11:02:10 Okay, so let's start.
11:02:10 So welcome to the lunch and dinners session. So the first speaker is Joelle.
11:02:17 So go ahead, 20 minutes less questions, do my best. So, let me thank the organizers in particular for their commitment to making this a success in challenging circumstances I feel like I've already learned a lot, scientifically.
11:02:32 And what I'm going to talk about I think you will see rapidly connections to too much presence talk earlier today and also to Professor bushels talk earlier in the week.
11:02:42 So I'm going to talk more about these unusual properties of one dimensional dynamics and focusing on how at least one aspect of the KPMG universality class, namely the ze equal to three hats, super diffusion does seem to be visible in solid state experiments,
11:03:00 which was a pleasant surprise.
11:03:03 So it will give a little bit of background on.
11:03:07 I guess the simpler cases and then a little bit about KPZ but i think is already came across KPZ is a very new idea in this context and people are still working out various aspects, but there has been an enormous amount of progress in the last two years,
11:03:21 even though I'm a theorist, there will be some experimental strong component in this talk before what.
11:03:27 Alright so I'm very quickly as motivation since you've already heard about this.
11:03:33 It turns out that even though we've known for a long time that one dimensional systems are especially tractable, even when there are in the thermodynamic limit and have a large number of particles and so on.
11:03:45 The first paper I'm going to talk about is just to review quickly.
11:03:49 And I'll talk about some of the older history as well of course but this slide is just our papers if you want to read more.
11:03:55 Why are there new kinds of hydro dynamics in one dimension.
11:03:59 What does that mean and how these sort of integral models in particular fit in between what you could view as the various other possibilities out there for how things move around, depending on conservation loss so the special case here is of course that
11:04:14 they have an infinite number of conservation loss. But the importance of that for dynamics was really not understood as well as it should be until five or so years ago.
11:04:24 So the next question is, does that actually matter in an observable sense for matter that we can measure in the laboratory.
11:04:33 And you've already heard about one case of that in this conference. What I'm going to talk about is, basically, I guess I'll first show some numerical evidence.
11:04:46 The lead us to conjecture. Something that there's, there have been steps toward proving as in too much this talk, which is that it seems like if you have a combination basically of interoperability and some notion of by Satrapi or non a billion this roughly,
11:05:01 then you do get this unusual super diffuse of behavior, the numerical evidence for that isn't the first paper here. The second paper here the story is basically going to try and convince the oldest folks who did the neutron scattering on spin chains back
11:05:15 back in the old days to see spin ons that actually they miss something, we thought that might be more impressive if we could convince them that if we went to them found new people, but they were good sports and the main point is you can see a regime,
11:05:29 which is not where we normally look at neutron scattering on spin chains.
11:05:42 And then the last paper here, which just got online published in parallel today, in fact, is understanding how to reconcile the sort of high temperature limits of KPZ with the low temperature limit that we all know about of literature liquid type physics.
11:05:47 But where there is good evidence I would not say an absolute proof, which is hard and experiment, especially on solids, but there's good evidence for is equal to three house.
11:05:58 Alright so this next part I'm going to go through very quickly because I think people here know it well so standard physics of many particles tends to depend on a calibration to it gives ensemble.
11:06:10 We know that there are exceptions so MDL systems for example certainly don't thermal eyes in a conventional way, no matter how long you wait.
11:06:18 But another possibility is that maybe there is a notion of equilibrium, but it's different from the one we normally think about because there are extra conservation loss so instead of the Gibbs ensemble.
11:06:28 We have the generalize Gibbs ensemble.
11:06:32 And turning that into a practical machinery to calculate how things move around, was maybe the recent progress.
11:06:40 So very briefly, much of what we do depends on the assumption that things relax and in a way that gives us finite and then your response coefficients finite diffusion coefficient and the original example due to Einstein.
11:06:52 There's a whole philosophy of how returning the equilibrium, from a spontaneous fluctuation is the same, ultimately is returning the equilibrium. When you're pushed away.
11:07:02 So a whole lot of standard physics is built on diffusion.
