So I grew up without a TV and I read, read, read, read, read all the time, which a lot was my political formation as well. And one book that really made a big difference for me was All Quiet on the Western Front, which I read very early, also like 9 or 10, and that was like, okay, this is not okay. They have these kind of situations where you need no war and no misery, and I got to do something in my life to, you know, to get rid of the bad stuff, and that kind of was a driving principle. I wanted to do something with my life to essentially trite, as it sounds, make the world a better place. And I felt that I was very, very privileged. We didn't have a lot of money, not a high style lifestyle, but a lot of travel and education. And so for me, I just felt like, wow, I've just been able to experience the beauty, you know, and the richness of life. Everybody has to have this right. And so that's kind of what I felt very strongly. Now, in terms of science, as I grew older, I just, I really appreciated the cell and biology as I kind of started seeing it as a metaphor, if you wish, for human society. And so if you think about it the way the cell works and the way an organism works, it's all for the greater good of the whole. And so it just seemed like, wow, you know, we as a society, you know, human society could learn from our own bodies.  Really, it's just such a phenomenon that we are actually alive every second of the day. It's stunning. And you think of all those pathways at the molecular level and the cellular level and the organismic level and at the environmental level, the ecological level. I mean, it's gorgeous. And so like, how could you ever do anything to upset that balance? And so that is kind of a driving force as well. So the first time I went to Nicaragua, it was quite an experience. Essentially, I was wandering up and down the hallways followed by roosters. And this is a situation where there was running water twice a week and no electricity, you know, on and off electricity. And I was trying to figure out what in the world I was going to do. I just knew I wanted to use science in this broader context and to essentially use it for the better good. The idea was that it would be essentially using these techniques. And then it became, well, no, it's more than techniques. It's about the disease. And then, OK, it's more about the laboratory. It's about epidemiology. And then, OK, it's more than those two. It's about writing proposals. And then, oh, management. And then it became like this is the entire scientific context. And so that became essentially the mission of Sustainable Sciences Institute was to be able to train people in the entire scientific enterprise. But while I was doing that, I had to actually create a whole scientific program. And it just kind of snowballed. And I just, you know, so many people were interested because there was this very unusual. And there was no other program or people really doing this.  I couldn't do that. And so instead, I stopped my career and I actually canceled my postdoc and said, I got to do this. I don't know what this is, but I got to do it. And I just followed, you know, kind of we went, we did a course in Ecuador and from there is another one that we went to Bolivia.  And I just had incredible volunteer support from from everyone in the world over at sea. What I like to do outside the lab and outside of science. Well, I love dancing. And more than that, I love my son. He's nine and a half and he loves soccer, football. He travels a lot with me. He loves traveling. And he, like I said, he's really obsessed with soccer. He and his father. So our house kind of revolves around the World Cup and around his soccer team. And he's been everywhere, you know, Cuba, Mexico, everywhere I go that I can bring him. But he loves Nicaragua, except for the mosquitoes. Yeah, and he's aware of what mosquitoes can do.  I think that having a fundamental understanding of the mass and sciences is extremely useful in life in general.  And understanding health and disease, it is very, very helpful as a fundamental basis. It's a very useful framework for everybody to be well versed in these items, especially, you know, understanding prevention, public health issues, you know, in terms of why you would live your life healthy and how to live your life healthy. And what the basis of that is, even at the molecular and cellular level, I think will allow you to integrate many elements of society later on. And so I would say that that is a very relevant framework, kind of as a platform, even if you're not going to major in the sciences for the rest of your life. But what you do later on can always be built from that and around that. So I think it's actually very useful in the long run.


Mr. Constancio, today the European Central Bank published the financial stability review, the spring edition. What did you single out as the largest risk to financial stability? We are at four risks. The first one is a possible reversion of the movement of asset valuations, which could lead to capital losses. The second risk is the risk of weak profitability of many financial institutions in the climate of low interest rates, which affects banks, but also down the road, possibly insurance companies. The third risk is the risk related with the debt overhang in the Euro area. Not only public, but also private debt ratios are quite high. And the fourth risk is related with shadow banking, or rather the entities that are not banks but are also involved in credit intermediation in financing the economy, and in particular the asset management and the investment funds industries. You also, right now there's a really hot topic that is widely discussed, it's sort of dwindling market liquidity, or you may also call it sort of liquidity risk. You're also mentioning in the FSR that there's strong or sharp movements in markets such as commodities, forex, even European government bonds, which usually or tend to be very liquid markets. Now what are the root causes of this, and how are you addressing these? Well indeed, market liquidity, the facility to buy and sell in the market, has been decreasing particularly in the bond market. In what regards commodities and exchange rate market, the reasons are not related so much to liquidity, but to changes in fundamentals that justify the movements of those prices. You were mentioning sort of the trend setting, the financial risk taking, this is rather high currently, but then economic risk taking, and that's also what you're mentioning in the FSR, is not as strong as financial risk taking. Is that, are you sort of lamenting the fact that there is too little investment in the real economy? Certainly, and of course it takes time for what we are doing in improving financial conditions being transmitted to real investment decisions. Indeed, by promoting that in part with our policies, we are trying to reduce the cost of capital or the cost of financing for the real economy, for economic agents, households and firms to take expenditure decisions, either in consumer durables or in investments. And finally, I want to ask you quickly about one of the risks that you highlighted, it was shadow banking, last time around in the last financial stability review, you mentioned it, but it was amongst others, this time you singled it out as a separate risk. Why is that? Well, it's still a potential risk, as it is explained, but indeed what we are realizing is that the sector is increasing very quickly, and also another thing which is the main potential risk in this sort of segment of the financial system, which is that most of the liabilities are short term, and we see that many of those institutions are investing more and more in longer maturity instruments, in more illiquid instruments, and that creates potentially a problem of liquidity risk that has to be monitored, and indeed, if the necessity is justified, regulators will have also to address that potential risk down the road. Thank you very much, Mr. Constancio.


