to my co-host to sort of Brown back in Honolulu, Hawaii, and me being here in the Munich, Germany. And we're still in the claws of COVID corona. We're using this time to look at something that used to run us, which is the hospitality industry, which is pretty much down right now. And we started to find out that some clues for a promising future might be in the future. And I think that's a promising future might lay in the past. And for that, we bring in our guests today, once again, from a vineyard, a cocktail vineyard in Napa Valley, Mr. Larry Stricker. Hi, Larry. Good to have you back. So we're going straight to the first slide, which shows us the beginning of your guys conquering the world in the resort typology. And this is how it all started back on the island of Wahoo in Hawaii with Conrad Hilton and your friend and business partner and colleague Edward Killingsworth. And this is the Kahala Hilton. And our additional consultant here, exotic escapism expert, Anna and us have been talking about how innovative and also provocative and risky that project was because way back it was far, far away from the booming YTK at its time. So if we can get the first slide and second slide up here, this shows us not only at the top right how far away it was because in the distance of that picture, you can see one of our iconic out-of-practice volcanoes diamond heads. And we've been zooming in on this picture here because sometimes for the general audience, we're not architect. It's easier to identify the size through automotive than through architecture, which often looks timeless as in best cases, as in this case here.  So this would have been a few years after the hotel opened. Exactly, yeah. So going to the next slide, per our pedagogy and methodology of using vehicles as that guy's element, here is my, you know, me as a German, I'm an Americano. So I love what we call Schrockenkreuzer, which are the street cruisers, the big boats that only you Americans were able to make. And this is one of the last ones. This is my Lincoln Town car that made sense when I was still living in Paris and in the desert to some degree because I needed some exposure to protect me from the extremeness of the elements, not so much more in Hawaii. That's why I traded it into our pying mobile, easy breezy, one that you just sort of kind of take care of. Yes.  How Hawaiian call Diamond Head because they reminded us of the shape of a fish of that name. Yeah, the eye. And why I, exactly, and why do I bother you with my big boats because it was built the same year as the project we're going to talk about today in 1993. So let's go to the next slide. You just sort of tell us more about the top picture, please. Well, there's an aerial photograph of Diamond Head or Leahi, as you just pointed out. And as you can see, it's a crater with an empty part in the middle. This is an old photograph, as we noticed, because there are no highrises yet in Waikiki that we can see at the top of the picture. But if we look beyond that Waikiki area, in the far distance, we see the Waianae Mountains. And that takes us to the location of the hotel or the structure we're going to talk about today at Coalina. And that is the Ihi Lani Hotel, which we see in the bottom picture. Diamond Head and Waikiki, we go traveling out to the Waianae, look at this hotel in detail. And that's an interesting similarity, Larry Ryden, in many ways between the Coalina and Ihi Lani. Yeah, I think the Ihi Lani and the Kahala came, you know, further to you, as far from the airport to the east, as Ihi Lani is from the airport to the west. But they were both, you know, rather, they were the first hotels in a very isolated area. And they had, I know, it took a while for Ihi Lani to gain some recognition. And the first year, it was principally used by the staff of Japan Airlines. So we forget that the Kahala also had some rough first year and with room rates at a terrible low of $25 a night. So it's amazing how things have progressed. The other interesting comparison to Kahala is that when our client from Japan Airlines, Chuo Kojima, when I first met him, he said they had researched several resorts in Hawaii. And fortunately, they were all designed by the same architect. So that's why we were selected. And of course, the Kahala and Kahala Kalani, Manalani, and Kapalua was still around back then. Yeah. And that reminds us of a survey, a ranking that your friend and partner, Ron Lindgren, had shown us in one of the last shows with the wellness world of wellness, which, as I recall correctly, actually was from the early 90s, which exactly represents that you guys were topping that list with these four projects in the world. They were all by you and all in Hawaii. So next slide. Next slide is our mandatory biochromatic environmental check. As we've pointed out that your project, I would say intuitively, if not intentionally, we're very ecologically conscious and successful.  And why that is, we go to the next slide. You, Larry, tell us a little bit more about what we see. Well, we see the extra large lanais on all the guest rooms. And here we're seeing on the, where the guests are standing there, the open railings, and just above that, the planter railings, or the railing, the lanais with the landscape planters in them. And from our previous experience, we found that we, when the value engineering comes along, we lose half of the planters. So I just looked at my original rendering of the lighting, and I did show planters on every floor. So we were able to retain half of them and still come out a hero and helping save costs on the instruction. This is a very great advice to the emerging generation.  And we threw in the top slide quotations from previous shows, which shows from left to right, it's sort of organic evolution from that actually the Kahala had rather small openings. There were still significant opaque pieces left and right of the floor to ceiling sliding doors. And then slowly but surely through Ron's Halikolani and then next out in your case, you got it bigger and bigger, in your case to 100%. So these are truly the largest lanais and the largest openings to lanais that you can have on the island, which is really spectacular to have. Go to the next slide. What we see is because you guys designed it obviously from inside out as much as from outside in, and as Suzanne was always reminding us that the kind of renovation intervals in the hospitality industry are like five to seven years. So at the bottom left, we see when it was still under the Marriott ownership, and that was a renovation I think in 2011. And then on the top right, we see the most recent renovation for seasons to go over. And we're happy to say and to illustrate that substantial things have stayed unchanged. We still got the same large sliding doors to the lanais and he even got the wooden sliders, the French wooden sliders, which is great. We're using again the automotive to point something out because, and this is relative to the great achievement of having stayed pretty true to the original authentically. But I was looking for when you look at the backdrop of the bed at the top right, I was looking if there had been a woody Lincoln town car, but there wasn't any. The only woody that you've got in the 90s was the one that you see up there at the top left. So we wouldn't call this heavy-handed as you had to with the Mamalani renovation, but still we would advise at the next renovation, which then obviously would occur in five to seven years, even if you did not do these things, but keep it rather even cleaner. But you had an interesting background story about the original interior that was also rather troubled and challenging, right? Yeah, I think the original client rep from Japan Airlines, the group was called Ten Pacific Hoteliers, and they were inspired by Tukahala and particularly Tukahala Kalani and wanted to achieve that level of success. However, during the design process and the development of the hotel and economic functions within Niko hotels took over from this Ten Pacific Loop, and it ended up being more of a, you know, not the luxury level that we had designed the hotel for, and then Marriott came and took it over from Niko and brought the level up a little bit, but then it's come full circle now with four seasons, and it's back to the level of luxury that we originally designed. That's well deserved. So let's go to the next slide and talking evolution. While the Tukahala was very sophisticatedly, but still double-loaded corridor, the evolution that you guys work actually was shifting to way more trophically exotic single-loaded corridors as we have seen in the Palm Desert Hotel up there and in Yomana Lani, and then in the Ihi Lani, the Ihi Lani has this great central courtyard atrium that we can see here, and that's not only open to the very top with a glass roof, but also open as we see here towards the Maoka, towards the mountain. And when I took this picture here together with your friend and partner, Ron Lindgren, because when he was there for the Gokomomo Sampyongin we were cruising out there and catching it at this beautiful sunset light and we took the picture here. And I witnessed, I was sneaking close to the windows. I can see some of them still being able to be split open, so you can actually get some pretty nice breeze through if you want, so you can get crop ventilation. And that's the most important thing under the current virus that we have, because outdoors you're safe, indoors there's trouble. So you were ahead of the game, Larry, for that. So we also want to point out, go back to the vegetated planters, and the desert palm hotel and also in your Manalami who are sad to not having seen them operated anymore, so planted here thanks to the four seasons and kudos, they're still doing it. So we're very happy to see that, that they want to see the legacy alive up to its detail. So thanks to the hotel management. Next slide. Well, when the Iihilani hotel