11:07:07 This talk is mostly about two kinds of exceptions to diffusion.
11:07:11 But just as a reminder of, you know what you would expect, probably if you waited long enough, in any real solid with photons and all the other complexities, you'd expect something like a diffusion constant where you do have a conservation law, number
11:07:24 of particles let's just talk about particle number is the simplest case.
11:07:28 And then if we started with a narrow peak and the number of particles that would spread.
11:07:33 It would be a broadening Gaussian is a solution of the diffusion equation. And the way we translate that to a magnet is, well, in a magnet let's say that the total magnet ization is concerned because of the symmetries of the Hamiltonian let's assume that,
11:07:46 then the sort of zero with order guess is that the organization density will behave in the same way, and that is a dynamical exponent of z, will the two.
11:07:57 So this is what experimentally, you might expect to see a lot of the time like if you had a dirty crystal with a lot of momentum relaxation and scattering.
11:08:05 This would be your best guess.
11:08:08 So where things can become different. We know that the number of conserved quantities in a system, and whether there are more than one effects whether you get the fusion or other behavior.
11:08:16 So for example, the behavior of water and air is not diffuse in general because it's described by this more complicated set of equations. And this is in the simplest limit zero authority hundred MX because there are three conserve quantities.
11:08:31 There are three of these equations.
11:08:34 And so now you could ask, Well, if I had an infinite number of conserved quantities would I have to solve an infinite number of equations, and the magical fact is no not really, but you can derive all these through a sort of reduction of the Boltzmann
11:08:49 equation, and maybe the key physics point is that the Boltzmann equation in standard fluids has a lot more information than these 300 dynamical equations the Boltzmann equation as the full one particle distribution function, these three equations on the
11:09:03 slide are only about three integrals over that. So hundred remix is ultimately the problem with how local problem, local equilibrium becomes global.
11:09:11 So I'm going to talk about the one dimensional spin chain, and in particular the XXZ spin chain for this talk, so there's the Hamiltonian which you've probably seen before.
11:09:20 It has a lot of concern quantities. This is from a paper of prison.
11:09:24 And the main point is you know we need some practical way to deal with these enormous lists of conserve quantities.
11:09:30 So to do that, it turned out in fact that half of the conserved quantities that sort of odd ones had been missed for a very long time for at least 40 years.
11:09:40 That was understood starting in 2011 and one can once what has new conserved quantities, it starts to become possible to answer a lot of questions about dynamics that were not possible before.
11:09:50 So even though beta solved the ground state of this model in 31. And the third MX were done in 1970 ish. It seems like every 40 years something interesting happens and we're still I think in that interesting period from 2010 or so.
11:10:07 Alright, so I'm going to come back a bit to what happened between 2010 and 2019 But first, This paper by Tina is an advantage in prison was very exciting.
11:10:19 I think the people in the field and I'm going to talk about experimentally trying to see something related to what they proposed which are what they observed, which is that infinite temperature at the Heisenberg point.
11:10:31 In other words, the point where the X y&z couplings are all the same.
11:10:34 You don't see the abusive behavior you instead see a kind of behavior, both in the exponent and in the scaling function, and we also we reproduce this after the fact we agree with what they said that the sort of noisy burgers equation or nonlinear version
11:10:52 of diffusion gives rise to a behavior that is faster than diffuse of behavior but slower than ballistic behavior that's equal to three halves.
11:11:00 So, as a quick picture that this is what I mean by saying the blue curve is not spreading as rapidly as a ballistic system but more rapidly than defensive system, and this appears all over the place in classical physics.
11:11:14 I would say this is almost the first occurrence first occurrence I know about anyway, in a quantum coherent system.
11:11:19 Why, as you've already heard is still sort of being worked out but parts of it can at least be shown and I'll give a reference later on.
11:11:26 So, I'm going to skip a little bit of the background on that yeah maybe this is a good slide to show for give credit where credit is due. So a lot of the.
11:11:37 When I said five years ago interesting things started happening a lot of that is in these two papers. I'm going to talk about a way to understand what happens in the ballistic case first because that was done a few years ago.
