Good morning everyone it is Wednesday and we are on the floor of the New York Stock Exchange with Jim Kramer. Jim stocks slightly up. What do you make of the temperature of the markets right now? Warren Buffett's birthday today. Warren Buffett we speak with Becky Quick. Warren Buffett has been known to turn around the futures to the point where people regret that they had a short going on, whether it be an Apple, whether it be in the rails, because whether it be in USG, USGip, which is registered trademark, Gipson board registered trademark USG, probably the most in-demand in a situation where you have water damage. This is a man who does substantial amount of demolition in New Jersey, a man by the name who runs a company called Suburban Michael Haley, who has dealt with mold from Sandy. The big impact will be mold. Now remember because there was no there was no wind. Wind is the way you get the private insurers. Flooding is going to be the federal government. Let's stay close to that. It could be as much as 100 billion in flooding. Now in real money Jim you talk about how you expect a faster, more robust rebuild than Sandy. Yes and I think that fast because this is Texas. I think that it's a Republican administration. Even the Republicans who are against spend I think will cave because Texas is a state that gets its way. So if it's a faster rebuild does that mean it's less of a distraction for tax reform? No I think that what happens to during the 12 days of September the debates will be about repeal and replace because I think that Paul Ryan has no no desire to do what the president wants. Could be about repatriation which is the only thing I think could have a possibility. But repeal and replace will be back on the agenda because they can't help themselves and that's when I speak of real news of course I favor the president's economic agenda. When I speak of fake news I suggest that perhaps it won't be so easy to get through because you have to have a budget resolution and you have to have a debt ceiling. Debt ceiling regardless fake news by the president but I have to point it out. These days I want to say fake and real because I'd like to be on the real side of the president but I also have to report some of the fake news too.  And Jim you mentioned repatriation with that we should watch shares of Cisco. Yes Cisco is not down after a very disappointing quarter. Seattle will report very good data center numbers according to some research that I've read which means that that's a that's almost zero some these days with Cisco. I remain concerned that Cisco's tremendous turnaround is is a three or five year process. All right. Speaking of the broader economy GDP growth for the second quarter revised up to three percent. Why isn't the 10 year reacting more to this. Well I think the 10 year also reacts to there's a lot of fear. There's a lot of huddling that we could have a North Korean event. I think that the 10 year is stalled because there won't be any repeal there won't be repeal replace and there won't be any change in the tax code. So there's no big spend. Now I think the 10 years wrong. I think you can go up a little bit because I think the government is going to have to find a way to pay for this rebuild. I think it's not only agenda enough because it's still happening but there when you when the fourth largest city is flooded. Remember New Orleans is not that big. Fourth largest city is flooded and it's not a disenfranchised group. Having been down the New Orleans where the people who are really hurt the most were very disenfranchised in this country. Texas is different. Texas has tremendous pull in the country. So the rebuild will be real and the budget will come under pressure because of the rebuild. We talked about the 10 year obviously big implications for the banks. We talked about Warren Buffett earlier. The banks can lead a rally here. If Becky Quick says what do you think of back of America. I don't know what Buffett is going to say about the board of Wells Fargo. Given the fact that they let a lot of this go on. It's questionable. And you guys own City for Action Learners plus remind us. City is the only one that is trading a book value. So the more they buy the higher the earnings. And that's what I love about city. All right. Moving on. United technology is close to a deal to buy Rockwell. Rather amazing here is that let's get this deal done. Greg Hayes has got a deal done. I think United Technology stock has been trading up in anticipation of the end. I think the most salient fact that I've seen and I mentioned this a little bit in my real money piece. But you guilty add is up 10 percent since they bought kite. What does that say about acquisitions. It says game on. There'll be many acquisitions when we come back after labor. The floodgates are opening. But Jim what does this deal potentially mean for Honeywell. I don't know. Rockwell Collins Honeywell. No. No OK. Also Amazon's Alexa and Microsoft's Cortana are teaming up. What did you think. Well I think that what matters is that Best Buy is endorsed Google. And because Best Buy doesn't want to help Amazon. The long lives are out for Amazon wherever I look. Target switching on Amazon Web Services. Now Amazon Web Services is the cheapest. And people don't want to do it. I have Viva systems on last night which is a lot of different verticals for the cloud and the natural place for people to do business in the cloud is Amazon Web Services. Cheapest most efficient. But be aware that because the Amazon's overstepping into the retail business with Whole Foods there are a lot of companies that are pulling back and reassessing working with Amazon Web Services. Yeah. So do you think Walmart is watching this and they're not too happy that they're linking up Microsoft. Well no Walmart isn't happy. They're already telling people don't you really want to do business with us. Don't do business on Amazon Web Services. Totally. All right. Meanwhile Jim on Stop Trading on Squawk on the Street you talked about Universal Display. Yeah. OLED. This Deutsche Bank piece basically says that they've got Samsung they've got the Chinese and perhaps they have Apple. There's a heavily shorted stock.  It just looks like they say well Kramer doesn't know what he's talking about. Deutsche Bank is the people you're arguing with you're not Kramer. You also talked about Kevin Durant some incredibly harsh comments for under armor. You know just people don't wear under armor even insinuates that University of Maryland which is a Plank's home based on wear under armor. This is the kind of interesting war that tells me that the expensive sneaker is going the way of the small screen TV. People don't like it. Any implications for Coles which of course carries under armor. No Coles is doing pretty well. I thought that was good. Under armor being in Coles is her finished line and footlocker. Totally. All right Jim let's also talk about earnings to watch we have Lululemon. Obviously we're hoping it's not like a footlocker. I think Lululemon could have good quarter. I think Lululemon's fashion. The fashion plays have done pretty well. I think that they've managed to make a accelerate fashion which is what you have to do. That's what Ralph Laurence will work on. Everyone's working about how to get the fashion right and if it's wrong just quickly changed. I think Lululemon could be okay. I think Lululemon could be okay. Now what happens with Lululemon is it's often forced down by bears and then people come out and say listen you know let's look through this thing. Maybe it's not as bad. So Lululemon is what I call football stock. It's often influenced by shorts and then the real story comes out. So don't make the first move Lululemon. All right. And the last earnings to watch on my list was Campbell's soup. They're reported. Yeah. I mean Campbell's soup. I know Dougie Cass has got some really things about real money pro about Campbell's soup. The Durant family seems to be reluctant to sell. You know Campbell's is one of those situations like a lot of these companies. If Kraft Heinz doesn't buy them they're overvalued given the fact that my daughter did an extensive price check for me. Whole Foods vs. Kings yesterday. I just said listen I went prices checked out and Whole Foods came in dramatically under. Wow. Yeah. Dramatically under. All right Jim before we let you go forget the stock market tonight it's a big night for fantasy football.  A lot of people feel it's most exciting out of the year. I've got a desk that I will do a selfie and show on Twitter that is really a war room. I am praying that my friend Adam Schefter can weigh in with me. In the meantime I've been watching Adam Schefter's daughter do some unbelievable interviewing of the new England Patriots. She's a star. Adam I hope you listen to that so that maybe you'll help me when we get to the middle rounds because I have done a video with Adam on ESPN which is about the notion I favor drafting quarterbacks higher and defenses higher that is considered to be sacrilege for the people who really know Matthew Murray has also said that same thing these are people you must if you're in fantasy Matthew Murray Adam Schefter don't forget Roto world okay Evan Silva and don't forget John Hansen fantasy guru who is great up-to-date stuff fantasy guru being an amazing publication. All right Jim we're going to follow this journey along with you. I mean look fantasy I know a lot of people who are interested in stocks follow fantasy and the draft is I've used many times to be a kind of a simulated stock draft that you do the same thing let's not forget apple breaking out here it does matter tremendously Nvidia if you listen to the best buy call the switch is the hottest product that's powered by Nvidia that's an action alerts plus dot com name don't forget if you think that apples good then in the launch is good then Broadcom is the company that is the most intellectual property and they're also the one that has a best 5g understand the program has been heavily under assault by both shorts and longs the longs feeling that perhaps the lack of a guide up by hawk tan signals the end of the broadcom run I think hawk tan is smarter than that but no one's better than Jensen Wong who is an Nvidia and don't forget my dog answers to the name and video and Chevron 2 for your other dog that's the other dog I pictured both of them Chevron was very forlorn out because I do feel that West Texas intermediate is going to trade down to 42 Carly Garner new price target maybe even as low as 38 I have up to date information on all of Katrina so let's get here this is as of this morning the Eagleford