was first built, there was the plan that that entire area of Kholina was going to become a resort complex like Kanapali on Maui. But because of economic reasons, most of those planned hotels never got built, and the Iihilani was just there by itself for a great many years, and lacking the synergy of other hotels, it made it less occupied than it might have been otherwise. So in 2011, the Iihilani resort opened next to it, and that obviously is run by Disney. So we go from the stripped down bare bones, honest, concrete of Iihilani to next door this very artificial faux tropical concoction which being created by Disney is supposed to be a fantasy. It is supposed to look like, but in fact it does. I find it not very wood details that really aren't wood. They have A-frame, thrusting, Polynesian-inspired roof that are kind of packed on to... I don't think those two make very good neighbors. However, that is the way they have worked out, and it is undeniably helpful for there to be more than one hotel rather than Iihilani all by itself. And I couldn't agree more with you, but it has a good example of what happens when you throw your design guidelines away. When we originally started Iihilani, the design guidelines were really very stringent and dictated a terracing of the buildings so they weren't all one height. And it appears that they allowed Disney to proceed without following the guidelines. I think you're right. Yeah, and I find it almost ironic because when you started out with what one called structural expression is that the Kahala Hilton with the sticking out bones exemplifies the best. You were slowly but surely almost like nature does with creatures with birds. But aren't really that necessary anymore. They go through the backgrounds and so you did in large parts. While at the same time, architect Tawaya, I guess, we're the ones who did this here, we're doing kind of the opposite and as you perfectly said, in a silly way. So it goes from according to Ron, structural expressionism to sort of a fake regionalism, which is kind of really ironic. Anyways, so hopefully it doesn't happen again, although we have some fears to share in the volume two of this show. It's going to happen next, so it might get worse. So along the same lines of sort of an extended postmodernism. So let's go to the next slide and lift up the spirit a little more because here we are in some parts you have been showing and sharing again the structural expressionism at its best and here in the sort of very most elaborated way of the quadruple bundle of columns that as Ron said, this is the most ultimate where the beams can just slide through the columns here. So very fine and that's in the pool area here. And the next slide shows a detail of it at night time and I threw in this sort of quote to one of the Polynesian pop shows we've been doing the solo and while here it's staying away from doing it to literally I believe that figuratively you do it very well the way the light comes through and the combination of water and plants is indeed very tropical exotic but with contemporary means that's much appreciated. The quadruple columns really tied back to one of the original projects that I worked on which was the Coppola Bay hotel. If you go back and look at the lobby columns there some very similar in structure. Absolutely and while the most crime being that that one was torn down to replace it with something equally hideous to what we're just talking about we get to that a little bit too again. This one here is then continuing that legacy of the quadrupling columns. Yeah absolutely and next slide shows us how cleverly that theme has been sort of exclamated and then alternated here while in the core of the building where the most loads are you had basically given the quadruple columns a solid core with these reveals on the outside very clever and you said Larry that's probably the way the columns meet the ground is a result of one of the renovations and you don't recall that that had been your detailing so I basically say next time guys when you remodel please consult Larry as far as the fine grain. I think in the main structure with the most recent core seasons renovation they did that would be in the recessed area with the quad columns which accentuate the four columns so that was a nice touch too. Yeah and we will see that later in the show but let's go to the next slide and you Larry share with us where that is. That's where the columns meet the ground there at the entry and again this was a much tighter site than the other say the Montalani. Montalani was 30 acres and this site was just under eight acres so it might be much more dense as far as the guest rooms but still the driving force was to create almost 100% guest rooms which was used to the ocean. Yeah and while we were very sad to see that sort of tropical exotic lushness of vegetation and water having been taken away in the Montalani and also in the entrance area we want to recognize and appreciate that it's still there here in the Elani although I can only imagine that probably the way how the water met the column was was solved in a more elegant way and probably it didn't have that extra glimpse down there so again I think overall Elani has which by the way we want to mention here is a young timer so it's only 25 years so a quarter of a century young so it's far away from being on the register but it's getting there so you can't start early enough to really treasure a killing's worth which they have been doing but again try to do even better in the detailing I guess which it appears that the water level is about 6 inches too low in that photograph Yeah exactly that's an easy way thanks for that. See guys consulting Larry wouldn't cost much just pouring a little bit more water he has really a very economical solution and explained to us how the columns go up here to accentuate the entrance in this great entrance feature here Well I think it's a matter you know and it was we look at this in scale to be the six-story Manawani which had similar Port Couchere we're looking at a much higher building and then again to create this terracing effect we do the same thing there was also from the entrance here considerable wind so we designed the entry to minimize the wind problem I think the last time I was out there we originally had the old revolving doors but I think it would be before seasons renovation they've done just pairs of sliding doors that that apparently were flying but then it is when it can get windy out at this end of the aisle yeah that was I was going to say that is a very windy location where this hotel happens to be but I also wanted to say about this particular picture I don't think I've ever been at the hotel at night to see the lighting which really accentuates those different levels that have been added here that have been put in addition to the main Port Couchere itself and they look really dramatic and they are very eye-catching and compliment and again to the architects of renovation they were enhancing existing features that you have designed there rather than adding some on their own and we will find out more why that was and who are the authors behind in our volume 2 of this show and let's phase out and go to the next slide just a second to last which while we were talking as having started out as the century modern guy where everything was square boxy rectilinear you already shared with us that the zeitgeist and also the zoning and bombing the zeitgeist has forced you to do different things and I recall Ron saying and that's why I was inserting here that quote to the show and I already tell of it with Ed that you guys should watch online that Ron said that Ed wasn't particularly fond of you guys basically how should one say sort of differentiating the box sort of kind of stepping down and also the pitch grooves obviously but again you guys were the next generation and you had to smuggle a modern agenda not only through more postmodernism but also what had to come after that which is the early 90s and that's the time I had to go to school and that was the most devastating a lot of times because we didn't know where to go so you guys were just keeping the course steering on course and only slightly and I want to if you don't mind sharing with us the little eye-winking detailing of the little zoom slide piece that I show at the top right well again some of this terracing was dictated by the design guidelines which had to do with the height and the year to the setbacks and then a lot of it was functional when you do stepping back it's always interesting how you carry exits down the terrace building so that's what we're seeing at the far left edge of the stepping and that's crowned with the presidential suite and the swimming pool with the posting beam trellis work around it so it all works with the stepping of the building and the terrace and it's talking swimming pool besides the big lagoon here which is a large natural pool that gets us to the last slide which shows us the main swimming pool on the ground level and again explains to us a little bit the relationship between the Halicolani and the Ilani the rep who was kind of the prime mover for Japan Airlines was really in awe of the luxury and the quality of the Halicolani and he wanted to emulate that in every way possible and that's one of our philosophies that continues through all the years of our firm that you don't have to be different you just have to be good and often times an architect sits down and says what can I do differently you know the only thing you can do is improve on what you've done in the past I think that there couldn't be a better closing note for this show you don't have to be different you just have to continue to be good and be that thanks so much for that message so there's more to come we're going to contemplate more on this your masterpiece the final killing on the Hawaiian island and until then please all stay as easy breezy and as easy breezy as you Larry, Juan and Ed and see you next week bye bye