11:11:47 And that will lead us now to the Heisenberg case where things stop being ballistic So in general, this XXZ model has a ballistic regime, when it's easy axis, sorry, when it's easy playing.
11:11:56 It has a diffuse of regime, when it's like easy axis at the Heisenberg point that's where you might hope for something in between.
11:12:06 But you would have to be very clever to hope that what was in between was this KPZ universality class.
11:12:12 Alright so the basic idea of those papers which has actually occurred before in classical physics, when you think about, like many solid tons, so integral classical systems have the same kind of equation.
11:12:25 And the way to think about it is that in either classical integral or quantum integral systems. The way Croisette particles move, is that even if you've got several of them coming together.
11:12:35 They don't randomize momentum, they ultimately pass through each other. But there is a delay, or a phase shift and quantum mechanics and that means that the effective velocity of one particle depends on the density in momentum of all the other particles
11:12:52 at the same space time point. So it's like a Boltzmann equation, except that the velocity is a kind of integral itself so it's an integrity differential equation.
11:13:01 But we now understand various cases of how to solve this either analytically or numerically. And it's really quite powerful and I'll try to convince you that it's powerful in the ballistic case.
11:13:10 But just by staring at this it's not at all obvious that something interesting is going to happen when you go to the Heisenberg point, but very briefly, so this is the picture I just described, that we're this equation comes from, and it's actually equivalent
11:13:24 to that infinite hierarchy you would write of Euler type equations.
11:13:29 Is that one solid time moves through another, for example, and I think this is for the classical nonlinear shooting equation, but there is a time delay quantum mechanically we know that in internal systems, it's not the particles are free, they have faith
11:13:43 shifts, when they scatter, but those spaceships are like a delay and semi classic so the surprise is not that everything is captured by some of the classics, but a lot of things are captured by this effectively semi classical Boltzmann type equation where
11:13:55 the quantum mechanics just went into that self consistent velocity.
11:14:00 So, the neat thing is this gives you a whole recipe to solve a lot of problems because now you have a recipe to get from sort of local generalize gives ensemble, which we think sets up quite rapidly it sets up on the scale of a few collision times in
11:14:13 general, but then the very long sort of streaming timescales how you evolve on the manifold of GG ease. That's what's given by these hydrodynamic equations.
11:14:24 And this even works, you know, not just for kind of one variable x over key scaling limits, but it's a remarkably good approach for long time XNT limits and just to kind of convince you that numerically.
11:14:34 This is a talk from two years ago maybe but these are pictures comparing what you get by microscopic DMRG simulations and from those hundred and chemical equations, and you can find cases where they lie right on top of each other and there are small but
11:14:48 measurable deviations from what some say ordinary hydro would give. So this is if you like a check on both because they're making totally different approximations, but neither one of them seems to be very approximate this is for the XXZ model at Delta
11:15:01 of like point five so reasonably strongly interacting.
11:15:05 So now let me finally come to this gap plus point.
11:15:10 The KPMG equation and then you know what we try to fit everything together and go to finite but not infinite temperature.
11:15:16 The point of this paper and also studying a lot of other spin chain so I won't show everything because the only experiment I have to talk about is the good old Heisenberg spend half chain.
11:15:25 But the point is you do get zero drift away no ballistic transport, but an infinite diffusion constants this intermediate behavior that is super diffusion and the conjecture which there is now a lot of evidence for is that that depends on the combination
11:15:39 of interoperability and a non a billion symmetry if you'd like, which in this case is a form of Saturday.
11:15:47 All right so and I wanted to mention in particular, there are leave Lynyrd type atomic experiments that fortunately already heard about in this conference, those are very beautiful, but we fool and Dubai.
11:15:57 I'm going to talk about the Heisenberg point so those tend to be in the.
11:15:59 Those are experiments that would have to tune a bit to get to the Heisenberg point.
11:16:10 But that you can be naturally tuned to the Heisenberg point basically by the cubic symmetry of the solid.
11:16:16 And then, yeah, I think I'll skip the second comment that we have thought a lot about broken interoperability.