corpus course it was basically shut down by flooding in excess water crewed has been off the market it does need to be sold or stored unknown how long that situation will be Permian Chris rusty Brazil really help me Permian crewed has continued to flow that is being there's no place to put that stuff which is one of the reasons why WTI is coming down refiners we back online earlier than people think corpus refineries apparently suffered little damage even though there was tremendous rain exports of crude are totally shut off again that's why WTI is going to come down what is receding in Houston so we don't really know the impact of Harvey now I also have up to date information on the insurers as of about eight o'clock the reinsurers are not even coming into play because there was no wins so the all states and travelers that have come down you want to buy them back the federal government is the only hope for for people who have bad flooding because the insurers are simply saying this is not a windstorm we can't help you so that's up to date on the reinsurers up to date on the insurers up to date on the refineries and up to date on the oil and all that is a scoop for those of us who those of you who are watching this video well it's great information and you heard it right here everyone one last thing on the futures the morning futures once again I have to chide these people as being idiots it's okay it's there's nothing wrong with calling to out the people of the idiots and the reason I say that is if you read confessions of a street addict you'll see something idiotic that I did before market so if I'm wanted to say an admit and confessions of a street addict something idiotic I can certainly call these people out of city on this is how we all learn yes exactly Jim Cramer thank you so much as always great information alright for more information on the stocks Jim mentioned please head back to the street.com


From the Amazon Meeting Center in downtown Seattle, it's theCUBE, covering Imagine a Better World, a global education conference sponsored by Amazon Web Services. Hey, welcome back everybody, Jeff Frick here with theCUBE. We're in Seattle, Washington at the AWS Imagine Education Conference. It's the first one. Theresa Carlson just kicked off the keynote about 900 registrants from over 20 countries worldwide. We saw it happen with the public sector before. They went from 50 people to 15,000. I think she said in seven years, I'm imagining that Imagine is going to have the same track. This education is so, so important. We're excited our next guest came all the way from the other side of the pond, the other side of the Atlantic. He's Peter O'Rourke, director of IT for the University of Suffolk. Peter, great to see you. Thanks, Jeff, for the welcome. Yes, it's fantastic to be here with this exciting crowd. And as Theresa said, it would be great to be here in seven years at a huge event. That's a huge event. We'll probably be in Vegas. They like to have those big ones down in Vegas. So what brings you here? It's a long way. Education is clearly super important. Digital transformation in cloud. We see it all over the place. But what's the application that you're looking at? What are you excited about in bringing kind of cloud economics to the University of Suffolk? Well, Jeff, the key thing in education has got to be about student experience. And that's the thing we've got to keep driving at all the time. What's exciting about partners like Amazon is the potential that they talk about. It's not what they're doing today. It's what they're talking about. What they're going to do tomorrow and the day after. And as I've just said, this is day one. This is an exciting journey to engage with these partners. So how have the student experience kind of expectations morphed over time as you get kind of digital native kids coming up into the school now and kind of, you know, we've seen it on the business side, the consumerization of IT because people expect their interactions with their companies, their banks and their retailers to be like it is with their phone and their computer. How are you seeing the expectations change from your students on what they want and how they want to interact with all the services that you guys provide them? Good question. And again, the mobile phone is the key here. People arrive at your organizations, whether they're universities or retail establishments, and they already know how they're going to work with you. And when you can't do that, that's a huge disappointment. So these people are using things in their daily life to arrange trips, theater tickets, cinema. And when you can't work like that, there's a huge disconnect. Right, right. The other big issue that happens that we're seeing more and more is mobile.  There's always lots of construction and new buildings and new labs and new academic offices and classrooms. So space is always an issue. How does mobile specifically, as you mentioned, enable you to provide a different experience, a better experience, a more varied experience when you've got all these other kind of constraints that you're faced with? How mobile can help with that? It's about allowing your users to consume their content where and when they want to. It's exactly how they live their daily lives. So, you know, maybe you can't make a lecture today, but why should that really matter? You should be able to pick this up later. Right. And the last piece of the staff, and, you know, a lot of the teachers weren't necessarily educated in CS. That wasn't kind of why they got into the business, especially if they say they're in history or philosophy or some of maybe the softer sciences. How are you seeing their adoption of technology to be, you know, don't be afraid of it. It's actually a great enabler. It can help you do your job better. How are you seeing their adoption of some of this technology in some of the softer academic areas? Well, again, good question, but it's a huge challenge. I think for too long, what we've tried to do from a technology perspective is to turn absolutely brilliant academic colleagues into technologists, and that's not why they came into education. Right. What's exciting about what's happening now is that we're able to enable them to use much, much simpler technology tools or interfaces that are actually doing amazing things in the background, and they don't need to understand how it does it. And that's the way it should be. Right. So, last question. What are you expecting to get out of this conference for a day and a half here in Seattle? A ton of educators, a ton of people from your industry, first ever event of this type for AWS, what are you hoping to take away? I'm hoping to take away a ton of exciting ideas that are almost impossible to install, but there's going to be one or two gems in there that we can work with people like Amazon going forward, and we're going to come back in a year's time and we want to talk about what we've done. Right. That's the exciting thing. That is the key, right? What have you done? Yes. And now with Cloud, you can do it. I think they talked about a project in the keynote. That was three months of ideation to actually start into ship stuff. So, you can do it. That's what we've got to do. Right. All right, Peter. Well, thanks for taking a few minutes of your day and good luck with the rest of the conference. Thanks, Jeff. Thanks for talking to me. Peter, I'm Jeff. You're watching theCUBE. We're at AWS Imagine Education in Seattle, Washington. Thanks for watching.


I'm Danielle Lohman and I'm a fourth year graduate student, I'm studying biochemistry and I work in Dave Paglarini's lab and my research is funded by both the National Science Foundation and by National Institutes of Health Biotechnology Training Program which is a training program that lets you interact with the multidisciplinary team of scientists and lets you do an internship. So there were really probably two reasons that I chose to come to Wisconsin and to be part of the biotechnology training program. I think the first is diversity of thought, so the biotechnology training program has scientists from all over. I mean we have biochemistry people, we have medical physics, we have biomedical engineering you name it and in all of those different fields we each kind of think about problems in a different way. So we choose different problems to work on and then we have different ways to solve those problems, ways to test them and the ones we actually have a solution we apply it in different ways. So I liked having that diversity and being able to learn from all my other, all the other BTP fellows. The second reason why I chose to be part of the BTP program is probably the fact that it offers an internship opportunity. So I love doing research in the academic lab but I think sometimes it's hard to get out of the university when you're academic and even harder for a scientist to get outside of the laboratory because I kind of saw that internship is a way to get my foot into the door of something else. So I chose to do an internship at a startup company, at a non-profit organization, they're based in Washington DC and they're called health security partners and the mission of the company is really to help solve global health security challenges. So these could be things like preventing the spread of infectious disease like Ebola, this could be slowing down antimicrobial resistance, it could be preventing bioterrorism. So really there's a lot of challenges that we face in our lifetimes and a lot of them have a lot to do with science, steeped in science and we need scientific solutions. So the Paglarini lab is really at the beginnings of discovery so we do basic science research so we're at the level where we're really just trying to understand how biology works and specifically we're interested in the mitochondria, the powerhouse of the cell and one of the, it's hard to choose which protein you're going to study so one of the ways that our laboratory chooses is we choose proteins that are connected to human disease because a lot of these proteins we know have ties to human disease and it'd be nice to know what they're doing then these patients may have a chance of having treatments that work. One of the biggest benefits of the internship experience that I've brought back with me into the laboratory is thinking about science beyond just the experiment that I'm setting up that day or tomorrow or next week and to think about how the research that I'm doing might impact the world and outside of the laboratory and then thinking even more more broad than that how science in general can impact the world.