Alright everybody, what is going on? Welcome back to another video. Today's video is going to be the first of 100 videos. This is my next big mission guys. This is my next big series on this YouTube channel. My YouTube channel is full of just different series and if you were here in the early days, probably before about 50,000 subs, you would have seen that I completed the top 100 players of 2018 before the start of the regular season. Now that was a goal that I put in place. It was a goal that not a lot of you guys thought I could do. I didn't think I could do it but you know, you asked for it and so I appreciate you guys giving me the feedback. I appreciate all you guys, all the comments, like, support, everything and I'm getting a bit of an inkling, a bit of a notion at the moment from you guys that you'd like to see me react to the top 100 players of all time. I believe this series came out in 2010. It's created by NFL Films. It's going to be amazing, I assume. So what I'm going to do, I'm actually here in Bali, believe it or not. I don't know if you've seen my Bali vlogs that I've put out but basically I didn't miss my flight but my flight got cancelled. So here I am, they've put me up in the Novotel here in Bali.  I've got an iced coffee, which is brilliant and I've got a bit of spare time. So what I'm going to do, I'm going to crack into these top 100. I don't know how many I'm going to do today but once I start, I can keep going. It's just starting. It's just like going to the gym. It's just like starting a diet, starting a new program of any sort. You've just got to start. You've got to get that foot out the door, into the car, get inside the gym and then you're good. So as soon as I start this with number 100, Joe Namath, Namath, excuse the pronunciation, then I'm on a roll man. I'm done. I'm going. I'm going to do one player for each video. There's going to be 100 videos. Now this is, I'm not going to lie, this is partly due to the fact that I want content to be able to produce and post over the period of November and December without any gaps. This is going to give me content to post for you guys. All you guys are going to enjoy it. Hopefully I'm going to enjoy it.  And I do do that sometimes, but most, if not like 90% of all football videos I've ever watched, I've done as a reaction on camera.  The knowledge that I've got so far, I've done it all on YouTube. This whole entire journey into American football. As a rugby player, I've done on camera for you guys to watch and come along with me. And that's awesome. I really like it. So we're going to continue with that. Number 100, Joe Namath. Joe Namath. Good old Joe. We're going to get into it. The top 100 NFL's greatest players. I cannot wait to watch it. I'm not going to, I'm not going to peak. I can see 100 to 92 right now on the screen. And the way we're going to do these videos, okay, this is going to be an intro clip. The next one's going to be starting at number 100. So what we're going to do, I've got my headphones. Instead of trying to pick up both audios through the TV and also through, you know, through my voice, I'm going to put the headphones on. I'm going to watch the video through the headphones.  So the audio that's coming through the camera microphone is going to be a lot clearer because it's only just going to be my voice. Okay, so from there, I'm going to have to download all the videos, put them all together and we'll be off. But what that does mean is that I can't pause and rewind.  So with that said, I would assume once I get home to New Zealand, not New Zealand, once you get home to Alice Springs, I will have the green screen. I've been away for two weeks in Bali, so a fair few packages have come through. Not only my green screen, but also some subscriber starter packs, some fan starter packs from you guys. So I cannot wait to open them. I'm going to go to my PO box.  It's almost Christmas anyway, so I do really appreciate you guys. I appreciate you bringing me into your either college or NFL team culture and wanting to include me and teach me about the team that you guys have loved your entire life. I feel that way about certain rugby teams. You guys feel that way about football teams. So with that said, I'm going to call it here. The next video you see will be number 100, followed by 99, 98, 97. I'm going to do as many as I can today. Like I said previously, once I start, I can't stop, especially if you guys are asking for it. And this series has most definitely been asked for. So with that said, have a great day. I'll see you soon. Peace.


All right, so let's look at azotropes a little more closely. Azotropes being for systems that exhibit strong deviations from ideality, either strongly negative deviations from Raoult's law, which we can see on a pressure composition diagram, or strongly positive deviations, also on a pressure composition diagram. These phase coexistence regions undergo a minimum or a maximum. Then the points at which the minimum and maximum occur correspond to the azeotropic compositions of these mixtures. So an azeotrope is a mixture with a concentration such that the phase diagram looks like this above that concentration. It's more interesting, more useful usually, to talk about these phase diagrams, not in terms of pressure and composition, but in terms of temperature and composition. So if we redraw these phase diagrams now as a temperature composition phase diagram, so plotting not the vapor pressure of the solution, but the boiling point of the solution, in this case, continuing with my pattern of drawing the more volatile component as component A, that more volatile component will have a lower boiling point than the other component. So the Raoult's law behavior, the ideal solution behavior, would have relatively smooth curves connecting these two positions. So system with strong negative deviations from Raoult's law. Remember the negative deviations describe deviations in the pressure. When the pressure deviates in the negative direction, decreasing the vapor pressure, we have to heat that system up higher in order to boil it in order to get the pressure up to atmospheric pressure. So it's going to exhibit positive deviations in the temperature. Pressure and temperature act inversely in this sense. So at that same azeotropic composition, instead of having a minimum in the vapor pressure of the solution, we're going to have a maximum in the boiling point. So you can describe these systems, these azeotropic forming systems, either as being strong negative deviations from Raoult's law, in which case you're describing the pressure behavior, or you can describe the system as having a max boiling azeotrope, meaning the azeotrope in this diagram is the highest boiling point of any composition of the system. This maximum corresponds to the largest possible boiling point we can achieve by mixing these two solvents together. And again, it's a phase diagram. So at low temperatures, we have a liquid. High temperatures, we have a gas. And then we have these tie lines in the phase coexistence region, describing the liquid gas coexistence regions. Either for A rich solutions consisting mostly of A, or for B rich solutions consisting mostly of B. Everything is reversed, of course, over in the case where we have strong positive deviations from Raoult's law. If I draw a temperature composition phase diagram, my more volatile component A will have the lower boiling point. And instead of Raoult's law type behavior, the positive deviations in pressure that result in a maximum in the vapor pressure will be, again, at the same concentration, a minimum in the boiling points. And again, with the bubble point and dew point curves, both meeting at that azeotropic composition. Low temperature liquid, high temperature gas, phase coexistence between the two. So if the strongly negative deviations case results in a max boiling azeotrope, if we have positive deviations strong enough to form an azeotrope, then we describe that as a minimum boiling azeotrope. So again, the azeotrope describes the particular solution with this special concentration. That azeotrope will either have the largest possible boiling point or the smallest possible boiling point. So now let's consider what actually happens when we boil a system or when we distill a system that does have an azeotrope. If we start with this case, let's say I prepare a solution not at the azeotropic concentration, but at some particular concentration. I make a 50-50 mixture of A and B or whatever concentration I want, prepare it in the liquid phase, and now I heat that system up until it boils. So I'm going to raise the temperature until I get to the bubble point. When I get to the bubble point, the first bubble in the solution forms. The concentration of that bubble is enriched in the more volatile component, component A. That's good. If I want to continue distilling, if I condense, boil, condense, re-boil, and so on, I can eventually purify component A by this process of fractional distillation as we've talked about before. So far, that seems just like what we've talked about previously, except notice what happens if the concentration of the solution is very B-rich if I'm over on this portion of the temperature composition phase diagram. If I take this system, heat it until it boils, the composition of the vapor reading across the timeline has become enriched in component B. It's more dilute in component A. It's enriched in component B. So the enrichment happens in the opposite direction. I can, again, perform fractional distillation to purify the system. But now what I'm getting out of my fractional distillation column is purified solvent B. So in this aziotrope, max boiling aziotrope system, it turns out I can purify either solvent A or solvent B, depending on which side of this aziotrope I start on. So that may be good news. In a non-aziotrope performing