I think an interesting question almost nobody asked themselves or at least if they asked themselves they don't really research and come up with an intellectual answer is the question of where should you live you know I was reading a book about Jeff Bezos and say what you want about him but at some point in his business career early on he decided he wanted to live in the most strategic place so he said he did his research and he found this is before Google by the way it's easier now but he decided upon Seattle Washington in the US because a you know he's an American so he wanted to stay in America be there was no state taxes see there was a big pool of employees that he could draw from that already worked at Microsoft he got down into nitty gritty details like how many flights there were coming into the airport how many non-stops from around the world for business meetings and while I probably wouldn't have picked that city I do admire the fact that he looked into this deeply because I think three or four most important questions anybody's gonna ever ask themselves I remember at age 16 being overwhelmed when I asked myself these questions you know it's like what's your religion world view gonna be one what diet are you gonna have diet slash lifestyle three what career and then for like who you're gonna marry or have kids with but that fifth one wasn't in my consciousness as much as it should be and sadly the school system hardly ever talks about this but this fifth question of where you should live and base your life is in some ways if not the most important maybe it's a second or third in that list because and by the way I've thought about this for years so the point of today's episode is I'm gonna try to fast-track and give you the answers in less than 20 minutes that I wish somebody had told me you know and I'm gonna throw out a few kind of frameworks you can use and you pick the one you like so an interesting framework is where will you have the best social life okay forget career for a second forget where's the healthiest place because you can go down we'll go down that framework to right so I think those are like the three best frameworks or where's gonna be the best social life and by the way you can just use the four pillars of the good life if you haven't gone to four pillars calm you should be getting my four pillars program which is you know how to everything or the quickest answer to how to find the health wealth love and happiness so the first you know a question you can say is where would be the healthiest place I could live second word be the wealthiest aka career third is love which is friends family romance that's social that's what I was talking about now and then last one will be happiest okay so let's start with that third pillar use the frame for framework of where would you be the most socially engaged friends family romance now interestingly the framework most people use is family right average person and it's been this way throughout history lives pretty close to where the majority of their family lives and I think that's valid to be clear but the modern world is all complicated there's something if you've been listening for a while talking about evolutionary psychology my mentor Dr. David bus you know there's a thing called evolutionary mismatches which means in some ways you can argue we were built to grow up around our family right but everything's been kind of chaotic for the last call it 200 years 300 years industrial revolution maybe even 400 years in terms of living near your family I don't know that that's a totally valid way because family now spreads out and a lot of people don't have you know that traditional mom and dad so I think that's a good framework but I think you got away the frameworks with multiple other frameworks right so most people go by family but friends is a super valid one and sometimes in the modern world because of I'm not gonna get into this but you know the collapse of the family in many ways right go in with the framework of friends makes a lot of sense but I'm gonna go a little further because like I said social slash love which is the third pillar in the four pillars of good life romance go where your best romantic prospects are you know if you talk to a scientist like Dr. David bus he always tells me tie everything is mating mating because ultimately you know we live on through our children and so I think it's one of the most valid frameworks of deciding where you want to live is where do you think you have the best romantic prospects where are those people who are your tight physically don't forget physical physicals valid you know or our eyeballs are attracted to certain types of people and now scientists are finding validity to that you know in this histio complex meaning people who have opposite or complementary immune systems so you don't have to discount your love your love of a certain physical type right so if you like blondes that may mean you know that on average those blondes have a complementary immune system and of course I'm oversimplifying a complicated subject but that's the point of this podcast is to get to the answers quick so don't think that relocating to an area that has people who look like the type you're attracted to okay you know I've always liked to kind of Scandinavia and that look my mom told me as a little kid when I was like two years old I would like chase the blondes around chase a little blonde when I was like two you know I would see a little blonde at two years old on the beach and go up to him and say hello so there's probably something to that you know genetically aka complementary immune systems and other things that we don't even understand now right so the next thing so so that romantic framework also personalities like you know I lived in LA LA is a big city big market but it attracts a certain type of person you know it's a lot of people who want to be influencers I always say every city has its good things and every city has its mental illness right or prone to a certain illness and this is people who migrate not people who are born there obviously if you're born in a certain city although you could argue your parents were attracted there and genetically most things are genetically heritable right so I always say LA is narcissistic it's the narcissistic it attracts the narcissist I think a lot of nice people live in LA it's not the worst mental illness now narcissism some people would argue obviously if you have NPD narcissism a narcissistic personality disorder which is the super extreme level of narcissism it's a nasty but you know New York is greed there's only two cities in the world with a trillion dollar plus economy for the city itself and one of those is New York and I've noticed there's a lot of good things about New York but it attracts greedy that's the mental illness hard-working you know ambitious but you know London attracts a certain type Miami for sure has its own Miami's a little bit like Vegas but globally you know Scandinavia has a lot of what I would say is more mellow people you know the people who stay there and don't migrate out people who migrate Dr. Bus has done a lot of research of this in the Mediterranean Islands people migrate tend to have higher testosterone you know more aggressive but again these are vast over simplifications but anyway you know Scandinavia I think anxiety is higher in closed societies you know I noticed that in Scandinavia Mormons in Utah things like Canada has a certain vibe so I think it's a really valid way to think about where you're gonna locate because if you get this location right a lot of things fall into line easily okay and you know I think at the end of the day there's not gonna be really anything you do more important than your mate who you have children with forget the romance for a second but who you have children with matters and it's permanent in your lifetime in your children's lifetime so you know people often ask about dating and that marriage dating marriage is not necessarily permanent there's no actual you know living being between you until you have kids so who you have kids with is really the defining moment of the next hundred to a thousand years of your lineage right so you there's a principle in economics called thick markets you need to live in a place with thick markets thick market means a lot of people of the type that you're interested in okay so it's you could say well time you know every city has somebody who's my type even if I live in the city where not many people are my type you know well that's a dangerous game my friend because if you're in a thin market this is an economic term but it applies to many areas if you're in thin markets okay the odds are against you and I'll tell you one of the most important lessons I've learned in business and life be careful of thinking you're gonna skirt the odds you know be careful of going oh well but you know Ty everything's gonna work out for me perfectly no matter how I play the odds that's not how it works you know it's not how it works my stepdad was pretty religious he used to say trust God but wear a seatbelt he was just saying play the odds don't try to say well I could make a whole bunch of bad decisions but yes you know I'll be bailed out by God that was his opinion he might have a different one right so to the extent you can you need to really think about cities through the lens of that social love aspect friends family but don't forget romance and you know honestly if I had a choice and this would be a tough choice horrible choice and I had to choose between a city that would have all my family a city have all my friends and a city that would have you know the best romantic part prospects it would be tough let me put it to you that way some people think it's cut and dry like family you know remember now in the model world especially if you become successful financially you could fly in your family you could fly in your friends it's harder to fly in especially when you're in the early dating stage looking for a mate UK it's hard to fly everybody in in fact if somebody was gonna fly in before you ever met him you know they may be you may not want to meet him because they're a little bit kooky I mean maybe not but I've flown in some people before I met him but not really it's kind of a strange there's a whole other podcast I can do about that concept but what I would say is you know you need to be in thick markets with early prospects so living in the right place romantically now I want to put a caveat by the way this episode I'm just keeping short I can talk about this especially if we talk about the other frameworks because there's you know this is the framework of love slash romance using that to determine where you live but we could talk about you know they have trying to find the physically healthiest place in the world you know I've lived in Puerto Rico that's like one of the healthiest places vitamin D close to the equator warm just one of the healthiest places you know career wise if you go down the wealth path I've lived