Ahem. I have an important announcement to make regarding the future of the Ground Line Review. So due to ongoing global concerns, the subscribe jokes that I make at the beginning of all of my videos will be going on hiatus until I determine that it is safe to start using them again. And I determine that that time is now. So take an awfully good look at this very awkward shot of Usopp and subscribe to the Ground Line Review for regular One Piece content uploaded straight into your YouTube feed. Hello and welcome to the Ground Line Review, your source for everything One Piece and I say I come bearing some very unfortunate news for those of you who have not already heard, which is that due to the current goings on in the world, which I'm still paranoid about mentioning on YouTube, the broadcast of the One Piece anime is being suspended and Toei has conveyed this on social media with the following message. To all our fans, due to the state of emergency in Japan caused by the pandemic, we have carefully considered the safety measures for the spread and have decided to suspend the simulcast and Japanese broadcasting for both One Piece and our new series Digimon Adventure for the time being. Once on the return of both series will be provided as soon as we know. Thank you for your patience and understanding during this time. Please stay safe and healthy. And I think we can all concur with that last statement of course, but this is pretty devastating news for One Piece fans. And I know that this sentiment is maybe a bit ironic coming from me as someone who has been traditionally quite critical of the anime, especially with one of my more recent videos which had the sole task of detailing why Manga readers tend to dislike it. However, at both the beginning and the end of that video, I did go on to state that the most important thing was that you were a One Piece fan, no matter how you choose to consume this wonderful series. So as such, this is horrible news for anime watchers. However, I think we all completely understand the need for this sort of hiatus to occur. And of course, as of right now, we have not been given any indication of even a vague return date for One Piece, which is a pretty big scary question mark to have hanging over the series because who knows, things might get under control and we might have it back in full swing in say a month or it may take significantly longer than that because no one knows. Now, of course, this obviously does not just affect One Piece. That's just where this channel is designed to focus on. But the announcement from Toei also mentioned Digimon, but also Toei is not the only studio under these conditions. As other anime series that have been affected by this include Pokemon Sword and Shield, as well as the second season of Re Zero, which I was very much looking forward to because I am in glutton for punishment in that brutal, brutal world. And also the world of cinematic releases have been hit pretty hard as well with the third Fate, Stay Night, Heaven's Feel film and the Violet Everguard movie being delayed amongst a slew of others. And obviously that's probably less of a production concern, but more an issue with people not necessarily being able to go out to a cinema to see a film. And also if anybody is interested in Samo Dubs for whatever reason that may be, Funimation is also delaying those, which will affect series like My Hero Academia, Black Clover and Darwin's Game. The latter of which I recently started watching actually. Not the dub though, definitely the sub. But yeah, One Piece is far from the only affected property, although it is the only series that this channel is particularly concerned with. And also just for Manga Readers, be aware that our situation is also not looking too great as there was a confirmed case in Shueisha's office, which has resulted in the weekly shown in Jump Publishing schedule being put on a temporary two week cycle. So we have one chapter, then a break, then another chapter, then a break. Although one of those breaks is for Golden Week, so we would have had that anyway. And I guess I think when it comes to the manga, there is a bit more optimism to be had just simply in regards to the nature of its production. Manga is drawn by artists and small isolated officers with a couple of assistants for major titles like One Piece, so it's much easier to enact social distancing. And that's probably much less true for the main Shueisha office which would function like any other. But oddly enough, the manga industry seems almost designed to weather a pandemic because when it comes to artists, social distancing is effectively their lifestyle. And that is not true when it comes to the anime production, however, because they obviously work with much larger teams in very communal areas and so the risk factor is much, much higher, which sucks. It really does. And I feel for the anime fans at this time. But the most important thing is that the staff of Toei and in fact all of Japan stay safe as well as the rest of the world. Now to address some other less than fantastic things, I have seen some comments on social media which look rather unfortunately to be from manga fans and very sorry. But a select few are celebrating this hiatus and I just want to take a brief moment to say, please don't do that. It is very, very unhelpful and it serves no real purpose. The anime going on hiatus does not help anybody in any way. Obviously it doesn't help anime fans who are now deprived of their weekly injection of the One Piece drug, but it also doesn't help people like me who want the anime to be better because this won't actually change anything. It's not as if this time will allow Toei to restructure their business model and make episodes with less filler or better animation. This is nothing like that. Instead it would just appear to be something of a freeze on current operations. So with that in mind, celebrating this sort of thing is just an exercise and sharding for it I guess. Very pointless and it's bad for manga fans as well because it is absolutely undeniable that the anime provides a consistent flood of new manga fans because it acts as an easy gateway into One Piece. So make no mistake, the anime coming to a sudden halt does hurt this community at large. Now for those of you anime fans who are a bit devastated at this sudden lack of One Piece to consume, I would be remiss at my job if I did not mention the possibility of, you know, giving the manga a go. And I will show you exactly how you can do just that. But here's the thing, I do understand the arguments that anime only fans make.  And also some of you have mentioned that having a clear image with colors and a single shot focus is also very helpful in your personal experience of One Piece. I do fully accept and understand that. However, under all of the conditions that this world is currently facing, I really don't think there has ever been a better time to give the manga a go. Now, if you do want to pick up exactly where the anime is left off for now, which was episode 929, then you will want to start with chapter 934. The anime episode does adapt most of this chapter just over two thirds of it, I'd say. But if you go through the whole thing, then you will be caught up and you can just proceed with the glory of Wano. Now exactly how do we do this if we so desire? Well, the entire series thus far is available at viz.com with a monthly subscription of $2. That is it, two American dothere dos and it will give you not only close to a thousand chapters of One Piece, but also access to a ton of other series which you can see here, stuff like One Punch Man, Dragon Ball Super, Black Clover, My Hero Academia, Demon Slayer, The Promised Neverland, Dr. Stone, and a metric ass ton of other stuff. And no, I am not sponsored by Viz, I wish I was, please give me money, Viz. But what I am trying to convey is that $2 a month can go an awfully long way towards entertainment in this world at this time. But if you do elect to go down this route, I have a very important note here because the Viz website layout kind of really annoys me because if you say go into the search bar and type in One Piece, then it'll just take you to a page where it prompts you to buy copies of the volumes which we certainly do not currently want as the website gives us all of these chapters anyway. So what you actually need to do is click on the show and jump tab and then find One Piece in that list and it will take you to a complete collection of all the chapters of which there are many. Oh, just look at them all. And then you just read away to victory and let me know how your experience was in the comments below. And really, Anime Peeps, Wano has a lot to offer you in the manga because there is some stuff that has yet to come in the anime which is absolutely mammoth and well worth reading to discover. But just while we're talking about current events, there was some other bizarre news announced recently that the One Piece anime will be coming to Netflix in the United States, Canada, Australia and New Zealand, which is a very intriguing idea actually. And I have no doubt that this is being done to kind of synergize with the One Piece live action series which is in active development. I imagine that the basic idea is to build up a base of One Piece fans on Netflix. And then when the live action series comes out, there will be more people willing to bite given how they've already had an assumedly positive One Piece experience on the Netflix platform. Two huge caveats at this stage though. The first of which is that according to Netflix, at the moment, this will only be the first to quote unquote, arcs of the series by which they actually mean to say sagas. So they will have all of East Blue and Alabasta which does sound ancient, but it's actually quite a fair chunk of the series actually, like a whole 130 episodes, which is a lot of content, but it continues to synergize nicely with the idea of the live action series because that is unlikely to get past East Blue in its first season. And if it does, then something has gone very, very wrong. But this is pretty good news for these particular English speaking countries because it is reintroducing One Piece into something of a mainstream vessel, I guess. As much as it might be completely redundant for all of us fans, it will undoubtedly introduce new people into the series and continue to build a nice legion of global One Piece fans. But the second caveat is that this is only happening on June 2nd, I believe. So if you had any hope of introducing some of your more normie friends or family into One Piece at the moment, then there is still quite a while to wait before that may be possible. But this is still generally good news, and I think we really do need at least a bit of that at the moment. But yeah, sadly, that's about it. One Piece anime is on hiatus for an unknown amount of time and the manga is in a kind of precarious position as well. With all of this said though, this is not necessarily reason for despair and it might actually present a fantastic opportunity to reread or rewatch the series because One Piece has such an incredible amount to offer beyond its initial experience. In fact, that's the entire reason why I have this channel exclusively for One Piece because there is so much to dissect and reflect upon beyond just discussing new chapters, episodes and future theories. So if you've never done a big reread or rewatch, then I highly recommend it because there is a lot that you've either probably missed or forgotten about. And not only that, but experiencing the series in retrospect is very different because you also pick up on a lot of cool foreshadowing and you can just see how much things have really evolved in One Piece over time. So I can't recommend that idea enough if you are caught up with the anime and or the manga. And not only that, I also don't think there's ever been a better time to try and get people into One Piece in general. Given that at least the anime is frozen in place at the moment and the manga is moving slower than usual, this is a pretty grand opportunity for people to become invested in One Piece without feeling a bit too overwhelmed, maybe. It's still an overwhelming thing to take on. But at the same time, there's also no excuse for not having the time to read or watch the series now because an awful lot of people out there have unparalleled time on their hands that they will probably never see again once this period comes to a close. So if you do have friends or family that you want to get into the series, then now is probably when you should be doing it. And maybe you could even make it a bit more fun for them by watching or reading along with them somehow. Like hosting a long distance watch party, maybe have like a regular One Piece evening or something along those lines. And with the manga, you could do something similar like a weekly catch up where you just talk about the volumes you've read. And yes, I know it does sound like a wanky book club but just do something because it's always much easier for someone to plunge into One Piece when they have that bit of social backup. But yeah, that is about it. Dark times, but dark times filled with lots of potential. And however, where you go about your life, I just hope that One Piece continues to be a very strong part of it. But what do you guys think? Please do leave your thoughts in the comments below or even join my Discord server. And if you'd like to see more videos like this then please do go and check out some of my other content or even subscribe to the channel for more glorious One Piece business uploaded straight into your YouTube feed. But for now, this has been the Grand Line Review and I'll see you next time.