system, you always get the more volatile component out. In an aziotropic system, you can get either component out as a result of distillation. Turns out this actually doesn't violate our rule of thumb that when you distill, what you get out is a purified version of the more volatile component. If we think of the aziotrope as a separate component, pure solvent A has this boiling point. Pure solvent B has this boiling point. The aziotrope has this boiling point. So instead of thinking of it as a mixture of A and B, if I think of this B-rich solution as a mixture of B with the aziotrope, I'm somewhere between the pure B and the aziotropic mixture. Out of those two choices, the aziotrope and B, B is the one with the lower boiling point, and therefore the more volatile of the two components. So when I distill this mixture, it enriches in the two options that have the one of the two options that has the lower boiling point. The more volatile component is B. On this side, I'm enriching in the one that has the more volatile component out of either A or the aziotrope. As you might expect, things are similar but flipped around when I consider a minimum boiling aziotrope. So let's see if we can understand what happens if I distill this system. Let's say I start with a B-rich liquid at this composition in the liquid phase and I heat it up until I get to the bubble point. The vapor that boils off that solution has this concentration. If I re-destill it, sorry, recondense it, boil it again, re-destill, condense boil again, I can zig my, zag my way down. Notice in this case where I end up, where these two curves meet, is at the aziotropic concentration. So I can't distill my way all the way to pure A like I could previously. What I'm distilling towards is the aziotropic concentration. Likewise, if I start with an A-rich solution, heat it up until the bubble point, collect the vapor, condense, boil again, and so on, I'm zigzagging my way down toward the aziotropic concentration. So that's actually bad news if what you're interested in doing is purifying a solvent. If you have a mixture of two solvents, if you have an impure solvent mixed with another component that forms a minimum boiling aziotrope, when you distill that solution, you're always making it move towards the aziotropic concentration away from either pure B or pure A. So, and again, you can think of that as always moving towards the more volatile component. In this case, the aziotrope, the minimum boiling aziotrope, the lowest boiling point, any mixture of these two solvents can have is the aziotropic concentration. So if I have a mixture of pure B and the aziotrope somewhere in this range, then when I distill, I move toward the more volatile aziotrope. If I have something that I can think of as a mixture of pure A and the aziotrope, somewhere between those two concentrations, when I distill, I move toward the aziotrope. So, aziotrope is the endpoint of all distillations if you have a minimum boiling aziotrope. And again, that's bad news for a couple reasons. Bad news, because usually we want to purify solvents rather than complicate them. And also because, in fact, most pairs of solvents form, exhibit positive deviations from Ralph's law and have minimum boiling aziotropes rather than the more rare case of forming a maximum boiling aziotrope. So, another important thing to say about aziotropes, in addition to what we've just said, that if we have a minimum boiling aziotrope, all distillations will move towards that aziotrope in composition. Another important observation is that the aziotropes itself, unlike other concentrations of these solutions, has a sharp boiling point. In each of these cases that I've drawn so far, when we heat the system up to the bubble point, if we had continued heating, there's a range of temperatures between the bubble point and the dew point where the system can exhibit coexistence between the liquid and the gas phases. So, because this phase coexistence region has some width to it, it's a finite range of boiling points, a range of different boiling points that each of these concentrations can exhibit. For the pure solvents, A and B, as well as for the aziotrope, the curves meet at a single point, which means just like pure A boils only at this specific temperature, pure B boils only at this specific temperature, an aziotrope will also boil at a sharp boiling point, at a single boiling point. So, another important thing to remember is that aziotropic mixtures of solvents will boil at a single temperature, a sharp boiling point, rather than a range of temperatures.


Hi, my name's Leon Roe, currency trader and trading coach at Trading180.com and in this video I'm going to review the Euro dollar for the first quarter of 2023 and really get a look into how fundamentals affected price. And if you're new to the channel, a warm welcome to you and if you're obviously returning an equally warm welcome to you. And if you don't know, I am quite fundamentally driven. I use fundamentals for my directional bias and look for the technicals as timing. And if you are new to fundamentals or don't necessarily understand fundamentals or having a hard time in understanding the fundamentals and applying it to your technicals and really want to try to improve your trading. I have this video obviously that you're watching and several other videos and I will put links to the description and they should pop up in the top right hand side of the video. So whenever you see something pop up, that would be me just recommending a fundamental analysis video that I think you should watch. So let's get into it. Let's get into the fundamentals and look at the review. So just as a basic understanding and a reminder, I guess, is that there are three main, I guess, macroeconomic data points that we should look at when it comes to forex fundamentals and what really kind of moves price, at least over the medium to long term. And they are gross domestic product and inflation. And those two will have an effect on interest rates and what the central bank does with interest rates. And so looking at GDP first, typically, when you have gross domestic products and growing and expanding in the booming cycle of the economic cycle, it typically leads to currency appreciation, growth. And if you have contraction, then, you know, into leading into some sort of recession or bust slump phase of the economic cycle, that typically leads to currency devaluation or depreciation. Right. And so looking at inflation, inflation, central banks have a 2% target and a mandate, they are mandated to get inflation to the 2% target. Now, 2% inflation is actually an acceptable currency devaluation. It's seen as, you know, again, acceptable where it's not too hot, not too cold. The Goldilocks kind of the economy of inflation, if you get the reference, whereas if inflation goes above the 2%, then actually that is seen as unacceptable currency devaluation. So inflation rising is actually currency devaluation. And in fact, this should say, and I should have put this one below 2%, put that one out. Inflation, right. If inflation is below 2% and maybe trending away from the 2% target, so it's going to maybe one or zero and then it goes into the minus. In fact, that is unacceptable currency appreciation. So if inflation goes towards the negative towards zero, then in fact, the currency is appreciating. Right. Now, depending on what is going on with GDP and inflation will determine a central bank's decision on what they will do with interest rates. And there's the interest rate cycle and pretty much interest rates do go in cycles. And so inflation, inflation is above 2%, right. Central banks will typically tend to hike, right. And that leads to currency appreciation because what they want to do is actually counter, yeah, currency devaluation. So as you said, if inflation is above the 2% and trending away, then that is unacceptable currency devaluation. And to counter that, right, they need to hike rates so that and hiking rates has the effect of appreciating, creating demand for the currency, which create a currency appreciation to kind of stem currency devaluation caused by inflation. Now, if the central bank is on hold, then currencies, the currency, they accept the currency value, yeah. So they think to themselves that, yeah, we like the currency at this value, yeah. And the inflation, if inflation is below the 2%, then in fact, they will typically tend to cut interest rates and cutting interest rates has the effect or can have the effect of depreciating a currency because if inflation is below 2%, that is unacceptable currency appreciation. And so again, to counter the appreciation of a currency, they have to cut rates to try to depreciate the currency so that they can stop the currency appreciating too much. And also as well, it's well worth noting that if central banks hike too much, this will cause economic contraction. I'm not going to get into that in this video, but again, I have a video explaining that which I will put in the top right hand side of this video. So click on that maybe afterwards when you come back and maybe review this video. And so buy the rumour, sell the fact. Buying the rumour is what we do as fundamental traders and having a fundamental approach because that's where the money is made. It's secondary whether the actual fact comes to pass, right? But the money is made in buying the rumour. We need to get ahead of the curve. And so that is really what the point is with fundamental analysis. It's getting ahead of everybody else trying to get ahead of these technical traders who have no idea what's going on and buying at bargain prices and looking where something is expensive as well as a bargain or a cheap or a discount. And understanding that when things are changing in the future, then in fact, currently, whatever price of the exchange rate is of a currency pair, in fact, that is probably cheap or it might be expensive, again, depending on