in a lot of the big cities London New York Los Angeles those are great for your career you know and then right now we're talking about love I don't think New York and LA are good for your romantic prospects in fact I think they're actually dangerous because there's a lot of prospects in terms of attracted people but they're not necessarily good for a mate we're talking specifically about a mate a mate I define I don't like to use the word marriage or dating or too ethereal and easy to confuse but I'm talking about having a child with somebody potentially so that's that's how I define mating in that context it's a romantic attachment between two people with the purpose of having a child okay so so I think you know this this episode about them the mating side the love side and and I really think in some ways if I was 18 years old I probably guide myself with this framework over health wealth now happiness is a tricky one and I won't talk too much about that in this episode but you know I kind of my belief on the four pillars of good life health wealth love happiness is that happiness falls into place when you get the other three right when you're healthy physically when you're financially independent slash wealthy you don't have to be crazy wealthy but financially independent and when you have love friends family romance then I come now you can argue though you know happiness is comes from is its own extemporaneous attribute which I think is valid in the sense that there are some places that I go have lived in the world that I'm super happy I'll give example my farm I'm probably happiest in the mountains you know I've got some farms in different places and but they're not necessarily the best for you know health they're pretty good for health but for wealth career they're not the best because they're kind of isolated areas and for love they're not there's not many people who live there so so there's an example maybe you could argue that happiness you know picking a location on pure happiness you'd often end up probably in the mountains of Switzerland or Colorado but I don't know that I would I would think about having a second home in those places by the way theoretically if you can afford it and build up your income you can have four homes I kind of have four locations now so I actually now but that takes a while to build up you can't do that couldn't do that was 18 so you have a place where you're optimizing a city you live in you're optimizing for physical health a city for wealth career a city for love romance you know social and then a location for happiness I kind of rotate now and I have that so like last week I was in New York I don't live there permanently but you know like take you know there's a time in my life I'll give you an example where I was like New York or LA for career Puerto Rico would be for physical health really healthy place for Fred love Fred's family romance Europe and then happiness my forms but you still need kind of a primary place so I think a primary place can be built around that love mating framework now if you're already in love have a spouse you know have a mate have kids then even then I would still stay with that framework because you want your kids to grow up in a place where it'll be good prospects but I think you know then it's still the third pillar of good life love so maybe if mating you've already done that you still want to live in a place where family and friends you know really friends are super important it's interesting like some Scandinavian countries like Denmark the average person has this huge friend circle and in Denmark by the way and Sweden Finland and Norway Iceland they're voted the happiest people in the world and if you look they really have the four pillars health love happiness right so they have health they're the fittest people in the world least amount of obesity highest gym attendance wealth Sweden has five time the billionaires per capita of the United States you just go to Wikipedia and see their list of billionaires divided by their population right and you know love they have this huge social circles and then happy they they're voted happiest so the Scandinavia is a pretty powerful place I mean I've been coming to Scandinavia when I had a guy who was my doorman years ago Drago mr. X I used to call him so he was the best guy I've ever met with women he was a he always told me Ty go to Scandinavia so I followed his advice many years ago big going back and forth anyway I'll wrap up this episode because I'm doing my million-dollar body program and for those of you not million-dollar body you should go to million body calm million body calm it's my in-depth explanation and routine of what I did I spent a million dollars over seven years trying every single health hack to get in shape test my blood add muscle all that but part of the daily routine for the million body calm is you know recording while you do 18 minute walk on the way to get some coffee or green tea so I'm gonna wrap up here yeah I'm kind of dividing everything and I'm teaching and over the years now into this framework of the four pillars and then you could go in depth into health wealth love happiness I'm trying to like my life goal is to leave a complete system of everything they're all encompassing it's kind of like they call it in physics they call it you know it's kind of like equals mc squared it was this if you reduced the physical universe into one formula you know the grand theory of everything that's what Einstein equals mc squared obviously I'm not trying to compare myself to Einstein not as smart as him but what I'm saying is you know what is the grand theory of everything and that's my four pillars of good life so this podcast is part of that and you can branch out into the areas that are most interesting to you but it's pretty important and I think the biggest tragedy in this world is that people aren't taught the four pillars you know the grand theory of life because what does it profit a man to gain one thing and lose the other right like what does it profit you to gain all the wealth in the world but you don't have health if I trade you a billion dollars but you'd have to be bedridden for the rest of your life you wouldn't take the billion dollars so there's actual forget mazl's hierarchy of needs there's actually a more simplistic yet more profound hierarchy of needs right so four pillars is health will flow of happiness you got to move towards all four of those and that's the hard part about life is more life's about juggling things you know I know billionaires and I very few billionaires I'd actually exchange for their life right I know people have great physical health and but I wouldn't exchange for their life so it's a it's this exchange test anyway we'll talk about that in another episode alright leave a comment below on what because I didn't get into all the details I'll record a more detailed follow-up podcast so if you could leave a comment below a review and then in the reviews leave a comment of what you'd like me to talk about more on this subject of where you should base your life where you should live


Hello, welcome to SSHuritech, so see this side and this is continuation of SSH tutorial. So today we gonna discuss about event handlers. So before going forward, if you haven't watched part 54 of this video series, so I would strongly recommend to watch that video. So let's start with event handler. So in our last video we have discussed about error handling and how we can handle the errors if error will be occurred in our package. So first we can configure at the source, transformation and destination level and then by event handler. So in event handler let's create a scenario and then we will discuss how we can handle the error. So go to SSH DT and here I would like to add one more package. Then I wish to rename this package event handler. Then I wish to use execute SQL task. Then double click on this execute SQL task. Here I need to make a connection. So here I would like to create new connection as I have already created the connection. So I am going to use that one click on OK. Here in SQL statement I would like to use select 1 divided by 0. So it will reflect an error once our package will be executed. Now click on OK. So on every execution this package will be failed. So how we can handle the error? So go to on event handler. We can click on on error event handler. So here as we can see in event handler we have many more options. First is on error, on information, on post execute, on post execute weld date and many more options. I am very interested to use on error. If error will be occurred in our package then this will be executed and inside this executable as we can see we can set at the package level and also we can set as the task level. So this is our task as we have only one execute SQL task that is why we are getting only one. So I wish to use in package level. Now click on OK. I have created a table with the name of errors and it has only one column with the error description. So once our package will be failed then I just want to capture the error description why our package will be failed. So here I need to use execute SQL task double click on this. Then on the connection I am going to use existing connection. This SQL statement here we need to use insert into errors and error description and here we need to specify values and question mob. So we will get the value from the variable. Now click on OK. Now go to on parameter mapping. So here I need to add a new parameter. Then in the variable name I want to use error description. So this is our system variable and we can also use UDefine variables. So data type would be where care. So we can select where care then parameter name. In parameter name we need to specify index. So it would start from 0. Then parameter size would be anything so I want to use as 500. Now click on OK. Now we can save this package. So our package will be executed then if error will be occurred then our event handler where we have specified one more execute SQL task. So this execute SQL task will be executed. Now click on start. So as we can see package failed we can check in event handler. So this executes SQL task executed successfully. Now we can stop this package. Go to on SSMS. Now we can refresh this table. One record has been inserted. So we can find select 1 divided by 0 failed with the following error and error is divided by 0 error encountered. So this is our error that's why our package failed. So here after capturing the information if I wish to send an email so we can use send email task inside this event handler and we can connect with execute SQL task. And we can configure send email task as I haven't discussed about the send email task so I would discuss this in our upcoming videos. So we can use according to our requirement. So thank you so much for watching this video. If you like this video please subscribe our channel to get many more videos. Don't forget to press the bell icon to get the notification of our newly uploaded videos. Thank you so much.


