value which is given by the Maxwell distribution finally so we can even write the distribution down we can even write down what is p of v comma t given v naught this follow apart from some normalization factor which we will write in a minute has got to be so the following it is got to be the exponential of minus it is still a Gaussian retains that property so it is v minus e to the m omega c t v naught e to the minus gamma t that is the mean value v bar of t squared divided by twice the variance so it is twice k Boltzmann t one minus e to the minus 2 gamma t and it is k t over m so this is m out here the normalization does not care about what this average is because you are going to shift this out anyway when you do the integral so it will just be m over 2 pi k Boltzmann t 1 minus e to the minus 2 gamma t this to the power 3 halves for each dimension you get this to the power half that is it you have not derived this I have just said that it is a Gaussian and once I assert it is a Gaussian then if you accept that it is completely determined by its mean and its variance that is a normalized distribution this is the three dimensional analog of the Onstein-Ohlenbeck distribution but with a magnetic field present so physically it is very appealing it is very simple I will at some stage try to derive it is called the Fokker-Plank equation we will write it down we will write this what we will do is what I will do is by a shortcut I will show that every time you have a stochastic differential equation for the random variable of the Langevin type you have an equation a differential equation for the probability distribution directly so one can solve that in principle and get this result moving on next one was just a definition says consider a classical Hamiltonian system with n degrees of freedom and a given Hamiltonian and L is the Liouville operator statement if F is a function of the dynamical variable such that the Poisson bracket of F with H is 0 then the Liouville operator acting on F must give you 0 identically so this is obvious because you are already given that this is true but we know that L acting on F is equal to I times H with F so that is of course equal to 0 identity it is just the definition of the Liouville operator. Now what is the reason for using the Liouville operator our reason was that the formalism looks a little simpler both classical and quantum it looks exactly the same but of course you need to exponentiate this Liouville operator and that is not a trivial matter in general the classical case much harder as we saw all the proofs I gave were all for the quantum case because I was using the cyclic invariance of the trace but if you try to do this with phase space functions then we run into we have to integrate by parts it is a little messier to do so oh yes it says here the next proposition for a dynamical system with Hamiltonian H of q, p that time development operator e to the iLt is unitary whether the system is classical or quantum it is true is a unitary evolution remember that in classical mechanics in Hamiltonian mechanics if you solve the Hamilton's equations of motion so you solve Hamilton's equations of motion the given Hamiltonian and given initial conditions so what you are doing is to go from q naught p naught at any time t you solve the Hamilton equations of motion then along the phase trajectory you are really going to qt p right I put subscripts but really this should be inside the bracket for this guy and for each degree of freedom this is true now we know this is true q naught p naught equal to 1 to start with these are canonically conjugate variables and we know that at any time qt pt is also true equal to 1 so time evolution preserves the Poisson bracket it is also orientation preserving because this transformation it turns out is what is called a symplectic transformation a canonical transformation and it preserves orientation that is it does not change right handed to left handed coordinates and so on in phase space so it is in fact a transformation whose which is measure preserving which is canonical etc etc I leave you to find out what is the generating function for this transformation what do you think is a generating function every canonical transformation has a generating function not necessarily unique generating function for a given canonical transformation you may have more than one generating function what do you think is the Hamiltonian itself so you have to establish this you have to establish this and then you discover of course that the equations of motion themselves are the equations which tell you how to get qt and pt from the generating function they are exactly the same in structure we cannot be standard gen canonical transformation the simplest one which is non trivial is as you know the one that takes you q to p let us write it the other way is the one that says q equal to p and p equal to minus p so the Poisson bracket of this with that is minus the Poisson bracket of this is one the determinant of this transformation is one so it is measure preserving and it is canonical the generating function for this depends on whether you want a type 1 type 2 type 3 type 4 generating function are you familiar with the types of generating functions what type would this transformation be if I say it is a type 1 then I must have a generating function f 1 which is a function of little q and capital Q I leave you to check that if you choose this generating function you are done it generates this transformation but you could also choose it as type 4 and it is a simple matter to verify that that is also generate that also generates precisely this transformation so the type of a canonical transformation is not uniquely specified for the transformation you may have more than one generating function for the same transformation now the reason I said this is a standard the basic canonical transformation first of all it is linear so the Jacobian is all constants and things like that the matrix of this the Jacobian matrix is precisely this which is the matrix that you need when you write the Hamilton equations down in the form of simple gradient or something like