what happens with gross domestic product, inflation, and interest rates. So it's all about buying the rumour. The fact, whether it comes true or not, is secondary. And so let's look at central bank policy differentials because that's what we're ultimately trading in currency land. And Euro dollar, obviously, the most traded currency in forex. And so when we're looking at GDP, inflation and interest rates, we're comparing those, you know, Europe's data with the US data and seeing where the differentials are. Yeah. So if one central bank, for example, is hawkish, right, very hawkish, hawkish meaning that they are likely to hike interest rates compared to a currency that is not as hawkish or maybe a bit dovish, which means that they may want to either hold or cut rates, then there's a differential there, right? Because we know that hiking interest rates appreciates a currency, cutting rates devalues the currency. So the biggest kind of divergence you can get is when one current one central bank is hiking rates and another is cutting, but that doesn't necessarily happen all the time and every day. But, you know, what we're looking for is differences as to why one central bank is likely to be a bit more aggressive in their hiking of rates currently compared to, for example, another or why one central bank is likely to, for example, continue hiking and leading their hiking in terms of the other central banks, say central bank B is likely to hold first, kind of like a leading and lagging dynamic, but we'll get into that maybe in another video. Anyways, let's look at the differences between the euro and the dollar in January, February and March. And so what was happening in Europe in January? So euro, according to Bloomberg and an article in Bloomberg, traders were wagering that the ECB will raise rates by another thought of 140 basis points. The euro's gains also reflect a certain of optimism over Europe's economic outlook given lower gas prices in China's reopening, which is seen as a boon for the trade. So to give us a bit of context, what was happening was in November, December, it was expected that the Europe would go into a recession because of higher gas prices. This is due to the Ukraine and Russia tensions in the war that was going on. And so Europe were expected to go into a recession, but due to a some really warm weather and natural gas prices actually coming down, it helped the economy. And so the economy actually didn't go into a recession, actually avoided the recession, it started to grow a little bit. And although inflation was high, it helped the central bank by them actually being able to high crates because if they went into a recession, then hiking rates in the recession actually makes things a lot worse. And so, yeah, inflation, although it was rising, Europe had a dodged a bit of a bullet in terms of avoiding a recession. And so the traders were placing bets that in fact, with rising inflation and a decent economy, that Europe were able to hike a lot more, so about 140 basis points, whereas in the US, at the time, this is from the same article, only around 60 basis points are further fed tightening, tightening meaning hiking is priced for the rest of 2023. So you can see that the European Central Bank was being seen as being way more hawkish than the Federal Reserve were. So markets are now leaning towards a 25 basis point height, rate rise from the Fed come February, the smallest in nearly a year. And so, again, you can see the hawkishness between the two, the European Central Bank was seen as being way more hawkish, and the Fed actually were seen as, again, less hawkish, slightly dovish. So what happened on the charts in January? Let's look at January. And so this is from the beginning of 2023 at the beginning, and we can look at until February the 1st. And again, what was expected happened. So in our private mentoring group, this called group, we've been long, and I've said I've been long since the end of December, right at the beginning of January, somewhere around there, and we had a long bias on the euro dollar or getting on the long on the euro.  And so many of the traders will attest to this, mainly made decent amount. And so, yeah, for the whole of January had a long bias, right, getting in long on that euro dollar. And that's pretty much what played out. So let's go to February euro dollars. So Europe, European Central Bank may need to deliver another half point interest rate increase after a planned hike of that size at next month's meeting, according to the Governor Council member class not. And so, I think in February, they did hike by 50 basis points. And the the consensus was that they probably may need another 50 basis point hike in order to try to combat inflation. But there was a shift, in fact, with the Federal Reserve, right? Whereas, well, in this month, we had the Federal Reserve officials could shed light on how many policymakers saw the case for a larger interest rate increase at their last meeting, whether they anticipated the need to take rates higher than previously thought contain persistently high inflation. And so remember the previous month, we saw that the market was expecting probably around about 60 basis points for for the rest of 2023. What would happen was is that inflation was was a bit sticky. And so persistently high. And so, to get again inflation down, you know, the the market kind of changed its view or slightly amended its view to think that or the Federal Reserve did as well was that the rumor was was that the they may actually hike more than expected. Yeah. And so with that being said, the market had to price that in so though the euro was still hawkish, in fact, there was a, you know, a much more hawkish sentiment to the dollar, right, which then should mean that the the dollar would have to be revalued and appreciate a bit more against the dollar, right? Because that there was a change in sentiment. And if you go to February, so February 1st to March the 1st, this is basically what you saw, right? You saw prices start to, you know, make lower highs, lower lows as the rumor of a 50 basis point hike was coming into play. Yeah. And again, it was a rumor because it actually did not happen. So I think they had by 25 basis points, but the rumor was that they may hike more than expected. And so that had to priced in to the market, whereas the month before, they were seen as maybe being a bit dovish. Yeah. So that is pretty much what had happened during the charts on February now into March. So Euro money markets, money markets traders briefly priced in a 4% ECB terminal rate in the wake of the releases, which would exceed the peak in borrowing costs at the turn of the century that compared to a 3.5% expected earlier this year with traders now betting the ECB will keep raising rates through February 2024. And so, in fact, that was very, very hawkish for the Euro in the market was expecting even more rate hikes than they had previously expected. Sorry, the month before. And so again, just similar to what happened with the US in February, where there was a bit of a change in hawkishness. In fact, money markets had priced in and higher terminal interest rate. And so, you know, from to four from 3.5%. And so that was quite hawkish for the Euro, whereas in Europe, the statement is, it says, now we are starting to fill those long and variable lags with, sorry, with which monetary policy works, Bellarina Uruchi, chief US economist at T-Row Price Associates told Bloomberg Television on Friday, the first sign of that is, I think, what we are seeing with Silicon Valley Bank here, lots of businesses and banks, we are going to find this year aren't able to operate at these higher interest rates. So again, to give this a bit more context, we all know what we should know all about, you know, Silicon Valley Bank collapsing and other banks, I think, Silver Gate Bank or something like that. And there were banks in the US that were failing. And this was brought on by higher interest rates. And so one of the factors was high interest rates. So let's go back to when I pretty much was talking about hiking too much causes economic contraction. So borrowing and lending costs were obviously affecting the banks as it was going higher, as the Federal Reserve were hiking, and that was just one of the effects of hiking interest rates on the economy and on, you know, companies and banks. And so the sentiment really was that how can the Federal Reserve continue to be very hawkish and continue to hike if there may be more banks in problems. And yes, there were European banks, you know, that were in problems. I think it was Deutsche Bank had a bit of a bail in now as well. But it was seen that the US banks were in a lot more problems than European banks. And so when you have, you know, a bit of a credit crunch and a credit crisis where the US is most affected, it means that if, you know, there's credit crunch, that would mean a contraction in the economy. And a contraction in the economy may mean obviously a recession sooner rather than later. And again, hiking in that environment is not prudent, because if you keep hiking, you're going to exacerbate the potential for a recession, right? You're bringing the recession closer to you. And so the, you know, Europe, while they had, you know, the quite hawkish bias, which did, you know, later change to be a bit more cautious as well alongside the Federal Reserve, there was still a hawkishness or they will still and still are more hawkish than the Federal Reserve currently in terms of interest rate hikes. So what happened during March? And this played out again, a more hawkish European central bank. There was a bit of a bit of a wobble, but ultimately we ended up going higher. And in fact, sorry, I haven't actually should actually cancel this one sec. Sorry. Right. So here we are. We used to do year to date. Yeah. So here we are in March. Yep. So from here to here in March, we had prices really