Ok, je to, da se počutim, da se dobro sega izgleda se izgleda se izgleda se izgleda. To je izgleda, ne? Tak. Tak. Tak. Ok. Ne zelo, da se ne zelo, da se prišlo, Nikolo? Zelo, da se ne zelo. Zelo. In zelo jaz označenje, ker sem čest, da je učinil, tako je zelo je začal na tjude. In ga je razstajala, da je advancesk, da načem v že, da bo vzela, da je označen, da je označen, da je označen, da je označen. Moj, da se kot pa, da je označen, da je označen. Predstavito, da sem to je želila, da sem bošnja, da sem tečnega. Slepšo, ki sem tukaj, da je. Nemo, da ga zelo, da se je. Zvom, da se bošnja v loči, da se je občal, da se je zelo. Selo se je zelo, da se je zelo, da se je zelo. V zelo se je natunal. Pistaj, da se je zelo, da se je zelo. Zelo se je zelo, da se je zelo. Tukaj, da se je zelo, da se je zelo. OK, a da sem si pozna, da se je komputila, in so in utopili zelo in nekaj je trefo ja... V odličnoj napisteva, nekaj nekaj je ta dobrovodnja,atorskri obdej, zelo igno, in je je v masternji, o da bo matov, zelo, patiš, če bo cah nato, če se... OK, se je to je現在. Nekaj je, nekaj je Nikola, nekaj je Vnikola, nekaj nekaj je, Trai kritične in izvrstke ideje, no, trai kritične in izvrstke z heading, in glasbe, ztega, nič doagnana vse je. In sve glasbe je v delovoh, ki so tudi z njenim sej, kot tudi nekako. Mi je neko što. Teh da sem spodljel, pomembnem po požeštih. Moj jo v deteženju, s kaj sem tukaj lahko vsej so počutiti, da res predstavimo na vseh prijev. Zato. To mi počutimo, jaz njih jaz sem tukaj neko počutil je z vsev. Tako, nekaj sem počutil, nekaj so počutil vse, nič. Dobro. Dobro za če nekaj vse. Zelo je jedna qeština? Ne. Ah, ne! OK. Spod njih imam alunje, da pa ne poželijo mi. Mi moraš da? V tom, da ja... Dobro. Pistim, da se ovega na dobro, njih imamo dobro, z delala vzifli avanje in z delala vzifli z našem vzivnjom. Ben sem zelo vzivnjom vzivnjom in je zdaj ne ovo, da je zelo vzivnjom vzivnje, ne bom zelo vzivnjom in in lobimo in Časovosti s n Profilice in skupaj. S njom núč flowers. To je jinama nr.  In je instotne, ja ne zelo lahko jaz bo potrebjemo o zač Official Quell, because jeel anglobi kako skupivo kratum in pa created. and simulate a spin Hamiltonian. So once again our focus is going to be on a spin Hamiltonian, like the one that I've been discussing yesterday, so the transverse fieldizing model. But in this case, but now we have that interactions decay as a power law, so Vij is now a power law of the distance between the two spins along x. There are various ways to describe long range interactions, so what is important to notice is what we were discussing yesterday that as a function of alpha one has two radically different situations. If alpha is larger than the dimension of the system and notice that in this case I'm focusing on the case of a one-dimensional system, so I'm talking about, you see here, a one-dimensional chain. Now in this case the dimension is one and in general one can say that one has two regimes for long range interaction. The regime where alpha is smaller than one and the regime where alpha is larger than one, so smaller than the dimension and larger than the dimension. The case when it's equal to the dimension I will not comment too much, it's a little bit in between the two, but more similar to alpha smaller than one. The difference between the two regimes is that in the regime alpha is smaller than one, one needs to introduce a rescaling in front of the energy. One needs to introduce a rescaling in front of the energy in such a way that the energy of the system is extensive. The cat rescaling Stevano has already been talking to you about and you see basically that also for general alpha so also when alpha is away from zero but it's still smaller than one you need to introduce such a rescaling but the rescaling has to be able as a power rule of the system sides. I also put some coefficient in here but these are not essential. What is crucial is this term here which rescales the internal energy. On the other hand when alpha is larger than one this is just a normalization coefficient so it doesn't modify the behavior of the model and sometimes or most of the times when alpha is larger than one so when alpha is larger than the dimension of the system we prefer to redefine it and define a new exponent sigma which is nothing but alpha minus the dimension and this is convenient for some reason that we're gonna talk about later. So basically all this normalization condition derive from the value of this submission here so if this submission this is the submission over all possible distances of the interaction energy of the system and this submission is the one that determines if the internal energy is convergent so the thermodynamics is extensive or if it's divergent. Ok, this is a bit mathematical I don't want to spend too much time about it just to show you that one can show or prove exactly even the divergence of that submission and one can basically prove exactly that the divergence of this submission is the one that I indicate here. So now just to look to make the formalism more mathematical to look it nicer I change alpha into s but this is not so important. So one can use the standards Euler-McClurin formula that converts a submission into integral and one can just say that the submission that we are talking about which is this one is equal to the integral of the same function plus a reminder and the reminder can be shown to converge I don't want to prove it to you right now just you can basically show that this reminder is smaller than the integral of f prime alone than the modulus of the integral of f prime so the modulus of this is smaller than the modulus of the integral of f prime but obviously f prime converges because if s is between 0 and 1 f prime converges because it's the derivative with respect to x of 1 over x to the s so this guy converges and the only diverging part is the one that you find here and this part it's straightforward to do the integral of the x of 1 over x to the s is just go like x to the 1 minus s and so it diverges like n to the 1 minus s so basically it's this term is this integral term in the Euler McClurin formula that gives you the divergence that I have been talking about here okay there is one can do much better than what I have done down and one can prove that this summation goes like this where you also got the right coefficients and some corrections but this is not so interesting for us so what it's interesting for us is that the divergence is proportional to n to the 1 minus alpha so that we have to put in front of this guy i coefficient n to the alpha minus 1 which rescales the energy okay so I believe this is enough mathematics but this is kind of a basic mathematics you should be convinced that we know how to treat these divergences what I also want to convince you about is that this system has a quantum phase transition for any value of alpha and basically you should be able to have an intuition for that from the fact that we had a discussion yesterday about the fully connectedizing model so the case alpha equal to zero and we have explicitly made the calculation of the quantum phase transition so I have given you some details and hopefully you have been able today or maybe in the next few days to reproduce that calculation in details but also the case where alpha is equal to infinity so the case where alpha is equal to infinity it corresponds to the nearest neighbor case no so this is the case alpha equal to infinity when alpha is equal to infinity only sides that are at distance 1 between each other survive 1 because I have set to 1 the lattice spacing of my system and so you should know from your basic courses that also the nearest neighbor limit so anizing model with nearest neighbor interaction as a quantum phase transition between a symmetric phase where there are exponential correlation and no paramagnetic order and a ferromagnetic phase where there is ferromagnetization along the x-axis you have seen this stuff during your courses I already asked this question yesterday but I will re-ask for completeness is there anybody that doesn't know about the quantum phase transition in the transverse field design model apparently not so