that the symplectic the symplectic matrix itself so if m is the Jacobian of any canonical transformation then m times a matrix omega times m transpose is equal to omega where omega is the this matrix is 2 n by 2 n matrix with 0 identity minus identity 0 and the statement is Suresh's statement is that omega itself m equal to omega itself will generate we will satisfy this condition now the reason why this is regarded as a fundamental canonical transformation is that there is a very deep theorem due to Darbu which says that anywhere in phase space in an n diamond degree of freedom systems phase space anywhere locally you can find a canonical transformation which looks exactly locally in any phase space any Hamiltonian system so that is the significance the fact that there exist this is the same statement as saying Suresh would say it means that there is a symplectic structure to the phase space this fellow acts like a metric and such a transformation is possible so anyway this is big machinery of canonical transformations. In quantum mechanics however you talk about unitary transformations you know that when you have a time independent Hamiltonian then the time development operator u of t for a given t naught this guy here this time development operator is such that it when it acts on any observable this gives you e to the i h naught t over h cross e to the i minus i h t so this time development operator is equal to this guy here and h is Hermitian so this is unity automatically so the whole idea of writing the Louisville way of writing things is that you write you identify this u of t with e to the i l t whose action on any observable is to produce a conjugation with respect to this operator here. So if you like in the quantum case this l is a super operator it is acting on operators on Hilbert space and it is producing a thing like this again you can show that in the space of these operators on which l acts as a super operator this is a Hermitian operator that is what we just we demonstrated by defining an inner product in the space of the operators and so on. Classically there is no such extra structure here this is in just as a function it acts on functions of a space but this is a partial differential operator and it involves exponentiation so formally writing both classical and quantum mechanics down as unitary time evolution is a very simple and compact way of dealing with matters at least in the formal sense so that was the purpose of the exercise there. Then the next one was the response function a of 0 b of tau bracket either Poisson or a Hermitian bracket where a and b are physical observables can never be negative for any tau greater than equal to 0. So the question asked is whether this thing can be negative so we are asked to find out if a of 0 b of tau equilibrium and recall that this thing here x y this stands for either x comma y or x y over I h cross in quantum mechanics this is classical this is quantum mechanics and the statement asked was whether with respect to the equilibrium density operator e to the minus beta h naught whether this quantity can be negative or not for tau greater than 0 c can it be negative we have seen that it is actually real if a and b are Hermitian which is the case we are dealing with it is actually real but does it have to be negative or positive definite there is no such constraint that it should be positive definite it very very a common instance would be if you plot it as a function of tau if you plot it phi of tau for some arbitrary a and b it could go like this it is sort of physically expected it will die down as tau becomes large but it could oscillate to change in sign but yeah you can change the sign of a instead of a you look at minus a so that immediately says so it is no no such requirement on it at all in fact in the magnetic field case you know that there are these signs and cosines and they will of course cross the axis and go down next the Kubo canonical correlation a dot of 0 b of tau semicolon reduces to the classical product in the in the classical limit and the answer is yes of course it does so we call what we had we had a of a dot of 0 b of tau equilibrium if you recall this was an integral from 0 to beta d lambda and then a trace row equilibrium which was e to the minus beta H0 this fellow here times e to the lambda H0 a dot of 0 e to the minus lambda H0 b of tau the trace of this whole product of course in the classical case things commute this goes across here cancels the integral just gives you a factor beta and you have the expectation value with respect to row equilibrium of a dot of 0 b of tau so classically that semicolon is just deleted finally the generalized susceptibility is the Fourier transform of the response function with respect to the time may be true or false it is false what is it the Fourier transform of green function so it is the Fourier transform of theta of t times phi a b of t that is certainly true but just the introduction of this theta makes a huge difference at once in fact there are immediately relations between as we will see the spectral function and this and let me write all those down so chi let us forget about the a b chi of omega is integral 0 to infinity dt e to the i omega t phi on the other hand this fellow here is also equal to integral minus infinity to infinity dt e to the i omega t theta of t this is the green function and that is the Fourier transform the Fourier transform of phi itself is phi tilde of omega this fellow is integral from minus infinity to infinity d t e to the minus d to the i omega of t phi of t in this fashion compare these two there is an integral going all the way from minus infinity to 0 plus 0 to infinity here and that is missing here so this was our spectral function for which we wrote down representations and so on. Now there is a relation between these two we already know it we already know that phi we know that phi of omega equal to an integral from minus infinity to infinity d omega prime phi tilde of omega prime over omega prime minus omega minus i epsilon in the limit as epsilon goes to 0 from above and there is some factor here i over 2 pi or something like