kind of move around 400 pips from the low, nice buying opportunities at these lows before prices went to the upside in March. And so, you know, we're seeing the divergence between both central banks again play out into April and into May as nothing's really changed per se. The European central bank are still more hawkish than the Federal Reserve and are expected to hike more than the Federal Reserve. And you're seeing obviously prices drift higher. And so with that, doing a bit of a fundamental review, looking at the actual data, looking at GDP, we can see that the US is are the blue columns and you've got the European growth rate as represented by the dots. And so we can see that from January into April, we've seen a slight decline in terms of GDP growth rate for the US. But in fact, in Europe, we had a bit of a bit of growth, right? Prices have gone to the upside. Yeah. The number is lower in terms of growth rate. But remember that the European central bank was supposed to go into a recession. And the fact that they avoided recession to negative quarters of growth, right? They avoided that. And so that was seen as an absolute positive for Europe. Yeah. So we've had a bit of a divergence there where we had one since one economy contracting and one actually growing, although be it quite slightly. And then we've got inflation rate. And so the US inflation rate again has come down to around 5% here on this axis. On the right hand side, we've got the European inflation, which is actually around 7%. And you can see it slightly ticked up as well, the latest inflation data. So with that being said, let me go back. So inflation obviously for the US is coming down, whereas although it's come down recently for the European central bank, it's A, a lot higher than the US and B. It's on the upturn slightly. So it looks like again, the European central bank are likely to be a lot more hawkish than the US. And we can see what's happened with interest rates since the beginning of the year. And you can see in February the European central bank hiked by 50 basis points, whereas the Federal Reserve actually hiked by 25 basis points. And then you had another 50 basis point hike by the European central bank. And then you had only a 25 basis point hike from March into April. And so whereas the European central bank has hiked by 1% or 100 basis points, the Federal Reserve only hiked by 50 basis points or 0.5%. So again, very hawkish from the European central bank. And so again, seeing that on price, it's no wonder you're seeing prices grind a lot higher. And towards the end of the year, what's expected is that the European euro of dollars should reach at least 115. So let's see if that actually comes to fruition. Right. Anyways, just some notes. It's things you must be aware of. So data must support the narrative. You must have the data support your trade idea. Now we're dealing with trade probabilities, right? There are no certainties and no one has a crystal ball. And so when you've developed a trade idea and you've got a trade idea, you can continue to kind of hold the trade or have that bias if, for example, let's say the European central bank hiking rates, they want to hike rates. And let's say the data support in that narrative would be a continued rising inflation and supporting that may be a decent economy, right? Economy still growing. That data will support the European central bank hiking, right? Now, if Europe are going to go into a deep recession, then it's going to be difficult for the European central bank to hike in that environment. And so you can't start to say, all right, then well, I'm just going to start buying the European central bank if the data doesn't support the narrative, inflation starts coming down. Then although, yes, in this day, currently today, the European central bank are more hawkish than the Federal Reserve that can change if inflation starts to drop like a stone, then the European central bank are going to say, well, what's the point in hiking if inflation is coming down naturally and normally, there's no need to hike. And so data must support the trade idea narrative. And there are, again, no probabilities, no certainties in trading. So then the probabilities, we deal with the probabilities and there are no certainties in trading and think bigger picture. So there's lots of data points that can get you confused and distracted. The best thing is to think about the bigger picture, observe the higher time frames and look at the daily and weekly time frames, try not to get drawn into every single lower time frame, every five minute, you know, support or supply zone or trade setup, because you can have situations where you might get a pullback, right? Now, in March, you had a nice move from this high to when it's low to this high, right? Now, there was a pullback of around 200 pips. Yeah, this pullback on the daily was around 200 pips, something like that. From that high to that low, 217 pips. And so if you were to zoom in on this, on to like, you know, some sort of 15 or five minute chart, a lot of traders will try to, you know, we'll say, oh, well, you know what, Leon said that, you know, I should be bullish. I've done my fundamental analysis and I want to be bullish on this, you know, this currency pair. Now, yes, you're making the right choice in terms of being, you know, your directional bias, but ultimately, you still have to understand that there's, there's value, right? You're buying at highs. Don't buy at highs. If this is a move that has gone, you know, several hundred pips from this low to this high, in fact, what you should be doing is looking for discounts. Yeah, discounts. And one of the discounts I look for is fair value. And so if you go back to, if I go back to the day time for NCHAR, between this high and this low, yeah, 50% of that would represent fair value. So what happens is that you can see here, that price came down to fair value, right? And that was really the area that you probably now want to start to look for a trade sell. If you're looking for every five minute, 10 minute trade sell, you could be right about your direction, but because you're buying at highs and the, you know, the institutions want to buy for discounts, pullbacks, you know, 200 pips might seem like a trend on a five minute timeframe, but it's really just a pullback and if you understand the fundamental bias, just really kind of zoom out and look at where you are in context of, you know, where expensive is, where cheap is, and don't FOMO in at highs, right? Don't FOMO in in these areas, wait for the pullback, wait for a decent price pullback fair value, and then look for potential loan trades, right? And that's not necessarily me telling you, you know, a strategy or anything like that, but just giving you the context of why you should kind of zoom out and look at the higher timeframe, the bigger timeframes and give yourself a bit of context. Then once prices pull back into a nice, you know, zone and maybe support resistance or supplies, you know, demand zone that you want to look to get involved in, then maybe go down into the lower timeframe, start to look for cementries or whatever your setup may be. Yeah, so look at daily, weekly timeframes for context. Directional bias really doesn't change too often, and so, you know, I've been long on the euro pretty much now since the beginning of the year, as I mentioned before, and so that's what I'm releasing this in, I'm recording this actually in May, so it's been five months since I've been long on the euro and it hasn't really changed at all. Actually, it hasn't changed at all. And so directional bias, once you get a good trade idea, doesn't necessarily change from week to week. Some traders will say, oh, well, what am I going to be going to be long this week or short this week? If you have a good trade idea, you know, you can be in a trade for months. And again, I've created a video, I think it was like maybe a couple of years ago, a few years ago, where I was detailing how I was short on the euro dollar for a whole year. In fact, I was short for over a year, but I just made a video similar to this, where I detail month to month, you know, my euro dollar short trades and my bias and the reasons why, and again, I'll put that in the link in the top right hand side. And so directional bias doesn't change too often. It's not a week to week thing. You can have a directional bias for a good few months, if not longer, once you once the data does support that narrative. And yeah, that's pretty much it. So if you're still around watching this video, thank you for watching to the end and also as well. For the next video, I thought I'll put it out there. If you've got, you know, for the second quarter video, I'll do these every quarter. So if you want me to analyze a pair, just suggest it in the, in the chat below, if you're watching this on YouTube and the pair with the most, you know, likes or the most suggested pair, I'll do a similar analysis to this video or the same analysis to this video on that currency pair. So it could be pound dollar, it could be pound yen, it could be Aussie CAD, you know, just whatever you want. But again, the most popular pair, the most suggested pair, I will do a second quarter analysis on that for you guys. And yeah, finally, there is mentoring available. You know, we can get access to the private discord community where you can take your fundamental analysis really to the next level and go to trading180.com. I don't really have the mentoring open 24-7. I do have periods where I have mentoring as I like to keep the group small and really kind of focus on smaller groups. And so whenever the next opening is, it'll be on the website for you to join then. So guys, take care. I hope you enjoyed the video. Suggest a pair that you want me to look back on and give you the analysis on and again, the most recommended pair is what I would do. Anyways, guys, take care. All the best. Speak to you soon.