If cat agrees not to make fun of me or say any mean shit, I will equip it. Frank, I wanted that. Hi, Asmonds. He's talking to all of them, all of the Asmonds. Who the D? Asmond. Is that like your version of Estefond? Like people call me Estefond sometimes. Yes, yes, Asmonds. They just throw a T in there, they throw a D in there. Are we done yet?  Somehow we're done. Is that faux? Okay, now let's go turn it back in. Okay, so we need to turn this in at the camp right here. And then we can hear it. Right? Then we can hear it, right? No. Because so after this, we have the quest for killing James Cork.  I don't have that quest. I know that. Oh, I have to turn it. Sorry, my bad. Red, blue, and bandana. We did skip this the last couple of times. Oh, nice. Let's try one. I have been in case of three, three, three hours in there is still 13,918 people in front of me. What do I do? Yeah, that's a lot. I'm so bored. I can't leave the computer BC and ready to grind. Well, you know what you could do? You watch the stream. I mean, at least you have a BFA subscription, so you can go in there and just laugh. I'm just kidding. I don't know. I mean, look, there's nothing to do, right? Like, realistically, just being real, like, how are you going to have your mind on anything else other than, other than, wow, I want to be trying to log in. So, look, might just deal with it. Might as well just deal with it. Check out streams, whatever. Let me start getting your life in order. Get caught up ahead on stuff. Or you know what? Maybe take a nap. Maybe put the stream on in the background. Take a nap. And you wake up right after. That way, you don't lose valuable lifetime. Good day to you. I always forget to do this. I always walk out of here and forget to do it twice. And we're ready to go, Hogger. Yep, that's right. Let's go, Hoggers. Esfan, I love you. Preg me, please. What? What? Excuse me? How many armbands do you guys have? I only have two. I only have three. This is just a great game. Yeah, this is a really big one. This is a really bad drop rate in the West. I need a lot of help. Hey, McConnell, what's your ping? I need a lot of help. Stop, stop, stop.  OK, we're healing you. We're healing you. Esfan's the number one red paladin. Yeah, that is true. Uh, Azman? No, stay there. We can heal. Don't run. Stay there. How many, how many armbands do you guys have? I have five. OK, I still have zero. Guys, I don't have a target. I need a target. I don't have a target. I need a target. I don't have a target. I need a target. I'm done. All right, Beast. You better not. You better not, McConnell. Come back. We need the group XP. Are you going to, like, wait to turn it in with us and you get more XP, McConnell? Esfan, if you don't want to level with me, that's fine. Well, why, like, why, why are you doing this? Like, I don't understand. Like, why do you immediately go on to the next person? I'm trying to, I'm trying to hit 60, bro. Yeah. 30. Yeah, you're going, listen, you're going to get more XP when you stay here and we all go turn it in together. Like, what is so hard to understand about that? I've said it like 10 times. Here, big pull. Use the tag on that. See, he, like, gets all his stuff and then he goes AFK and then, like, it doesn't work. I'm waiting, dude. But, like, you need to help.  Like, you know what? Number one, I'm tired of being called a leech. Number two, nobody called you a leech. I'm tired of being held back by my group members and I kind of just want to go solo.  Yeah, like, we probably shouldn't have done this from the beginning when we saw so many people were here on a kill quest.  But, I mean, we were still so behind on XP that it didn't really matter. But at this point, like, we're all going to be level 10. I still only have one. Like, how many do you have? I have five, seven. I just need one more. Okay. There's always another leech by the logging camp. No one is ever there, but they drop the armians. Oh, you're right. These ones. I totally forgot. Hey, you know what? You're done. Yeah, I'm done. There's a second spot for these that I've totally forgotten about. And we need to go back that way anyway. Follow me. Okay, everybody, Pepe, please. If you don't, Pepe, please, you're banned from the internet. Everybody needs to tab back in. Tab back in from the game, everybody. If you don't, Pepe, please, it's a ban. Everybody's banned from using the internet for the rest of their lives. Yeah, that's right. Okay. Okay, good. Enough Pepe, please. You guys can play the game again. You're allowed to play it again. Very good. Yeah, so nobody comes to the nulls up here. I always forget about them, too. Yeah, this is way better. Look at this. This is good grinding, too. Okay, cool. I'm good. So now we can go down. Here's what we can do.  Let's all drown. You guys want to drown together?  I think drowning feels better, though, you know? It's like we're all doing it together. Yeah. Yeah, come on. Come over to us. That's one. Well, that's a swim, because like your muscles use more oxygen, right? So I think your breath goes down faster. I'm pretty sure that's for plants, not people. Oh, right. Because photon synthesis. That's right.  Or we can't? I mean, there's a lot of people here. I don't think it's an effective use of our time because of these. So what's all the coast here? Oh, really? You think there's more up there? Oh, yeah.  Honestly, we should keep farming this. Yeah, I was just saying that in my chat. This is really, really, really good. Oh, the Murloc thing about this Murloc. Oh, my God. Yeah. That's true. That's really good. That sounds really good. Okay, I got my eight. Okay, I'll start. I think we farm this until 11. Do you agree with it? Yeah, I'm fine with that. Okay, yeah. Great idea. Let's go. Hey, where'd McConnell go? I'm healing.  He just left the group. Hey, I'm going to go hop into my guild discord real quick and check on people. Hey, what's up, guys? I'm on stream still. How are you guys doing? Are you guys like getting through it pretty easy? Just finished down one. We're killing it. Just got so many guys teaching. Okay, nice. I think we're probably going to stay in L1 until 12, probably, and then we're going to move to always dark shore. Yeah, I mean, hopefully, hopefully I hit 60 before I have to go home.  Wait, what happened? Disconnect. Hey, disconnect. And somehow I went from 2K in Q to in the character screen. Everybody log in. Oh, no. Everybody log in. I just realized what happened.  Oh, dude. Oh, brutal.  I just skipped the line. Dude. 18,000. Me too.  Yeah, I'm at 17K. Oh, dude, so am I. I'm calling conspiracy. Blizzard kicked everyone out in the server, so people have been waiting. I think they did. I bet they did. Hey, Omar? Omar. My man. What's up, dude?  Yeah, you and Brian both.  That is literally five hours. I think, you know, if you guys could maybe just give me a little bump, maybe like a 16,000 person bump, you know. Maybe you could pay me back that way, but if not, then hey. It's definitely, that's exactly how long we've been here. Maybe next time you want to come on, then it'll be a little bit different discussion. So, okay. Thanks. You said I'll think about it. Yeah, you said I'll think about it. So, yeah, we'll see how it goes. I think people are going to log off pretty soon because it's going to get late, Asman. Yeah, any day now. Like in now. Okay, maybe not. I think that honestly, I'm just going to go and weigh down. You want to do the sleep strat? We're going to do the sleep strat. I just texted my G-knock guy and he said it wasn't you. He said it's not you, it's me. I've heard that before. Frick, I'm on front page right now.   Hey guys, welcome to the front page. Where, uh... Yeah, well, that's how it goes. Yeah, guys, we just got disconnected. We just got disconnected. Yeah. Look at that. Nice and tasty. Okay, I'm at the Method Classic launch event. And we're here with a lot of people. They're playing games. Of course, everybody's here. They got a big game. They got a big game. We're here. They got a big thing going on. Big computers. Most people are in queue. And we're having a great time. Because, why? Because we're playing Classic WoW. And what do we do in Classic WoW? We stay at the login screen. That is exactly what we do. So, we're going to keep staying at the login screen. And we are going to have a login screen marathon. At the finale of the marathon, we are going to play the game. So, hopefully we get to that point. I don't know. We are going to try to make this marathon last as long as possible. What does that mean? That means that we probably are not going to get to play for a little bit. But, if we're lucky, then maybe we will. So, here's what I'm going to do. I'm going to get a sleeping bag.