I believe that if you know that the nearest neighbor system has a quantum phase transition and yesterday we discussed the case of alpha equal to zero basically you will not be surprised to know that for any value between alpha equal to zero and alpha equal to infinity there is also a phase transition how can we see the properties of this phase transition well the first thing that we can try to do is is as a called also in premarkov transformation which some people call also I think quite rightfully a spin wave approximation so we try to transform our spins into bosons and this transformation is one of the very basic tool of many body quantum theory maybe you have already seen it around and it basically consists to approximate the spin as a bosonic state the idea somehow is that n spin as n states a boson as infinite many states no, because I can put an infinite number of bosons in the same site but into some approximation one should be able to reduce the dynamics of the boson as if it has only few states and if it has only few states then the dynamics should be the same as the spin well there are ways to make this analogy formal like considering not just bosons but arc or boson so boson which have a strong interaction and the physics of boson with a strong interaction so with an arc or constraint is basically the same as the spins but in our case we are not going to do that we are just going to reduce so we are going to employ really the austen premarkov transformation in bosons which have no constraints so this is the transformation you see here so basically you transform the spin ladder operator in bosonic ladder operator or if you wish you transform the sigma x and sigma y component of the one half spin into combination of bosonic ladder operator and the value of the spin around the polarization axis that now we choose to be z is going to be given just by the density of the bosons so if there is no boson on one side the spin is one half if there is one boson inside the spin is one half is minus one half and if there are more than one boson this state will be the wrong one that we don't want to consider so this is an approximation as I already said but it's a very powerful approximation because it allows to reduce this model that is not treatable analytically in the beginning into a model which is fully solvable because once I have replaced my spin operator into bosonic operators the Hamiltonian is now a quadratic boson Hamiltonian and it can be solved by a bogorubov transformation is there anybody here that doesn't know what it is a bogorubov transformation are you sure guys? sorry Stefano I couldn't hear you someone does not know but others maybe know I don't know maybe okay maybe you repeat to say something more okay fantastic somebody says he doesn't know what it is very good so well let me give you some words about the bogorubov transformation so it's very important this is also so we are using very standard tools of many body quantum mechanics okay obviously this is a school of statistical physics this is also statistical physics as we will see in a moment but I understand that maybe some of you they do never encounter this concept before what I just wanted to say is that if you plan or are planning in the future to work in the field of quantum physics and many body quantum physics it really important that you go and attend some courses on these topics or also revise these topics independently on some books and if you write me I can suggest one some so basically the bogorubov transformation it's a 2 by 2 transformation so what's the idea the idea as you see sorry so I start here as I said I took the spin operators and I mapped them into bosons now these are bosonic fields these are bosonic operators and so these represent bosons that are up on the lattice but this is not a pure Newtonian it also has this anomalous term you see this term is a bit strange because it doesn't conserve it doesn't conserve the number of bosons you can basically create two bosons from the vacuum without paying without destroying anyone so this non-numbered conserving operator may seem a bit strange but we know that in many body quantum physics it's not so anomalous it appears already in BCS theory of superconductors and it appears also here because the idea is that if you have a many body system you are always in the grand canonical ensemble so many body quantum theories is almost always describing the grand canonical ensemble where the number of particles doesn't need to be conserved in some sense so you can have Hamiltonian where there is this kind of operators but what do you do in that case so in that case is pretty simple so first of all since the interaction is translational invariant you do a Fourier transform you do a Fourier transform this is standard tool I guess you know it and you go to momentum space since the interaction is translational invariant in momentum space you don't have any coupling between the sides but the anomalous term so the non density conserving term it shifts its couples different commenta so let's try to break down this Hamiltonian let's try to break down this Hamiltonian so this Hamiltonian it's a sum of n independent Hamiltonian or n half independent Hamiltonian k lives on its own now you see there is no coupling between the momentum k's so you can consider this h as a sum of h of one Hamiltonian for each k there is no scattering between plane waves or between Fourier modes however there are modes that are coupled and the modes that are coupled are just the modes that have k and minus k so let me repeat it once again to just maybe could be boring for someone but for somebody that haven't heard about that it's important I went from real space I went from real space to momentum space in momentum space I have n modes as many modes as are decided in the lattice these modes are positive and negative k because of the system being symmetric and all these momentum modes are independent from each other but the coupling that emerges due to the pairing term and this coupling couples states which have momentum k which states that have momentum minus k so basically you have n half Hamiltonians which represent the Hamiltonian of modes with k and minus k coupled to each other now we want to remove this coupling because we want to really to diagonalize the Hamiltonian we want the Hamiltonian to be diagonal like this one this one is not diagonal in momentum space because it still couples momenta which have different values basically each k is opposite we want to go to an Hamiltonian where there is which is completely diagonal where you have some quasi particles which are fully non-interacting how can we do that? well since these are basically two-state system we can do just a volume of transformation which is nothing but a 2 by 2 matrix so it's a transformation which it's a 2 by 2 matrix and it helps us redefining the bosonic operator as a linear combination of creation and annihilation at k and minus k so you see it here I take my old operator and I express it as a combination of a new bosonic operator and a new both creation operator but at minus k if you do this in metric space it's going to be evident to you it's just a rotation in the spin one half space so it's just a rotation in the space of 2 by 2 matrix in the space of 2 components vector and it's a rotation in the space of 2 components vector because basically 2 states and so in order to resolve that coupling we only need to make a rotation in the space of 2 components vector which is the space of which is the space of spin one half vector which is s1 but this is ok I don't want to bother you with group theory and s1 symmetry of the spin operator what it is important is that you understand technically how it is done and technically is just introducing new bosonic operator b which are linear combination of the old here I am writing only the old as a linear combination of the new but if it's a linear combination I can always invert it to make it another linear combination and then I have to determine which are the u and v which make the Hamiltonian diagonal I don't want to do this explicitly now you can do it yourself it's very simple just plug this expression