Okay, first of all, I, of course, have to thank the organizing for inviting me to this meeting. And I will talk about, in the main part of the talk, I will talk about the work that we actually have done with Boris and our postdoc, Monevel Pina. And at the very end, I will mention some very recent results that we've done together with Valeriy Kravtsov. But before I start to talk, of course, I have to, I want to, no, yes, I want to congratulate Boris on his birthday and recollect, as a previous speaker did some very old history, how I have first heard about Boris, which was probably the year of 79, if my memory is correct, when my supervisor, Tolya Larkin, came back from St. Petersburg, which was at this time Leningrad, of course, and said that he has seen a miracle. And the miracle was, as he described it, a boy who was, and he, as he described it, Aronov, who was, as you know, the supervisor of Boris, was drawing diagrams on the board and this miracle boy was writing, was writing the result in his head, which he computed in his head in the real time. So, and what I want to, what, was it like that? So, unfortunately, I couldn't find the photograph of the Boris at this time and this is the best, what you see is the best possible approximation to that. And although, as you know, Boris has changed a lot over time, I still, I'm sure that inside him still leaves this miracle boy of 79, and I wish that he continues to live there. Okay, so now let's go get to my talk. So my talk, as we were requested, as was requested, has two parts, has a sort of general introduction and then I will talk about the actual work that we have done with Boris. And then this general introduction, I would like to describe the situation, the theoretical and experimental situation with this old subject of Josephson junction arrays, which to me look very unsatisfactory. So, and what we are going to discuss, what I'm going to discuss in the new part of the talk will be a specific case of Josephson junction chains, which we expect to show very unusual behavior, but not directly related to what was observed, to what was observed experimentally in large arrays that were studied some years ago. So it's not, but it's not surprising because the regime is different. So these two parts of my talk are only vaguely connected. The main idea is that the main connection is that there are some strange intermediate phases which sometimes appear and the starting of these phases in many cases is pool. Okay, so let's start with this general introduction. So very naive model of Josephson junction array is that you have Josephson energy, which is cosine of the phase difference and which competes with the charging energy, which is proportional to the voltage squared and due to Josephson relation, voltage is the same as the time derivative of the phase. And thus, these two phase and the charging energy are represented by the canonically conjugated variables. And as a result, if you have large Josephson energy, it wins over the charging energy. Or if you have large charging energy, it wins over the Josephson energy. And you have basically two regimes. In one regime, you can call it insulator. That is, if you see it very large, you expect that low-temperature resistance should become infinite. You form an insulator at high-temperature at low-temperature in the opposite regime. You expect to find a superconductor. So that's a sort of naive and simplistic scheme. The reality, microscopic reality is very different. The reason for that is that on each island, there might be offset charge. Instead of this charging energy, which is simply quadratic in the charge, you have on each island the offset charge. Not only it is completely uncontrollable, but also it slowly changes with time on the timescales. Well, it depends on who did the sample and how patient was the person and how patient you are in waiting for these charges to relax. But they always, always move. So, well, this is a picture from the work of Aetnist and very similar by Zimmerman and very similar picture was observed, for instance, by Juro Pashkin, who is somewhere here in the audience. And you also see the same that if you study individual islands, the charge slowly drifts and some very patient people like this Zimmerman Aetnist told me that he waited for seven years and they didn't stop to drift. So, okay, so the one very important thing to have in mind when comparing, when thinking about realistic arrays is it completely uncontrollable and slowly, slowly changing charges here. So, let's compare and let's now discuss whether the simple picture that I gave you first is indeed observed in the arrays. So, in other words, what we, so the disagreement or some puzzle appears even at a very, very basic level of the face diagram that is observed, that is observed. Namely, in this simple picture, it's either the charging energy which wins or the superconducting energy it wins, which wins. And therefore, you either have superconductor here or insulator as a change disorder or you can also say that you change magnetic field. And therefore, you frustrate those on interactions and therefore you change from insulator to superconductor. However, what I'm going to show you that in many cases, but not very unpleasantly not in all, there is some intermediate regime which appears in between, which demands theoretical explanation which is absent. So, very first experiments after this picture was, after this radical picture was publicized, many experiments indeed show something which vaguely resembles either this, either the resistance curves up or down. So, and so, but also even at this time, there are all data in which resistance remained simply constant. So, my procrustus doesn't work. So, what I, so, so this little cartoon, which unfortunately doesn't work very well, shows the Greek hero as you know, procrustus who used to take people in his chamber and either cut their legs if they were too long or stretch them if they were too short. So, that's exactly what people try to do to fit the experimental data with this theory. And for instance, here you see very nicely superconducting regime. You see a single point here and then you see that this must be a quantum critical point between insulator and superconductor. But of course, if you remove this line, well, you see yourself. So, even worse here, in which you do see the same experiments at the nonzero magnetic field, you see that, well, naively you would expect if you look at this picture without these lines which guide your eye, supposedly. So, you will say that there is some intermediate regime and that's exactly what you see on these plots, but that's what is published. So, the situation actually became worse but was completely missed by community because for some non-scientific reasons, this work was basically abandoned with experimental work because these two people, Panitia and Siria, working in Grenoble and studying a race of some special topology, observed a huge regime of EGA over EC in which they see temperature-independent resistance. And this regime covered, well, more than one order of magnitude. So, very recently, a very similar picture was observed by Misha Gershengdon, who is somewhere here, maybe. Or maybe not, oh yeah, here, yes. Who observed that in some key, who observed that in a wide regime of the resistance is constant in a relatively wide regime of parameters, the race that he studied were also very a bit unusual. And what is important is that he measured, actually he represents his results in terms of the gap in this not real gap but sort of fit to this exponential activation or behavior. And this gap becomes exactly zero in some range of magnetic fields. So, all that, it's not always like that. Sometimes his arrays show this dependence, but some arrays show this strange bad metal behavior. He also, in keeping in tradition with Penetrientseret, never published his results. No, it depends whether it is, whether it depends, no, no, no, sorry, yeah, yeah, yeah, sorry, yeah, sorry. Okay, and finally, something very similar was observed by, very recently by Buschia for Superconducting Islands on Grafien, which is also a very good geoluson junction system. So, to summarize, and that was the end of my introduction, to summarize that many geoluson junction arrays show very wide intermediate metal state. And so, in this metal state, the resistance can be differ depending on the parameters on the magnetic field or on Ej over Ec by one or two orders of magnitude. And so, and featureless in the sense that there is no trace of some non-linear, some current voltage and the current voltage characteristics. So, it's really like a metal, but on the other hand, as your allies in this geoluson junction arrays, there are no normal electrons. So, it is, so, the proper way to think about it is that this state is some strange normal liquid of bosons or of wish, if you wish, of Cooper pairs. So, now, after that introduction and to the, under the rational review of the unsatisfactory situation in this, and our understanding of geoluson junction arrays, let me discuss geoluson junction chains, which you will think are even simpler object. So, and show and convince you that in this supposedly very simple object, there is still something very unexpected going on. So, the main point of my, the main point of my talk will be of this, that there is some non-trivial, non-ergodic, intermediate, non-ergodic phase, which appears in this geoluson junction arrays. And when I, when you hear the words non-ergodic, you usually think that non-ergodicity is something like a glass, but in the sense that it's due to large potential barriers, which forms spontaneously, and the four are the glass, which was made in the form of this beautiful Etruscan vase, or sorry, Egyptian vase remains in this form for thousands of years. But a non-ergodicity could also mean something different, that if you have strange kinematic rules, such as in this little child model, child-child play, in which you have allowed to move the cars only vertically and horizontally, you might get stuck, you know, like in a traffic jam. So, let's go to this, to my, to this subject of geoluson junction chain, and see where non-ergodicity happens. First of all, in this chain, if we discuss thermodynamics, oh sorry, so for a moment I will discuss just the ideal chain. Of course, if we, a bit later, I will talk about the effect of the disorder, which turned on this physics that I am describing, and this effect will turn out to be not qualitatively important, and that's very important. So, what we know about this geoluson junction chain? Well, first of all, we know what is its behavior at zero temperature, and at zero temperature the problem can, you can think about this chain as experiencing phase slips, which are exactly equivalent to the vortices in two-dimensional X-Y model, and therefore you expect Berezinski-Koslowski-Stowler's transition at some particular value of Ej over Ac. So, here you exactly at zero temperature on the real axis, you expect superconductor, here you expect insulator, and somewhere here you will say that, okay, that must be quantum critical point. Quantum critical point. So, you expect basically the same behavior that I was drawing before, that is a resistance, when you go down here, the resistance goes to zero, here it goes to infinity, and the same song and dance that I already performed. So, of course, we have to introduce these random charges, and the main claim of my talk is that this phase diagram is mostly wrong. In fact, what happens there is that there is indeed a region of good metal, which appears at large Ej over Ac. There is some region of insulator, which is here, but what happens at minimum increase temperature is completely different story. Namely, that there is a line which separates insulator formed at high temperatures from the metal, the metal which appears at