So, since many of you asked me about references, I wrote something here. As a matter of fact, you don't need any of this for the exam. So, as I will give you some notes, but okay. Here in case you find something on the cover of the first lecture, so density measures and whatever in these two books, for example, that I partially followed, so Sakurai or Messia. And about the chain of harmonic oscillators or identical particle, bosons or fermions. Well, you can find some discussion in Messia, for example. General discussion on this formalism of second quantization, I think, is in this chapter as well. But you don't find the details of the calculation here. You don't hope to find something. That is not. And about the remaining lectures, there are some notes. Maybe I could give you some other references, maybe to some reviews. But so far, I prefer to do it later. Okay, so, yes? No, well, just, okay, h just depends on two variables. And I just brought it in this way because I would like to stress the similarities of the Hamiltonian. Then we will call it h without joining. No, because it's equal to... So the dog of this operator is equal to itself. So, otherwise, yes? So, indeed, okay, we were talking about the quantumism model. So this is the Hamiltonian of the model. And yesterday, I told you that... So we consider the case h larger than zero, no? And j larger than zero. Now, actually, I would like to point out that this is completely general. So this restriction is just a matter of convention. Indeed, you can always... You can find the unitary transformation that changes the sign of j and h. So we can just fix the sign. We show interest in the spectrum and study this particular region. Okay? And in particular, okay, you see, well, we saw this yesterday that the Hamiltonian commutes with this operator, which is the spin flip operator. Okay? And the symmetry in it is broken when h is sufficiently small. You have seen. But there are also other symmetries. So if you can see, instead of spin flip in this direction, you can see a spin flip with a x. Then you see that you can change the sign of the magnetic field in this way. And there is also another transformation, which consists of... Consider the product of a sigma x, sigma y, sigma y, and so on. And this changes the sign of j. Okay? So... So this means that we can focus on... Just on this particular case. Yeah. No. It's x, y, x, y, x, y, alternating executable. Okay. So yesterday, we introduced the Jordan v, no. Transformation. c dot l equal product of j smaller than n, sigma j z sigma l plus... So we have c l, j is smaller than l, sigma j z, sigma l minus. We also introduced other operators, pyonaphermias, the finest a to l minus 1, which is equal to c dot l plus c l. And this a to l, which is equal to i, c l minus c dot l. This operator satisfies the anti-commutative... anti-commutation relations. c dot l c n is equal to delta l n. c dot l c dot n is equal to c l c n, which is equal to zero. Then we are here instead of the anti-commutative a j and a k is equal to twice delta j k. And this is the Jordan-Binger transformation, and these are generally called Jordan-Binger fermions. If you use this transformation, we will discuss also the inverse. What happens to the Hamiltonian? I wrote the result of the mapping, but just consider one term just to see how it works, because yesterday we didn't do it, but maybe we should have. So let's assume that we consider the term sigma z of the Hamiltonian. It's the trivial, the simple one. So sigma z, you have seen that it is simply given by i times a to l a to l minus 1. You have seen that, no? If you write a in terms of the power matrices, then this corresponds to this as a sigma x, and this as a sigma y. And so if you use the sigma that i, sigma y, sigma x is equal to sigma z, then you realize that you find this expression. Let's write that in the inverse transformation. The transformation is a sigma, so a in terms of the power matrices, a to l minus 1 is called j is more than l, sigma j z times sigma l a to l is equal to j is more than sigma j z, sigma l y. So if you multiply the two, you have just an expression of sigma x and sigma y. So this is for sigma z, so we already know a part of the Hamiltonian. What about this other part? Now, if we consider sigma l x sigma l plus 1 x, we want to write in terms of the disperseance. So we have the same x, we have a string of sigma z up to l minus 1.  And this is the first operator, sigma x.  This sigma z is written in terms of the of the Majorana fermions in 12 and 12 minus 1. So this means that this, okay, now you can see. Okay, this clearly commutes with this operator, this product. The reason is that we have the sigma z up to l minus 1, but this is written in terms of operator is an n, l and l plus 1. So they commute. So you can put this string on the right and then you find that it's equal to a to l minus 1. Then when you consider the product of this times this, only one sigma z remain. So this is a sigma, sigma lz. Then you have this a to l minus 1 minus, okay, let's write one. What is this? This is 12, 12 plus 1. Now we rewrite the sigma z in terms of the Majorana fermions here. Okay, you don't need this, no? You already wrote this. You need the main lecture notes. Yeah, there was notes in capital letter. Okay, so this is equal to, let's continue here. This equal to a to l minus 1, i a to l, a to l minus 1. Then here you have a to l plus 1. What is this? Ah, 12 minus 1 is important. This is the subscript. And this is an i. We have this expression. Now we know that the Majorana fermions anticommute at different sides. So we have minus sign, let's put the i here.  But what is this? This is equal to 1 because of the anticommutation relation. So when you square the Majorana fermions, you find 1. So this is equal to minus i, a to l, a to l plus 1. Is it no or yes? Yes. Okay, yes. But there is a subtlety, you know? Because when you consider here the sum, you have also a case when you have l equal capital N. So what happens when l equal capital N? We impose periodic boundary condition. So this means that the sigma capital N plus 1 is equivalent to sigma 1. But we have to treat these cases separately from this. Because we have to see where this operator is mapped. This is sigma n, sigma n plus 1. So we know that for this simple operator for l smaller than capital N, we find this expression. We find that expression minus i, a to l, a to l plus 1. Now the question is what happens when you consider the term sigma nx, sigma 1x, which is part of the amethyst. Let's do the same. So sigma capital N, capital Nx is equal to the product of the string, the string of sigma z up to N minus 1. Sigma, this is a j. Sigma z. And you have a to n minus 1. And you have sigma 1, which is simply given by a1. So this is what we have. Now here we define an operator by z. Is it happening? So now we define this operator by z. So let's use this operator. This is a product up to N minus 1. So if we multiply on the left by that operator once, we find that this is equal to pi z times sigma capital N z times e, a to n minus 1, a1. Because when you can say pi z times sigma z, you remove one sigma z, the last one. So you find exactly this expression. So you have this expression. Now let's write sigma z in terms of the Majorna fermions. So this is equal to pi z. And then we have i, a to n, a to n minus 1. Then you have a to n minus 1, a1. a to n minus 1 times a to n minus 1 is equal to 1 as before because of the algebra. And so we end up with i by z, a to n, a1. So what's the difference between this term and this term? It's in this part, no? This pi z. Now pi z is commutes with the Hamiltonian. So what does it mean when you find an operator that commutes with the Hamiltonian? It depends. Yes, and it means that you can find the basis of the Hamiltonian, which consists of eigenstates of the operator, pi z. And on this basis, this operator acts like a number, and the number is just the eigenvalue. The eigenvalues of pi z are either 1 or minus 1 because it is a product of sigma z matrices. So this means that depending on which eigenstates we are considering, here we can never sign plus 1 or sign minus 1. And this is exactly why when we wrote the Hamiltonian yesterday, we had these two signs, plus 1 or minus 1, which depends, indeed, on the eigenvalue of this operator. You need to check the expression I wrote yesterday. I wrote something like that, 1 plus pi z over 2 times something plus 1 minus pi z over 2 times something. What's the meaning of this? This is a projector on the eigenstates with eigenvalue equal to 1 for this operator. Indeed, when you calculate this operator by minus 1, you find 0. So this term doesn't contribute. And the same for the other term, with minus 1. So I said, OK, if pi z is equal to 1, then the Hamiltonian is equivalent to this one. If it's z pi z is equal to 1, 2 minus 1, then the equivalency with the other Hamiltonian. So let's try it again. So we start from the Hamiltonian in this model. Then we are looking for the eigenstates of this Hamiltonian. We know that we can this operator communicate with the Hamiltonian. So we choose a quantum number, which is the eigenvalue of this operator. So we define something like this. So we write the eigenstates in this form, where you have this quantum number associated with pi z. And then there can be other quantum numbers that we don't know. And when you apply pi z to this eigenstates, you find plus minus the same. And now, depending on which eigenstates you consider, what you find is that this h applied to plus minus the equivalent is equal to h plus minus. Well, these are the matrices that we wrote yesterday, which are given by h plus minus is equal to the sum. No, no, this is not graphic h, but now are you ready? So this is 1 over 4, sum over l and n up to n and l, calligraphic l, n, a, n. So this is the meaning of the expression that I gave you yesterday. I wrote the Hamiltonian this way. So this means that I can find a basis of eigenstates in which I can choose a quantum number, the eigenvalue of pi z. So this operator has eigenvalues plus or minus 1. So the states have these properties. And now, depending on the sector where I'm working, so depending on the second value, this Hamiltonian is equivalent. It acts identically like this with a plus sign or minus sign. Just explain what the expression of this is. It's OK. And OK, I define this matrix yesterday. And now you can actually write everything because we computed all the elements, all the blocks, all the elementary constituent of this Hamiltonian. So you can reconstruct the matrix. This matrix is h plus minus if you want. And you realize that they have the form that I gave you yesterday. OK, fine. So now that we hopefully understand the Hamiltonian, what I wrote yesterday. So this is, you have this. And I remember it. So we don't need it. We don't need this. We don't need this. Now we don't need this. So let's see that it's not important. That's all right. H. OK, now this is a graduation. H is equal to 1 plus pi z over 2 h plus 1 minus pi z over 2 h minus. Where h plus minus equal sum over ln from 1 to 2 capital N of Al. That is 1 over 4 h ln. So this is the application of ln of ln plus minus. OK, the matrix. Now you have the matrix. And I suggest you to rewrite it in a different way, which is this. You can write h plus minus. Now you express the indices in this form. 12 minus 1 plus j to N minus 1 plus j prime. It's equal to 1 over capital N sum over sum a set of numbers. That we will see in a moment. OK. Plus minus e to the i L minus N k plus minus. And then write this. This is a 2 by 2 matrix. K plus minus j, j prime. And then you have that j, j prime goes from 0 to 1. It can be either 0 or 1. And then you have L that can be equal to 1 and 2. And then which is equal to from 0 to N minus 1. OK. Now this seems to be a bit strange what I'm writing here. But I want to exploit the symmetry of the matrix of yesterday. OK. And