into here the dagger is obvious you plug the expression for this ak and this dagger into the Hamiltonian and you can then assume that all the terms which are not diagonal so that are not of the form b dagger b or b dagger vanish and if you do that you will immediately find this u and v v so I can do this bogolub of transformation and I can define new bosonic quasi particle these b and b dagger are bosons so they satisfy the same commutation relation as the a's and the a's were bosons so they satisfy the user commutation relation and in terms of the new operator b the Hamiltonian is diagonal with a certain energy spectrum omega k ok please, I have a question ok ok I wish you know if I wish you know if the transformation is unique I mean for an operator ak you have a unique bk and b-k basically basically there are two which are equivalent so that is the one that I am showing you and this is another one in which I also exchange the role of the creation and annihilation operator ok so basically there is one and there is the one that instead of giving me b dagger b gives me bb dagger but that one I can always bring it back to the first one just by swapping the two operator and adding a constant so it doesn't really matter ok so it's not unique but it's like if it were because it's the one that's not unique is just well, these are bosons and not fermions but in some sense it's unique thank you then my mathematical physicist friend they made me a long argument on how this transformation is simple etiquette so it's obvious that it's unique and the equivalent one for fermions state is unitary so it's not exactly unique but for the sake of all practical physical application the volume of transformation it's always it's unique both for bosons and for fermions so we have this transformation and we have this transformation and we have the spectrum of the system so now I solved my model I solved my model and my model is is diagonal and they we call this bogoljub of quasi-particle so the bidager beer we call them bogoljub of quasi-particle but I don't like so much to call them quasi-particles because they have not any finite lifetime so this model it's exactly solvable and the bidager beer are modes which live forever but people call them quasi-particles because somehow they have in mind that the spin-wave approximation is just an approximation and so it's expected to break down at some point and so this is why they call it quasi-particles but for the sake of being precise these are not quasi-particles they are modes of the Hamiltonian which make the Hamiltonian perfectly diagonal and so they have infinite lifetime what is interesting for us is what is the dispersion of the mode why is it this interesting for us well because I have been telling you that this system has a quantum phase transition as a quantum critical point for certain values of h now when the ratio of v over h reaches a certain value but close to this quantum critical point the properties of the quantum critical point they always depend from the supposed continuum limit not continuous but continuum the continuum limit so they only depend on the small momentum modes I guess this you know no in phase transition even in classical phase transition to say that what is responsible for driving the transition are critical fluctuations which have long length scales and if they have long length scales they have small momenta so it's interesting now to look at the expansion of this spectrum so these are the modes of the system asking what happens to the modes which have low momenta the one that are the most interesting from the point of view of the macroscopic physics and when I look at these modes their energy depends on this vk which is nothing but the Fourier transform of the interaction potential that was 1 over r to the alpha and so now I have to do the Fourier transform of 1 over r to the alpha which is nothing but this sum with the cosine kl do you understand this no? Do you see the Fourier transform of the interaction potential? Is there anybody that doesn't see the Fourier transform of the interaction potential in this formula here? Well, I guess that everybody sees it no, it's easy so this was the interaction potential so this was the shape of the interaction potential I want to do the Fourier transform the interaction potential is transversional invariant sum only over the distance between the sides that now itself and I have to put a cos kl on top so when I do this Fourier transform well, you can do some mathematics and show up that basically this is related, this is equal to the sum of the poly logarithm of this exponential of the momentum this is not so interesting as a redefinition of this Fourier transform based on the definition of the poly logarithm what is very interesting that when I go into k equal to zero limit so when I go a slow momenta this function is non-analytic so this function is non-analytic it has a momentum term in its Taylor expansion which is not nor odd power of the momentum it is a k to the sigma with sigma a real number which is equal to alpha minus d and since I am in one dimension in this case it's alpha minus one so I hope you are appreciating what's the strong effect of long range interaction in this case so yesterday we have been talking about interactions which have alpha less than d but now we see that also interactions which have alpha larger than d they can do something pretty deep and profound on your system they can generate a non-analytic momentum term into the low energy theory I don't want to talk for now of the case where alpha is smaller than d but different from zero we will see tomorrow also the case alpha is equal to zero so I am not going to talk about this for now for the moment let's focus on alpha larger than one when alpha is larger than one you see exactly what I was saying a minute ago the low energy theory contains a fractional we call this a fractional momentum term in the sense of momentum term which is non-analytic in k but this is deep this deeply changes the this deeply changes the physics of the system because now it means that in the continuum limit and sorry this is a misper it should be continuum in the continuum limit this system becomes a gas of bosons where the dispersional relation instead of being k-square is k-sigma so a gas of boson between analytic dispersional relation so I'm sorry this I have to ask does everybody know what I mean when I say I go into the continuum limit or this is something that you hear here for the first time there is no shame guys so if somebody doesn't know what I mean when I say continuum limit just say it and I will try to explain it a bit more so you have the chat also in the world nobody is writing in the chat and you don't dare to raise your hand you can you can put it in the chat okay I guess that the world continuum limit is somehow famous and it's the same in some sense this is not really related to quantum physics now this is exactly the same case that will happen in classical physics you can take a classically critical model and that's on the lattice like the ison model and do the relation to the continuum limit and you find that the ison the classical ison model is the same as a pi to the fourth theory in the continuum limit and this is somehow the same that's happening here I've taken my quantum ison model and I have done some manipulation to map into a gas of bosons and when these are still bosons on the lattice so this Hamiltonian still represents bosons that are hopping on the lattice but then I made a further step I make an expansion of my Hamiltonian as low momentum and when I do an expansion of the Hamiltonian at a small momentum I get a gas in the continuum so I get a gas that lives in the continuum space without the lattice but this gas now has a non analytic dispersion relation so as a dispersion relation which is not the standard k square over 2m that you know or maybe you also know the phonon dispersion relation that is k simply k, linear dispersion relation no the gas of bosons hopping on the lattice in the continuum looks like a non analytic gas with k to the sigma and then you can play the game of studying the properties of this boson gas in