11:16:22 So the point here is this is an actual crystal that was used in the old days, to kind of establish that you can see spin ons in an actual material. Potassium cut for fluoride.
11:16:33 It's very well described by the one the Heisenberg model, unless you go down to low enough temperature that the one the chain start to talk to each other, so below 25 Kelvin or so it becomes more like a three dimensional material, but a great thing about
11:16:46 this KPMG physics is that it's really not a low temperature phenomenon.
11:16:50 It's a moderate or high temperature phenomenon, but of course in a real solid you'd worry that as you go to high temperature eventually you melt the crystal and before that you produce a ton of photons, and the electronic system is not really a closed
11:17:03 system so I think the reason for doing the experiment is to ask, Is there a window of time that you can observe, where the physics is not ballistic and not diffuse it, but this intermediate behavior, and in particular when I say that people didn't really
11:17:18 look for this. In the old days, this is not contradicting something from the old days it's that people normally would look at high energy and low temperature, and try to resolve this kind of spin on physics, and they also tend to look near Q equal to
11:17:32 pi.
11:17:33 This talk is really about mostly near Q equal to zero.
11:17:37 And it's about the opposite limit of frequency and temperature it's about high temperature and low frequency so in other words long time limit. But hot enough that the system is really not and it's low temperature limit things have time to interact and
11:17:49 do interesting stuff before they ultimately become defensive as you go to higher and higher temperature. So the particular thing we're going to do.
11:17:59 So, yeah, let me maybe I think in the interest of time, skip over some of this.
11:18:03 The, there's the crystal structure on the left and we're going to measure the standard neutron scattering observable integrated over a window and frequency and ask, does that scale with wave vector cube and the black curve here are numerical simulations,
11:18:18 and there's only one sort of number to get out which is what is the scaling with momentum, and we sort of know because we've defined a window with finite frequencies it's hard to go too low with neutrons too high and you would hit other physics aside
11:18:32 from the point we care about. So there's certainly only you know one decade of scaling.
11:18:37 But you can say that, until you get down to, you know, low temperature things get complicated there's 3d cross and other issues but there's a pretty broad range of very easy temperatures to work at from say 150 Kelvin up to 300 Kelvin.
11:18:50 When the fit is much better to KPMG behavior, or at least let me be precise. The fit is much better to z equal to three halves, than it is to is equal to one, is equal to two.
11:19:02 In the values are say in a range of one in the third to one and a half plus a little bit.
11:19:10 And it is a nice success of by the way one dimensional numeric said find a temperature. So if you if you put the data in the right way, you can really see that these matrix product stage simulations are dmg computing something.
11:19:22 And the key is, I think most clear in the bottom right figure that you can draw a pretty good line through the points, even at room temperature.
11:19:29 So that is really a regime for quantum dynamics where we wouldn't have thought to look you know normally would say go look and atomic systems don't have to worry about phone ons and go look at low temperature to remain coherent, and maybe the surprise
11:19:47 me, which I like. And the papers out in nature physics a couple of months ago this of this references old. I guess the surprises that there is quantum coherent dynamics of a very interesting category that you can start to see nice signs of, even in a
11:19:55 real three dimensional solid at 300 killer. And I think that's the main point I wanted to get to, in my 20 minutes so if I can have one or two more minutes maybe I'll add a couple of other you know implications of that and the main one is just how does
11:20:09 that fit together with what we learned in school, maybe about how to approach these spin chains theoretically so there may be two things you learn if you care enough about one dimension.
11:20:19 You learn how to solve them for the small number that are solvable, which is through the beta onsets, but then maybe the other thing you learn is that even for spin chains that are not exactly solvable.
11:20:31 There's a very useful tool, which is sort of letting your liquid physics and bosun ization and things like that which is that for the the gap plus phase, up to the Heisenberg point but including the Heisenberg point of the spin chain.
11:20:43 There's a very nice way to look at it as free both sides.
11:20:46 But now all of a sudden you have a problem because free bosons rz equal to one.
11:20:51 They don't look a lot like z equal to three halves.