you remember that it was a periodic, there was a symmetry of periodicity, there was a symmetry in variance if you want, on the row of the matrix. Or anti, it was either block-circulant or anti-circulant, block-anti-circulant matrix. Yeah, I just called h. OK. Let's use a different, different, because otherwise you can come and let's use some. OK. What is e? I forgot to write it. Humi is equal to, OK, is equal to, now, let's write just the matrix, 0, i h minus i e to the i minus i k. Minus i, OK, there's a title here. Minus i h plus e i e to the i k. So I would like to express the matrix of yesterday in this form. Why I can do that? OK. First of all, in the case of block-circulant matrix, then you can imagine, because of the symmetry, this kind of transition in variance, that you can express it in a simple way in the Fourier transform. So what is the condition to have this kind of symmetry of a circular matrix? The condition is that when you sum capital N to an index of the matrix, you obtain the same element. It should be invariant under this transformation. So in the case of k plus, so in the case plus, you should have that when you consider this expression and you shift one index by capital N, then you should find the same expression. There should be an invariance of this form. From L, L that goes to L plus capital N. Now, if you do this kind of transformation here, you find that this becomes equal to this space, becomes equal to e to the i capital N k plus times the same. So in order to satisfy this condition, so in order to be periodic, then you need to, that this expression should be equal to 1 e to the i n k plus. So this means that we have that the condition becomes this equal to 1, in one case. And in the other case, you have now the condition that when you sum capital N to the index, instead of having a plus sign, you must have minus the same expression, because it was anti-block-circular matrix. So the other condition becomes e to the i n k minus. This should be equal now to minus 1. So this means that you can always rewrite the matrix in this form if you choose this particular coefficient k, satisfying this condition. In practice, what does it mean? How can you satisfy this condition? e to the i n k plus equal to 1. This is satisfied by k plus equal to pi j over capital N, where j goes, for example, from 0 to capital N minus 1. If you substitute, if you plug this into this and you realize that you find all the possible solutions, these are the square root of k. I wrote the matrix yesterday, and you can compute it. And this matrix has the property that when you move along the, for example, along the first row, you have all different elements. But then when you go back to the second row, again you find that there is this kind of circular structure, like this periodic. So the idea is to solve this kind of problem like you would do for periodic function. So you go in free transform, in a free series. Now, if you have the circular structure, it corresponds to periodic function, so you know that the solution actually are e to the i to pi j over capital N, which is what we are obtaining here. And the condition is that the phase associated with the number of sides should be equal to 1. But then we have also another case when the matrix is unperiodic. So it takes a minus sign. So instead of this condition, which is the standard one, we have to impose the other condition. e to the i times minus equal minus 1. Which are the solutions of this? You have simply to shift. Instead of considering integers, now you have to consider half integers. Why is this a case? Because when you multiply by N, you find 2 pi j, which is irrelevant, because it's in a phase, and then you have 2 pi times 1 half, which is equal pi, and e to the i pi is equal to minus 1, which is our condition. So in other words, both matrices that we obtained yesterday can be written in the same, exactly in the same form. And the only difference is in these numbers, that they are quantized in different ways. So different quantization conditions. So what they are seeing is that if we restrict it to the sector when pi z is equal to 1, we will see that these are called the momenta, are quantized according to this case. If instead we consider a sector where pi z is equal to minus 1, the momenta are quantized in this way. So we are splitting the i and functions in two different sectors, and depending on which we consider, we have to apply one or the other. This is the complication of the easy model, with respect to, for example, the harmonic chain, because now we have, instead of just one sector, we have two sectors to consider, they are different. Okay, so in the end, I just give you a picture of this. Let's assume that we plot the eigenvalue of the, in some case, for example, h larger than 1, and let's plot the eigenvalue of the matrix, say h, this spectrum of the Hamiltonian. The spectrum of the Hamiltonian will be something like this, so if you have a random state, then you will have other states. Now, because we know that, depending on the eigenvalue of pi z, we can be in one or the other sector. So this means that in one case, the second values will be the same of the eigenvalues of the Hamiltonian, h plus, but it can be also the eigenvalues of the other Hamiltonian, h minus. So you will have a subset, a subset of the eigenvectors, and it will be the same as for the Hamiltonian, h plus, and the other nearest will be the same for the Hamiltonian, h minus. So this is Hamiltonian, h minus, for example. No, as a matter of fact, this is h plus, and this is h minus, and this is the energies of h. This is the meaning of the equivalence. Is it clear? Okay, sorry. You can have this, because I draw some particular... I choose the color in a particular way, but it's just a matter of that. It can be any value of h, and you can always select... For each eigenstate, you can determine whether it comes from one sector or the other. The important thing here is that there are two possible sectors, and you can identify which one it is. And in each sector, the Hamiltonian can be written in the simple form that we wrote here, just the quadratic form of fermions, like in the harmonic chain. Okay, so... You understand this? I can erase something. Like in the harmonic oscillator, we like to solve the problem. Commutator to h, and h plus minus, say, and a linear combination of the Majorana fermions, and some linear combination, which we had called b-dag k, is equal to epsilon k, b-dag k. So we want to... Because the h plus minus are quadratic, and I said it's by simple combination relations, we can expect that if we compute the commutator with this quadratic operator and something which is linear in the Majorana fermion, we will find something which is linear, like in the harmonic oscillator in the Majorana fermions. So the idea is to choose just an ansatz for b-dag k, so I only know that there will be a linear combination of all the fermions. Let's call this b a l a n. And then I try to find a solution or some solution to this equation. Why? Because let's assume that I, as before that I found the solution for this equation, that this means that given an eigenstate of the Hamiltonian, again, we know that when I... when I apply b-dag k to this eigenstate, so let's assume that you have... OK, let's put this plus minus here and somewhere plus minus... h plus minus, so the quadratic Hamiltonian. So if we are able to find this operator, then we know that when we apply h, if h plus applied to psi e is equal to e psi e, so it's an eigenstate, then we know that when we apply h plus to b-dag k psi e, what we find using the computational... this computational action, that this is equal to e plus epsilon k of psi of b-dag k psi e. So like in the harmonic oscillator, what we added is that for each eigenstate of the Hamiltonian, we can construct another eigenstate by applying this operator and it will have this kind of disenergy. OK? And so this means that also we can define the ground state of this Hamiltonian h plus as the vacuum of the operator bk, the adjoint of bk, because we also know that if this holds, it also means that h plus minus... this depends on plus minus, so I should choose different... I can do that. minus epsilon k bk. So the ground state is defined as the state such that the bk applied to psi ground state will be equal to zero, exactly as in the harmonic chain. So, well, we have a different... OK, this holds for h plus and h minus. Now you could say, we are interested in the Hamiltonian of Bayesian model. So we have actually to see which are the eigenstates of h plus minus which are also eigenstates of h, because there are these two sectors. So depending on the eigenvalue of pi z, we can be in one or in the other sector. OK? So what I mean, let's assume... let's assume for a moment that the ground state of the Easing Hamiltonian, let's call this C is in ground state. Let's consider the state and let's assume that this state is a negative state of h minus. OK? Because we have the possibility either it's h minus or h plus. We don't know now, but let's assume that it's h minus. Yes. Well, OK, yes, there are... If you want to keep in mind that here there is a dependence on plus or minus, this is not needed as a matter of fact because as we saw here, they have different quantization condition. So the k are different for the two. This is why I can actually write in this way for both cases. Only the k's are different. So if you want, you can also put this label plus minus, but it's not really... just keep in mind that you will find different... So... Yeah. This is what will happen, yes. So let's assume that this psi ground state in the notation of before is just given by minus. And then we have some other quantum numbers. So this means that when you apply h minus to psi ground state, we find e ground state psi as ground state. So far we are not. Just assume that we are in this situation. If you're... You could also consider the other k's. No problem. So let's assume that we are in this situation. So the ground state is in this sector. Now let's consider the first excited state of this Hamiltonian. So the first excited state, we know that the first excited state of h minus is just b dagger. You have to apply b to the Hamiltonian, to the state. So we could guess that the excited state would be something b dagger of k applied to psi as in ground state. This is a negative state of h minus. We know that when we apply h minus to this, we find e ground state plus epsilon k psi that is b dagger k psi ground state. This we know for sure. The problem is that, okay, is this an excited state of h or not? This is the question. And in order to see whether it's an excited state, we have to apply pi z. So we have to check whether we are in the same sector as before. If you apply pi z to the state, what do you find? By definition here, pi z applied to the state is equal to minus itself. We were in this sector. Now if you apply pi z to this state, so we are as writing everything clear. Assumption, pi z applied to the ground state is equal minus psi ground state. We are assuming this. Then I saw this means that psi ground state means that the h minus of psi ground state is equal to e ground state psi ground state is implied. Now we consider the state b dug k psi ground state. Let's check what is the again value of this pi z applied to the state. Okay? Pi z is the product of sigma z. And we have that the bk is a linear combination of a of Majorna fermions. So, pi z was defined as the product of 1 to n of sigma z and if you write it in terms of the Majorna fermions, this is equal to minus i to the n product over all the Majorna fermions that you have. This is an m. This is pi z. Now when you consider pi z the commutator between pi z and a generic Majorna fermions you can easily check that it's anti-commute with the Majorna fermions. Why is the case? Because we know that all the Majorna fermions commute with the different