the continuum with non analytic dispersion relation and I don't know if you ever try to do this this is some time given in exercise in statistical mechanics in quantum statistical physics course so when you study bosons and condensation you have studied I guess bosons and condensation in the standard 3 and 2 dimensional cases now you can study bosons and condensation in fractional dispersion relation and it turns out that when you study bosons and condensation in fractional dispersion relation it's like studying bosons and condensation in fractional dimensions and this you see very easily if you try to compute the density of state the density of states is how many states I have this is standard calculation in when one study the bosons and condensation you count how many states you have a fixed energy so you have to integrate over the entire momentum space the omega k and the omega k it's now non analytic it goes like k to the sigma rather than k to the square and so when you do the computation you find that this goes the density of state goes like the energy to the d over sigma minus 1 notice that in the standard case of bosons and condensation you will have d over 2 minus 1 you know this formula density of states goes like energy to dimension 2 minus 1 you know this as usual if somebody doesn't know he can speak up now we have generalization of this formula the standard formula for bosons and condensation it goes beyond the case of local interactions and for long range interactions you have d over sigma minus 1 as be replaced by sigma but this is not surprising because the standard case of a boson gas will be k to the square no the kinetic energy of a boson gas is k square over 2m but now with long range interaction we have k sigma over 2m sorry I call cdc is 1 over 2m now we have this k sigma and this tells you also something else that the case sigma equal to 2 it's special and it is indeed special and you see also from this formula because when sigma is smaller than 2 this is the correct expansion when sigma is larger than 2 when sigma is larger than 2 this is not anymore the correct expansion here I indicated that I have a k to the square term and so when I do the expansion at low moment that when sigma is larger than 2 this term is sub leading with respect to this k to the square and it should be replaced by the k to the square and so it means that long range interactions they only modify the low energy behavior if sigma is less than 2 which is tant amount to say that alpha is less than 3 and this can be somehow sorry I am not skipping that I want to just to show you so this somehow tells you already something that sigma equal to 2 is a special case and then for sigma larger than 2 the system behaves exactly as if it were short range as if it were nearest neighbor and only for sigma less than 2 you have some real long range so you have some contribution from the long range interactions to the low energy theory and then when sigma is smaller than 0 we go back to the case that we treated yesterday the case of strong long range interactions ok now I hope I have convinced you that the that this system that the ising model can be related the physics of the ising model with long range interactions can be related to the physics of a Bose gas with a non-analytic dispersion relation and at the same so also the existence of the phase transition can be somehow related to the possibility for the gas to to condense the ferromagnetic phase transition from the spin in the language of this both in the Bose gas language can be seen as a condensation and I don't want to do the entire calculation here I hope so all of you some notion of Bose Einstein condensation have you studied Bose Einstein condensation in the past if somebody hasn't studied Bose Einstein condensation speak up as you very good so if you know about I haven't said one student does not ok, very good so you don't have notions about Bose Einstein condensation so let me see how to explain in a nutshell in a nutshell well in a nutshell Bose Einstein condensation of course there is when you have a Bose gas a gas of quantum particles which are boson what physically what it may happens that these are quantum particles so they have wave function when you lower the temperature at a certain point when you lower the temperature the particles become feather so they become more and more fat because the wave function the debris wavelength grows this is standard from quantum mechanics course as now we always say as the debris wavelength grows there is more and more overlap between the wave function of the particles in the gas and there are more quantum effects now it exists a critical temperature below which the quantum overlap between the wave function is so big is so strong that the particles that there is an establishment of coherence in between the particles so the particles tend to form a condensate so a coherent state where the particle lose their identity have behave like a very coherent homogeneous fluid now this is theoretically this is justified by the fact that the bosons can stay in the same state so bosons can stay in the same state and if the temperature becomes so low they all start to have zero momentum because this is a gas which only has kinetic energy it's a gas that only has kinetic energy so the minimum energy state is the state with k equal to zero so all the particles want to go in the k equal to zero state and when there are too many particles in the k equal to zero state you cannot use any more a statistical mechanics description because the statistical mechanics description somehow relies on the fact of the particles being to the energy being continuous and the particles being well distributed according to some distribution into the entire energy levels into all the energy levels but if all the particles occupy the same momentum state they all have momentum zero in the continuous representation of the gas so it means that the standard statistical mechanics description fails one way to see that the standard statistical mechanics description fails is that when you count the number of particles in the system you get the wrong result and this is basically what I'm trying to show here I put just this formula and I assume that most of you have seen the same formula in the case of nearest neighbor interaction but let me try to break down this formula, this is the number of particles in the gas at a fixed at a certain momentum at a certain chemical potential value mu so according to the standard notion of statistical mechanics from a chemical potential I can obtain the number of particles that are in my system and this calculation is easily done is just the summation over all possible energy states so this is the density of states that enters here that counts the energy states of the probability for a particle to occupy that energy state and the probability for a boson to occupy that energy states is given by the boson's distribution this is nothing but 1 over exponential of beta d energy minus 1 so this function here the 1 over this is the boson's distribution that you probably have seen many times this term counts it gives you how many energy levels there are at a certain energy and the integral over all the energy should give me the total number of particles in my gas this would be true if there were a statistical mechanics description that worked but this statistical mechanics description fails to work when the gas becomes a quantum of boson's and condensate because when the gas is in a condensate it means that you cannot describe it as an homogeneous distribution function because all the states are at zero energy and this you see from this fact when you do this when you do this integration and you do it at a small temperature because we are thinking about something that happens at a very small temperature when you do this integration and you approximate it at a small temperature you get something like this now you see that this guy vanishes as the temperature goes to zero but we expect our gas to have a fixed density no, we want our gas to have a fixed density and so this as the temperature goes to zero the vanishing of this term has to be compensated by