that i minus i over 2 pi there is no now look at this thing here I can write it as cos plus i sign definitely so this could definitely be written as minus infinity to infinity dt e to the cos omega t if phi of t has a definite parity if it is an even or odd function of t then one of the other of these two fellows vanishes on the other hand this fellow here if I rewrote this this is equal to integral 0 to infinity dt cos omega t plus i sign omega t phi of t this is the real part of chi and that is the imaginary part of chi after you do the integral you get the real and imaginary part if phi of t is an even function this portion vanishes and this remaining integral becomes twice the real twice the integral from 0 to infinity right so if phi of t equal to phi of minus t will imply immediately that chi of omega is equal to phi tilde of omega equal to twice chi of real part of similarly if this one odd function of t then this integral vanishes here and what is left is i times this fellow here which is twice 2 i times 0 to infinity but that is equal to i times the imaginary part right so phi of t equal to phi of minus t with a minus sign will imply that phi tilde of omega equal to 2 i imaginary part right so there is another intimate relation between these two guys now I leave you to put take each of these cases put it in here and look at what is going to happen so it is starting to look as if chi is given by take the real case for first take this even case first it looks like chi is given by an integral over itself over the real part alone what is going on that looks really weird right you are telling me the full susceptibility is the integral of the real part alone this fellow but it is got to be completely consistent we have not done anything wrong anywhere remember that this fellow 1 over this guy is the principal value plus i pi delta so if you put that in an equate real and imaginary parts you will end up with a statement that the real part of chi is equal to the real part of chi and the imaginary part will be an integral over the real portion here which will give you the dispersion relation this side is in general complex so the way to resolve the right hand side into real and complex parts assuming this is real which by the way is true here immediately is simply to resolve this Cauchy kernel with this guy as principal value plus i pi delta so it will give an identity for the real part will say real part of chi is equal to the real part of chi identity but it will also say the real part of chi is the principal value integral of the imaginary part which is the dispersion relation and the same will happen in this case but the question is how do I decide this that is decided by time reversal invariance because you see finally what you have is pi a b of t equal to a dot of 0 b of t in equilibrium so now we are ready to talk about the time reversal property we have computed this for various cases for t positive but now how do you find what happens for t negative it depends on the time reversal properties of these kinds so this is equal to epsilon a dot epsilon b pi of t this is this will imply that pi a b of minus t is equal to this where epsilon a dot is either plus 1 or minus 1 depending on whether a dot is invariant under time reversal or changes sign detour for this but the time reversal suppose a is a displacement x it has nothing to do with t so it is time reversal properties it remains x goes to x under t goes to minus t but a dot is then velocity that is dx over dt and that changes sign so in all cases epsilon a dot can be simplified a bit and we could write this as pi a b of t equal to minus without the dot because a and a dot are guaranteed to have opposite time reversal property so this is always this product with this thing here is either plus 1 or minus 1 and you can tell which one is which for example I apply a displacement to the Hamiltonian proportional to x the displacement the coordinate that is a is equal to x in that case a dot is therefore v and if I am measuring v as I do in the Laun Jouin problem then the correlation a dot b is essentially the velocity-velocity correlation and you are guaranteed from this from this fellow here that in that case you are going to get a symmetric correlation which is what happened we found v of 0 v of t is e to the minus gamma mod t so in all cases the time reversal property of this function of this of these operators or dynamical variables will tell you whether it is an even or odd function and therefore whether this is true or whether that is true so this is something which I had meant omitted to mention but we have it right here. Next came all the fill in the blanks and the first question was of course the internal energy in terms of the partition function sorry I forgot to write trace there so we know the average value is minus delta over delta beta log z that is trivial then the second portion was the second question was this probability distribution for the conditional velocity this is in fact the Fokker-Planck equation for the velocity conditional density and now there is a little subtlety here so let me point this out so you have delta p over delta t equal to delta gamma times delta over delta v v p plus gamma k Boltzmann t over m d 2 p over delta v 2 by the way not surprisingly you would have guessed that the fluctuation dissipation theorem has been put in here so I get the Maxwellian distribution asymptotically now in equilibrium p goes to p equilibrium this portion is 0 by definition p equilibrium has no time dependence then you have an ordinary differential equation but its second order but notice there is a d over dv that can be pulled out so this will immediately imply that d over dv of k t over m dp equilibrium over dv plus v p equilibrium equal to 0 that is the second order differential equation ordinary differential equation what can you conclude from this that this must be equal to a constant it must be true at every value of v including plus minus infinity but at plus minus infinity each of these terms is 0 p equilibrium vanishes therefore the constant is 0 therefore it is 0 for all because it is a constant so this goes to 0 and