Majorna fermions. Sorry, anti-commute. So it should be equal to this let's multiply this expression by pi z to the right, for example. We have pi z a j pi z should be equal to this expression here. Okay, now it's a written like product l goes from 1 to 2n of a l a j times the product from l goes from 2n to 1 over a l. You can write this product in this way reordering the operators, if you want. Okay, this is just the detail but just to tell you that if you do this then you start moving the Majorna fermions and realize that you pick just the minus sign. Okay, yeah. So what I'm claiming here is that when you write pi z applied to b-dug what you find is that minus b-dug k pi z times a gram of state so we find b-dug k psi gram of state. So in other words I'm saying that when you consider a single excitation when you add the fermion to the gram of state of the model you change sector. So instead of being in the same sector you go in the other sector and so this means that this is not really an excitation of the easy model. So this is an excitation of the Hamiltonian H minus but doesn't belong to the spectrum of H. Yes? Yes, okay. You have seen the spectrum is divided in two sectors. Then we in sector the Hamiltonian is equivalent either to one Hamiltonian H minus or H plus. Now let's assume that the gram of state is one of the two sectors, in particular the sector with the pi z equal minus one. Now, okay, we we can consider the excitation of H minus for example, because we know that some excitation of H minus will be excitation of the easy model. Okay, the simplest excitation that we have is just a single particle excitation you put a fermion. You add a fermion there. And so the question is, okay, is this an excitation of the easy model? You try. In order to be an excitation of the easy model it should be in the correct sector which is the sector minus one. Then the idea is we should check it. This is this sector. And now I applied pi z to the to the new eigenstate and let's see whether I find minus one. Unfortunately I don't find minus one. I find plus one. So this means that the excitation is in the wrong sector. So why this is an excitation of H minus is not an excitation of H. How long can I obtain an excitation of H? I simply can apply two. I can put two fermions instead of just one. Because if I put two fermions then I remain in the same sector. So this means that among all the excited states of H minus only the excited states with an even number of fermions are also excited states of the easy model. Only a part of the spectrum of H minus is also a spectrum of H. And the same for H plus which gives the remaining eigenvectors. Just to the calculation if you want. Let me think a simple way to see. Yeah there is this problem. We know that pi z is equal product from 1 to 1 to sigma Lz. That's right in this way. Now we have pi z multiplied by a Majorana fermions A. The Majorana fermions A as you have in your notes is equal to the string of sigma z times something which can be sigma x or sigma y. Right? It's written in this way. It depends on which operator it is. So we have here that the operator A I want to compute something like this with some L. And what I'm saying is in terms of spins in terms of spins will be for example A to L minus 1. This will be 12 plus 1. So this will be given by the product from 1 to L or sigma z times sigma x for example in this case L and then here pi z here. This string of pi z commutes with sigma z. It commutes with themselves at every position. So you can move this here pi z. So this is equal to product that j goes from 1 to L of sigma z. And then you have here to compute pi z sigma L x or y or whatever. You have one of the two. Pi z. The only term here sigma x is the one corresponding to the side L. So in the end you have on one side you have one sigma z in the middle you have a sigma x or y and on the right we have sigma z. So here you will end up with I hope you can see here with sigma z L, sigma L x or y sigma L z. These two probably may be some type of mute. It doesn't work. You can find this and this is exactly equal to minus sigma L x, y. This is related to the algebra of the polymerases. It's just a check you can do. It's not a problem it's just that the first single particle excitation of H minus is not an excitation of the easy model because if it were an excitation then the the eigenvalue of Pi z would have been equal to minus one. This is the problem. We have said H H plus minus something equal to E, some energy plus minus and something. We have this. We have identified the ground state we assume that the ground state corresponds to the sector minus one. Now we say I want to I want to consider the I want to focus on the sector with Pi z equal minus one. I just choose that particular sector. I know that in the particular sector the Hamiltonian is completely equivalent of H minus in that sector. So now I can compute the spectrum of H minus all the eigenfunctions and eigenvalues but now I must be careful because this equivalence holds only if Pi z applied to the eigenstate is equal to minus that eigenstate because I'm assuming that I'm in that particular sector then I check it so I said okay let's consider a single particle excitation in H minus and I realized that no, I'm in the wrong sector. The eigenvalue of Pi z is not equal to is not equal to minus one but is equal to plus one. So there is a problem. I should reject the eigenstate. Yes, yes. We are constructing the eigenstate and we say okay we will see that it's easy to find the eigenstate of H plus H minus and now we have to identify which one are the which are the correct one the eigenstate of this model because we have these two possibilities and so in this case we immediately see that if the ground state is in the sector with minus one then we see that the single particle excitation state is not it should be in the other sector. So we have to diagonalize the matrix H plus to get that excitation not H minus. From H minus we can extract all the excitation with an even number of fermions because when you have an even number of B here this operative commutes with them because it takes a minus sign every time so minus one to the to the 20 is equal to one. This is not complicated it's just a problem of understanding one another so I won't probably a graphical representation is better so we have all the eigenstate of H some eigenstate of H are eigenstates of okay this is H this is H plus and this is H plus some of these eigenstates are the same as H minus other are the same of H plus but it doesn't mean that these are all the all the eigenstate of H minus you can have other eigenstate for example this one this one this one the same here you can have this eigenstate this eigenstate H plus when I compute the spectrum of H minus or H plus I compute all these eigenstates but then I should understand whether it is the correct one is there is a corresponding eigenstate of this in model I have to ignore all these eigenstates because they are in the wrong sector and this is what we did we checked if the wrong state is here the first excited state is not there the single particle so we have to excited two particles two particles in order to be to be to remain the same set we see clear now we cannot reach from the wrong state from which from what we infer this for each eigenstate each eigenstate of H has a definite definite value of of pi z so either one or the other here I'm alternating them this is not true in general so they can also be you can have more states condense that you have to neglect it's just a drawing don't take it seriously so how can you we know that the the single particle excitation of H minus is not in the spectrum of the easy so this means that we have to diagonalize H plus again we diagonalize H plus and then we have to check what is the eigenvalue of pi z and now should be equal to plus one and then we select all the second state now you can do this kind of calculation what do you find now I'm telling you the result of this the result is that when you are interested in the ground state let's consider just the ground state of the model for any finite value of N capital N independently of H the ground state is always H minus pi z equal to minus one independent of H the ground state is always there what about the excited states of the model this depends on the value of H so if we now consider our phase diagram this is H this is H equals one zero so we have that the ground state here is is in the sector minus one and then what we find is that the first excited state there is a gap here general and the first excited state is I think I think is in the sector plus generally and there is a gap now if you consider the case A the case H is more than one you find that the ground state is still the sector minus but B there is a very small gap between the ground state the first excited state which is now in the other sector and this gap scales exponentially is exponentially small in the system in the system size so these two eigenvalues become degenerate these two these two eigenstate becomes degenerate in the in the thermodynamic limit in particular we know that this gap is equal to zero when H equals to zero because the two states are really degenerate we check yesterday that we have the spin either are in the X direction or in the opposite direction so in the case the gap is zero in the in general case for H larger than zero you find that they are closed in the final system but when you take the thermodynamic limit then it becomes degenerate and then here there is a gap this is the situation the qualitative the qualitative properties of the spectrum not the low energy spectrum not the ground state of the model we shouldn't be so surprised about this because we know that here there should be a phase so in the thermodynamic limit there is a symmetry which is broken so this means there should be some degeneracy in the ground state notice that this degeneracy exists only in the thermodynamic limit and if the symmetry is broken only in the thermodynamic limit if you diagonalize the model for final chain you use your mathematical for example to obtain the energy you find that there is just one ground state but this doesn't mean that that is the that is the correct ground state in the thermodynamic limit and in particular I can tell you that yesterday we talked about which is the correct ground state to consider so we said that you cannot pick any linear combination of the states in x plus and x minus but there are particular combinations which is just the spins given in x direction or opposite direction here you cannot consider any linear combination of these two the correct linear combination is actually the superposition like this is plus plus or minus minus divided by square root of two these are the physical ground state the physical ground state is not in the particular sector it mixes the two sectors okay and this is a very important complication when you compute correlation functions because everything is simple when you remain in the same sector but when you have to consider the presence of two sectors it makes the calculation more complicated so is it clear the picture or less this is just a description of the results that you will find computing the expectation value of pi z okay but we were talking about how to solve this question I give you 5 minutes she maybe not I said something wrong thanks because yesterday we we compute the ground state in the limit h cost infinity and we had that all the spins are aligned along z now if you apply pi z to this state you find plus pi z per plus the state with those spin up the sigma z applied to up is equal to up so I was wrong when I told you that the ground state is in the sector minus is in the sector plus sorry my mistake your problem is not a problem okay when you apply pi z to all spin up you find all spin up with the plus sign so this means that the state with all spin up is in the sector