a divergence of this term but this term does not diverge as long as d over sigma is larger than 1 so this sorry, please I don't know if you are using a mouth because when you are pointing a term we can't see it sorry, you cannot see it ok, that's very bad there is a red dot on the screen, I don't know if this is the mouse so if there is a red dot now I'm pointing at d on the second line no, it points to the integral it's moving ok, then this point I don't know what it is I'm sorry guys I thought I had made it in such a way that it was visible but ok you see now the mouse ok, now we see the mouse now you see it ok and also the red dot moved I don't know if it's this red dot is not visible for me so I don't know ok, very good so let me redo this with the mouse so I was saying this guy is the number of particles of the gas at a fixed chemical potential we have how to calculate it is the sum or the integral because we are assuming that we can treat this gas as a constant so this so I'm not telling it would be that I don't see the as you see so go on Nikolaj, sorry so this, the number of particles in the gas is the integral over all possible energies of the number of states as a certain energy which is the density of states multiplied by the probability for the particles to occupy the state which is the Bose-Einstein distribution so this is the Bose-Einstein distribution 1 over the exponential minus 1 is the Bose-Einstein distribution so this integral should give the total number of particles of the gas at a certain chemical potential as if I go to the slow temperature limit to the small temperature limit to the limit of cold gas I can approximate this integral as it is written here on the right and you see that there is a pre-factor that vanishes as a power of the temperature so if I want my gas to have the same number of particles because we want our construction to be at a fixed average number of particles the vanishing of this temperature term has to be counterbalanced by a divergence of this term here of this integral but this integral does not diverge as long as d over sigma is larger than 1 you see the limit of this is the small temperature limit because in the low temperature limit the chemical potential also vanishes so this guy vanishes in the slow temperature limit this guy tends to decrease proportionally to the temperature and if this is happening it means that the particles are entering in the Bose Einstein condensate state it means that I am not anymore able to see them in this description because this description assumes that the particles are somehow smoothly distributed along all the energy levels but this is not the case because all the particles are condensing in the zero energy state and the zero energy state is not accounted in this integral or is not accounted properly by this integral so this is the standard study of Bose Einstein condensation the fact now that Bose Einstein condensation will occur between in dimension larger than 2 because normally you will have that this is not sigma, this is 2 and you will have that Bose Einstein condensation of course for d larger than 2 but this is not the case you see this is not the case now with long range interactions the 2 has been replaced by a sigma and this basically means that for this kind of gas Bose Einstein condensation can occur at any value of d as long as sigma is small enough and this basically means and this is also another way to say that a gas with a fractional dispersion relation a gas with a fractional dispersion relation is equivalent to a gas with a local interact so a gas it's equivalent to a gas with analytic dispersion relation so with the standard kinetic term k to the square but which has an effective fractional dimension ok and this effective fractional dimension I reported here is 2d over sigma and this is exactly very easy to show you can take any calculation that you have done on your Bose Einstein condensate states and you have to replace the dimension d with this number sorry with this value and you will immediately see that this calculation that these expressions are transformed into the equivalent one for long range interactions well let's a simple example for example the specific heat you know that the specific heat is the alpha the number of degrees of freedom in a local gas in a local non interacting gas we always say that the energy is 3 alpha and kbt no 3 alpha and kbt because we are talking about gases that are in three dimension and the standard result for the equation of state is that the total energy is 3 alpha and kbt now here I have said kb to 1 so for me the standard equation the equation of state of a gas is that the energy is 3 alpha and t and this means that the specific heat that is nothing but the derivative of the energy with respect to the temperature has to be 3 alpha m but in a long range interacting state instead of having 3 alpha n which is I have to replace the dimension with the effective dimension that is 2d over sigma and I get the result that is in here so you see the presence of long range couplings modifies my effective theory and it modifies it in such a way that I get the effective fractional dimension because I can take the standard formula specific heat is equal to d alpha n replace d with the effective dimension 2d over sigma and I will get the results of a gas with a non-analytic dispersion relation well I hope that you got this point please make some question tell me what you did I guess this is a bit of a convoluted matter because I started from anising model I mapped into a quantum gas but the special thing of this quantum gas is that it has a non-analytic dispersion relation and then I try to show you that the gas with ananalytic dispersion relation it's equivalent to a gas with ananalytic dispersion relation but which lives in a fractional dimension is this picture clear at least in its history well let's make a 5 minute stop here in the previous slides you had a quantity which is not defined c so this is the dimension of the integral because you have the where sorry in here first line last formula sorry, this is the c here it's 1 over 2 m basically it's just a coefficient sorry I always speak about critical phenomena so I never look at coefficients it's the speed of sound or the mass of these particles depending on how you want to see so it's not really speed of sound because it would be k square so it's only if it is k square the sound normally is linear so if sigma is 1 this would be the standard definition for the speed of sound so if this were a phonon gas this would be ck but since it's k to the sigma if this were a square the c would be 1 over 2 m the mass of the particle the speed of it in between these two so we can make a break 5 minutes 5 minutes break you can behave like bosons it's a popular task


What's up guys micro with Jaspie's doing a quick recap for our 2023 tops chrome jumbo Eight bucks case break pick your team number seven that was done on fanatics live Oops, sorry. Here's the list here Positive if you need to Yeah getting into the recap Starting off with parallels rookies refractors All that good stuff of cuneas show haze Again, this was a full case of jumbo soda to 250 a Gold Shintaro Fujinami true gold out of 50 for the A's Rooks. There's a Corbin refractor Gabriel Moreno out of 125 Prison Gunner Francisco Alvarez the 350 for the Mets a Christian Yelich relic Alvarez refractor show hey Carlos Perez out of 199 Freddie Tarnac auto skin in some of the autos here Jared Young refractor auto bone-nailer another Tarnac Ziko Tovar out of 150 Blue Rayway toglia Papiersky refractor auto Swaggerty Cody Thomas out of 250 Palacios refractor auto out of 499 Ashcraft Von Grissom refractor auto 499 Spencer steer out of 250 Bryce Johnson E guy Rosario Matthew Libertor Marcus Wilson at 299 Walde Chuck JJ Blede Buddy Kennedy bone-nailer refractor auto Oscar Gonzalez made a Michael Harris to 150 a Riley Green authentic relics and autograph That one was 99 out of 99 for the Tigers and Adley variation and an Austin Riley 1988 tops Auto out of 25. So pretty nice break there. Thank you to everyone who got in thank you guys for watching And I'll see you guys in the next one. Bye guys