that is a first order equation and as you can see the Maxwellian distribution is a solution move this constant there and then you can integrate by separating variables all right the next one was just the calculation of d using the integral you need to use the fact that d is integral v of 0 v of t for any Cartesian component it is a trivial integral and the one with the pole at 0 this I had already mentioned earlier in class so you just have to add this lambda over omega your dispersion relation then the last part and let me say this is something which presumed that you know already what happens in an electromagnetic field is that the Hamiltonian which is p squared over 2m for a free particle goes when you have a magnetic field to p minus ea over m ea squared over 2m plus of course if there is a scalar potential you have this but in a constant magnetic field you can choose that to be 0 always so that is your Hamiltonian and therefore to first order in the vector potential this is equal to p squared over 2m minus e over m p dot e classical but if you have a constant magnetic field you can write a simple representation in the Coulomb gauge for the magnetic field it is half b cross r the fact that b changes with time does not affect this it is got to be uniform magnetic field so this thing becomes and of course by the cyclic property of this triple product you can write this as b dot r cross p or you can write it as r cross p but that is the angular moment does this remind you of something this is the gyromagnetic ratio that is the angular momentum so what is this equal to it is the magnetic moment formed by the current loop right that is all that is how the particle will respond it has no spin so there is no intrinsic magnetic moment the only thing it can do is it moves in a circle creates the current and this couples to the external field that is exactly what you expect mu dot p minus mu dot p where mu is the magnetic moment is the potential energy in the presence of a magnetic field so that is precisely what would this be correct quantum mechanically where would I have gone wrong pardon me yeah so I cannot write p minus e a the whole squared the cross term would be p dot a plus a dot p I have to be careful about that then you would get pretty much the same thing the coulomb gauge it does not matter yeah exactly so that is a further thing that it really does not matter in the coulomb gauge so I leave you to verify to check that out but you get expected result.


The Covid-19 pandemic has had a devastating effect on individuals on community supervision, such as probation or parole. Many have been re-incarcerated due to the virus, and some have lost loved ones. Additionally, the virus has caused disruption to their social networks, health care, and livelihoods. Those who are still connected to their support system have been able to maintain it, but those who were more isolated and depressed have struggled even further. This article was authored by Catherine Lamasters, Angela Benson, Christopher Corsi, and others.


solitary abuse incident reached a record high in Scotland last year. A large pre portraits of these incidents whereby repeat offenders. I am Pam Gawshall, member of the Scottish Parliament for West Scotland and I know that far more needs to be done to prevent domestic abuse and to support victims of domestic abuse across Scotland. My proposal for a bill which I am now consulting on, would set up a register of those who commit domestic abuse. Affenders would have to provide information for this register. Authorities would need to act upon it where appropriate and those at real risk would need to be informed if they were involved with someone on the register. I believe this key policy in my proposal for a domestic abuse prevention bill would prevent incidents of abuse by deterring offenders and protecting potential victims. I'm also proposing that school children should receive education on domestic abuse. More information should be available on access to support services for victims of domestic abuse, including for people from BAME communities and for people with a disability. And there should be more focus on rehabilitation measures of those guilty of domestic abuse. My consultation is open and I want to hear from as many people as possible, so please share your views with me. Thank you.


The study presented here provides new insights into the molecular mechanism of action of the TRPV4 ion channel. The authors have identified the binding site of the TRPV4 agonist 4PDD and the inhibitor HC 0670 for 7 at the base of the S1, S4 bundle, and showed that agonist binding leads to pore opening, while channel inhibition involves a to transition in the pore-forming helix S6. These structures elucidate the interaction interface between HTRPV4 and ROA, as well as residues at this interface that are involved in TRPV4 disease-causing mutations. This work sheds light on TRPV4 activation and inhibition and provides a template for the design of future therapeutics for treatment of TRPV4-related diseases. This article was authored by Kirill Dina-Destin, Irina A. Talizina, Aravind Patasati, and others.


friends. But I found that developers are as close to designers as you get in general. We're all problem solvers. I think most developers are designers. They're just designing with a different tool set than I'm designing with. And so their opinions, I tend to take, not higher, but I tend to really listen when they say something doesn't seem right to them because they're in the same business I am and they're making a lot of the same decisions and they're solving a lot of the same problems. So it's important to utilize their feedback and their experience because it's an educated feedback.


I made the most of my internship opportunity in Hong Kong by volunteering at every foreseeable opportunity and really being involved in getting to know my colleagues. Within the internship when you find like-minded individuals that you're working with and you start to collaborate and share innovative ideas and think about the way to solve problems in your project, that's a really great way to establish those relationships.