with pi z is equal to 1 we already know that this state is the ground state when h cost infinity so this means that I was wrong saying that the ground state is in the sector h minus the h was equal to h minus in the ground state this is the opposite I said something wrong here you have a plus I repeat I was wrong when I said that the ground state is always in the sector represented by h minus is in the sector h minus h plus okay so okay so so we still have to solve this problem like in the harmonic chain so what should we compute we should compute the commutator between h plus minus which is written like 1 over 4 some ln of al h calligraphic h ln am and some linear combination probably tired and I if you want I give you I tell you the idea you know you have to commute these operators then you find when you anticommute a n a j you will find delta jn and so on it's very simple I'm not doing it because I guess you are tired but the idea is that if you write this you see a matrix notation let's introduce a matrix notation because everything is easier so if we introduce this vector of a or the major affirmants a 1 8 1 okay again then this can be seen as a matrix so you can write this as 1 over 4 then you have some vector a scalar product this matrix h plus minus vector a is just this term and you can interpret this as b k if you do this what do you find when you consider commutator so I tell you that if you have the commutator of a generic form of this kind a is a matrix and here you have a vector a scalar a you find a very nice result that this is equal to this is equal to mv the scalar product a so you just have to apply the matrix to the vector which is very similar to what we found it's actually the same what we found in the in the harmonic oscillator and this you can prove at ease a and then you will find when you commute this with this you fix the index the colony index of m and then and so on so why this is what this is so nice because we wanted to solve this problem and now this problem is equivalent to again to compute the eigenvalue and the vectors of this matrix of the matrix h plus minus in other words that's this equation here is equivalent to to find h to solve the problem h plus minus applied to the vector which is called b bk so this problem is equal to epsilon k bk I'm saying that here when you write h plus minus in terms of the major you can just you you can reinterpret this as a scalar product between a vector of a and another vector which is h plus and here I'm saying that polygenetic polygenetic anti-symmetric matrix you have this relation notice indeed that our h plus minus are anti-symmetric and why you can always choose anti-symmetric matrices because the major and a fermions anti-commute so the symmetric part of this matrices don't play any role so you are always free to choose to put anti-symmetric matrices here and indeed you have this theorem holds for anti-symmetric matrices for any anti-symmetric matrix you have that the commutator between this quadratic form and a linear combination of the all the major and a fermions can be written just as the matrix applied to the vector corresponding to a linear combination scalar the vector of it so the other linear combination you can really maybe you can show you can show something you can see the eigenvalue and the vector of these matrices which are this one this is not so difficult because like we guessed the solution for the harmonic oscillator we can do the same here and the idea is that to again consider phases now as a solution but now we must take into account that the matrix is block so this means that we have to treat we will just we will seek for a solution of the form of the following form for the vector bk is equal to bk 2l minus 1 plus j is equal to l that is correct this times some vector b dimensional vector ok so I am saying that I am divided I split the indices in pairs 2 by 2 here you see this label the pair of the initial matrix and then these other indexes for the elements inside the two the pair and then what I am saying is that if I consider this index just the index of the pair then I can use the symmetry of the matrix which is periodic and so I know that the solution is just going to be a phase the usual phase which is the Fourier series but ok I must take into account that there is this the degrees of freedom of the pair the fact that now this is not a scalar so here I should expect that I have to multiply by some vector that I have to determine which diagonalize the 2 by 2 part of the matrix I am just saying I have this matrix I see this matrix as a block matrix so these are 2 by 2 we have seen that the blocks have the periodic periodicity so this means that I can seek for solution where for each block you have a scalar phase and so on but now here we have to find which is the correct the correct vector to dimensional vector you are seeking a solution of this form because this solution has this form as a matter of fact you can convince yourself or you can just read somewhere how to compute the eigenvalues and get back to the block circle matrix so what do you think if we plug this expression in the question for the eigenvalues what do we find h plus minus 1 over n sum over k plus or minus of e to the i l minus n k q plus minus this 2 by 2 matrix equal e of q plus minus index j j prime and then I have to apply this to this particular vector so I have here i i n k plus minus and I have this more vector v j so this is the first part this is this okay and this should be in the exponent here is written this and with this one but now I just changed the name instead of using k I am using q because then I have k on the other side okay 1 over n sum over q plus minus of this j j prime and then I am applying to this vector and we have to sum over n because it is a multiplication matrix time vector so sum over n sum over n when we sum over n now we have the sum over n of e to the i just consider sum over n we have sum over n of e to the minus i n q plus minus plus minus sorry q plus minus you have this no right now you remember q plus minus are given by 2 pi no 2 pi j over capital N so as a matter of fact you will find that independently of plus and minus the sum is just equal to the delta of q plus minus times n I repeat so e to the i when we define k plus minus they were defined by the condition e to the i q plus minus is equal to q plus is equal to 2 pi as this form 2 pi j over capital N instead of q minus as the form 2 pi j plus 1 half over capital N these were the two possibilities the two sectors, the two quantization now independently of the quantization because there is a minus sign here you simplify the 1 half so in the case you have the when you sum all the phases sum over n, especially you find the chronicle delta so the 2 q plus is equal to k plus and q minus is equal to so for this reason we first sum over N this expression and what do we find when we sum over N so we find we are computing h plus minus b the element and this is equal to 1 over N simplifies with this N and q plus minus is equal to k plus minus pi L k plus minus times e k plus minus applied to the vector b k plus minus and here there is an index and this is 2L minus 1 plus plus j prime let's see and here we have j prime j then we have the vector v j and there is a sum over j what I mean I am just writing this expression so this which I which is nothing but this thing here now is equal to we sum over N so this gives this constraint it has the q plus minus is equal to k plus minus I am using this here and so I end up with the iL this matrix multiplied by the vector vj b you are confused because there is j prime there and there is a sum over j prime here this is what I find and I want to impose that this is equal to epsilon k vk this should be equal to epsilon k and vk was e to the iL k plus minus and a plus minus and there was v vj this is what we are imposing what we are trying to solve now you see that this term simplifies so this means that our answers was correct otherwise you would have added some dependence on L here so this means that in the end what we have to solve is a negative model problem for this 2 by 2 matrix here e e of k times v should be equal which is v of k v of k should be equal to epsilon of k times v of k I know that this is late and it is confusing but what I mean is that we started with a very complex problem because a native array system if you count the degrees of freedom we have 2 to the capital N degrees of freedom which is a lot then somehow using the algebra of the Majorana fermions we were able to reduce this problem to a problem of finding the eigenvalues of a matrix which is 2 capital N times 2 capital N matrix so we reduce the the complexity of the problem exponentially from 2 to the n to n now here using the properties of our matrix if the factor is periodic or anti-periodic we were able to reduce the problem to find the eigenvalues of a 2 by 2 matrix this is the magic of the solution of the easy model that we started with a extremely complex problem and then you finally manage to reduce everything to a 2 by 2 problem you can you have the matrix to compute the eigenvalues of this do it not now but the eigenvalues of the eigenvector then next time we will tomorrow we will finish this and then we will start talking about dynamics don't be scared about all this part you don't need to be able to do all the steps so the diagonalization is just to know how to do it and just to understand the meaning of the fermions how to construct the space and that is important I hope that that you can understand that the structure then the details are just details technical details maybe you need more time you have to do all the steps and all the passages in a few weeks you will realize that this is simple I can understand now


Here's an example of a primary alcohol. So I hope that each time that we start seeing these, when you're looking at either models or structural formulae, that you're already starting to work through the naming of these in your head.


Hmm, and I would definitely power it so I could box truck this I'm gonna be cool Cripes, I'm running out of space. I think I need to take this thing outside All right, I decided this solar panel is what I'm doing. This is the smallest solar panel I have I don't want to put on this thing All right We gotta go forward turn the other way turn the other way. Yeah a lot more a lot more Street now turn that turn the other direction you're back up No, no, no, no the other way. Yeah All right, that's straight now Turn more little more that way same way we're just going. Yeah Little more Okay, we're gonna back Bellatrix you are steering right now, right? Which show me show me steering. Yeah, okay, which way are you not gonna crash into the bulldozer? Hey, you pay attention pay attention All right I need to get a switch on that car that those kids can actually use themselves because right now I'm just holding the wires together and then Want to get a battery. I mean right now the sun is like out drive around a whole bunch You know if you drive under one tree branch stops, so Yeah, even just a little battery would be good. It's like a little lead acid one. I have this this lithium suitcase battery I made a while ago However, it's not currently functioning. I don't know what the problem is something something's wrong with the BMS I don't know. Maybe I can resend it or something. I don't know. Maybe it's just not working But I did connect the car directly like to the battery So here's the battery suitcase I have These don't do anything right now. They're supposed to but they don't but if I open up I can get directly to the battery and I connected the car directly to the battery and man it took off I mean, but yeah significantly faster than it was going just on the solar panel It'll be It'll be great if I get this thing working. I Have to figure out what the problem is with this BMS bowel movement bowel movement syndrome machine