low temperatures, and the phase in between is what you will call a bad metal, that is, it conducts somewhat, but it's non-ergodic, and bad in all respects. So, I will give you two types of arguments for this phase diagram. One argument is based on the classical, on the classical, or more precisely, quasi-classical limit here, and another argument is due to numerical simulations, which essentially probe the system along this line, and I will explain why numeric simulations are in some sense weird that they can probe the system only along these hyperboles. So, and also speaking about the effect of the charges, this behavior here and all quantitative values, for instance, what is Ej over Ac for, for the transition indeed depends strongly on the presence of random charges, but this transition, this part of the phase diagram, which is the most interesting for me, it does not. So, let's talk about the first, let's start with a quantum phase, with this transition first. So, the argument for that is that I look what happens at large Ej over Ac. At large, sorry, at large temperatures. At large temperatures, this term, which is cosine of the phase difference is always limited, so mostly the energy goes into the charging energy. When the energy is in this term, it means that the average value of the charge is also large, and when the average value of the charge is large, and because, and random, well, on different sites, the elementary process, which is generated by Josephson term, which corresponds to the transition of one pair between two neighboring sites, as shown here, has cost you a lot, a large energy. This energy can be positive or negative, it's not important, but the fact, but what is important is that in perturbation theory, you start to get large denominators, which are proportional to this difference of charge, but whereas your numerator is always fine, it is always fixed, it's just Josephson energy. Therefore, what happens is that this term, if you average it over the distribution of charges corresponding to some finite temperature, what you get is that typical value of this term is this Ej over square root of temperature times Cc. Square root of temperature appears simply because typical charges are of the square, are of the order of square root of, typical charges squared are of the order of temperature. Thus, you expect that the perturbation theory in this term converges if this term, if this typical value is smaller than one, and therefore, again, using the same arguments that were invented first by Anderson and then used for many body localization by Baskoal and Eralschuler, you see that what you get is that this, for when this parameter is much smaller than one, is smaller than one, we get many body insulating state. This argument, so in other words, what I have tried, argued that this line and this, when it happens is when T over Ej is larger than Ej over Ec as you see this, squaring this quantity, you get this condition. So, what I argued is that this line T over Ej is equal to Ej over Ec corresponds to real transition into many body localized state. So, when I write here insulator, it's really not just insulator, but many body localized insulator. Okay. So, well, one can do slightly better to convince oneself that this is indeed correct by studying the propagation of the wave function of the pair in the forward propagating approximation in which you average over the all processes in which the cooper pair moves some distance r, not necessarily that it moves just step by step, but it may move first here and then there and so you sum over all these processes, overall permutations of these steps and what you get is exactly the same result which you expected from this naive arguments and you can even discern the coefficient in this equation. So, now let's talk about what happens when in the phase, in this phase just before, just before full many body localization. So, classical system seems to be completely trivial because if, well, it has in the classical limit, you will think that, okay, I have charging energy and Josephson energy, these are two independent quantities so I can compute trivially the free energy. However, the equations of motion are not trivial and because, well, they're not exactly solvable. So, the question is whether these equations, what these equations of motion, whether they reproduce when if you follow the time evolution given by these equations of motion, if you give, get the same result as from the aerodynamic average. So, one can actually use for this classical arc for what, to understand what happens in the regime of very large temperatures and that will be a classical equivalent, what I described for the quant, for the many body localization transition. One can use the very similar arguments saying that I have now distribution of the velocities of these phases and then I ask how the noise which is created somewhere far propagates through my classical system and what I will get in this propagation is the exact analogy of the, of the denominator that appears in the quantum perturbation theory. Everything is completely equivalent and therefore the noise which propagates and therefore you, you conclude that the noise which propagates a large distance from the source contains the product of these factors and therefore averaging over this distribution of these velocities what you get is log normal distribution of the noise of the noise values. So, well, what you say is that typically noise decreases exponentially when you go away from the source and so, but then you should ask yourself where the noise is generated at all because that looks like that everything in the system at high temperatures dies, dies, dies, but it's not completely correct because in which you can see by studying more carefully the, what happens in the system if you study proper, if you include the fact that there are some low frequencies or to be more precise the frequencies which might be in resonance with the frequency of the noise that propagates and then I immediately see that there are some very small denominators and you have to be careful with these denominators. So, the qualitative argument is that in order to get the chaotic behavior in this system you need to have at least three islands because for two islands, for two islands with two close frequencies or two close charges if we translated back into the Josephson junction language you have still integrable equations but for three close frequencies you can generate, you can, you expect a chaotic behavior if their frequencies are close how often it happens. It happens if the, if these frequencies are close with the, have frequencies of the order of which differ by the, by unity and that happens with probability square root of two, square root of t for any pair of frequencies and therefore t for three frequencies. So, you, so the, therefore the following picture emerges that you have some rare triads of islands which happen to be in almost in resonance with each other. These resonances generate the noise as well we can easily see numerically and this, but these triads are rare and they talk to each other through this silent and dead regions of the, of the space. Okay, so, so then you, if you ask about, start to ask about physical properties then you should say that how the transport happens in my system. The transport happens like, like electrical current or conductivity happens in my system is, it happens in something which resembles very much mode transport in the conventional insulators that you have, that some charge which is, which moves from one chaotic system to another and then to another and each such motion is associated with the resistance which is distributed according to this log normal distribution that we discussed, that they discussed before. So, the sum of course of the chain is the sum of the resistances and that all translates into the, into the prediction that the resistance of this chain is, has the resistance of this chain, sorry, logarithm of the resistance of this chain scales as internal energy or temperature times logarithm of temperature. So, also this picture means that tells you that there are some distribution of relaxation times associated with the motion of the charge between these rare triads and therefore, and therefore the properties, the physical properties of the system has this long exponential, relatively long straight dependence, time dependence of the resist of the properties. So, well then we check this numerically and we saw both that the conductance, so that of course we saw trivial fact that at low energies the, at low, sorry, at, at, yes, at low temperatures and energies the conductance is large, we approach superconductivity, but that's of course whatever, what everyone would expect, but at high temperatures, at high energies, well not extremely high, you see the energies are still pretty decent here, the resistance is roughly exponential in temperature or the energy. So, but what is even more interesting and important, what we saw numerically and that is that the relaxation is very slow and if we study that thermodynamic quantities, such as fluctuation of this internal energy and extracted from the extrapolation of these curves to the infinite times, then we find that this extrapolation never leads us to the pure thermodynamic result, which is shown here by red line, whereas this, all these curves correspond to finite time to the measurement, to the measurement of this quantity at finite times and so if you extrapolate them, they go at most to this dashed line, so there is always some difference between the thermodynamic quantities and the extrapolated ones. In other words, this picture of these triads, which stay, talk to each other poorly, but also their position is more or less fixed. That is, of course, they move a little bit around their position, but they do not move very far, so the system, the whole face space of the system is broken into different parts corresponding to different position of these triads. At least that's my qualitative picture of this non-ergodic behavior. You can also, yeah, so here I can, well, I don't need all these song and dance here at this part, because I can really go to this very far long times, but if I, but for do, to do numerical, to do, well, these times become, to get, these times become so long that I really need to start to do some extrapolation. By, well, you see, it's not very good to talk about temperature, because I'm basically arguing that there is no temperature. What is the right control parameter is the average energy, which is exactly what I fix in the simulations. Yes, yes, yes. Okay, so let me now very quickly skip this to the, to this part of the, on the quantum simulations and just tell you that the reason that we did exact numerical diagonalization to study the behavior of the system in, with a fixed number of charging states, and instead of allowing the discharge to fluctuate from minus infinity to infinity, we allowed it to fluctuate from minus q to q, and therefore, and this is exactly equivalent to the probing the system along this line. And what we saw is exactly the same quantity that is entropy, which we define as a von Neumann entropy integrated over the half of the system is in some, it does not reach its thermodynamic limit in the large range of parameters. That is, we, in this system, we expect the transition to the fully localized state somewhere here, well, here, and there is a wide range of, roughly speaking, a factor of three, where the entropy remains remarkably less than its thermodynamic limit, which is logo, well, because we used just five, five charging states, while the, that's the, which is shown here by red line. Okay, so since I got somehow out of time, which I thought it was different, let me just go to the conclusions, which you can see here, and I'm ready for the questions. Thank you very much.