11:20:54 So something about that low temperature physics has to crossover as you raise the temperature or wait a longer time or look at a different links scale so the point of this recent paper is to try to understand how is the function of space and time do you
11:21:22 But the nice thing is there is quite a broad range where you get an onset of KPMG hundred mimics, and as a general rule, the onset is not some terribly inappropriate scale it's just like one over temperature.
11:21:23 between these two regimes, as you lower the temperature, you start to see the leisure liquid physics all it turns out you have to go to really rather low temperature and rather long timescales because of some pre factors being small.
11:21:34 So, and I won't try to go into all the spatial dependencies and things like that but this is sort of a plot of what this looks like. In the auto core later that you can see that key to the minus two thirds behavior setting in for a bunch of different
11:21:49 values of temperature and the paper is basically systematic analysis of how far do you have to go before you start to see KPZ say in the auto core later and other quantities.
11:21:59 So, just to kind of conclude the main point I wanted to make is that, you know, I think the ballistic side of things, was understood a couple of years ago.
11:22:10 And it's great that they're experiments on that from the atomic and the Heisenberg point, I think the action really started with that 2019 paper I mentioned, and now there is experimental, you know, realization of that in a place where you might not have
11:22:23 thought to look.
11:22:24 So as far as you know what's been going on with theory in the meantime, and let me point out that with neutrons, there is no easy way to form to see the full KPZ spectral function.
11:22:34 You can do other things you know you can change temperature you can add a magnetic field we're kind of trying to do that but it's hard to get a strong enough magnetic field to preserve the system enough.
11:22:43 So experimentally.
11:22:45 You know one thing we're trying to do is to get other spin chains that are say more on the gap plus side and confirm that things are different, it's very easy to find things that are diffuse it but can you find something that is ballistic over a timescale
11:22:57 but yeah maybe the good news is if you choose the right material, then you can have quantum dynamics for surprisingly long time, and neutron scattering, even at high temperature is a good tool because it can get too low and the frequencies to see collective
11:23:11 behavior, not just single spin on physics say.
11:23:16 So I think this has already come up but I'll just repeat some key facts about the theoretical understanding so there's an increasing understanding of which spin chains have the probably have the KPMG universality class behavior, to be precise, I think
11:23:27 there's an interesting distinction here, which was Vedic as question earlier I think this paper by ETFs get all basically proves that z equal to three halves obtains under certain assumptions about, you know, having an interoperable system with some greater
11:23:36 cemetery than just you one.
11:23:47 confirm the observations of libertine at all.
11:24:05 It is also very hard to see experimentally at the moment but maybe someone will find a way. And then I think, you know, when I say we, it isn't yet proven I think there are nice ideas out there for I think they're probably right it's just you know, less
11:24:17 than a detailed microscopic calculation but I wouldn't make it seem like it's totally not understood where KBZ might come from. So I thought I would mention.
11:24:26 There are other papers now but I thought I would start with what was the first as far as I know, which is by Bolton done.
11:24:32 Okay. So with that, I'd like to thank all the people we work with both the experimentalists at Oakridge Alan Shay's a postdoc, Ellen tenant and Steve Nagler are very accomplished people in the world of spin chains and ladders, and my group my current
11:24:47 are tests and Nick there's Nick and postdocs Maxime DuPont was really the hero of a lot of what I talked about and let me, let me mention that he's very interested in doing quantum dynamics on quantum computers which is actually the topic of the feature
11:25:10 program that was just recently approved so Maxime is very much interested in this kind of boundary that other people are interested as well. And then of course there's been some very good people working in this area who pass through Berkeley in the past
11:25:14 Thank you very much.
11:25:16 Hands up, people who want to ask questions.
11:25:17 and there are three of them. So let me stop there. Thanks.
11:25:22 Yes, you need.
11:25:25 Yeah, maybe just to break the ice users in.
11:25:29 Yeah, so. Yeah, thanks. It's a wonderful talk. Lots of material covered up. So you mentioned earlier so again at low temperature second was this is free for about 30 minutes, which are kind of the typical wireless.
11:25:50 Now, The question here is it, whether if I start from that and various temperature.
11:25:55 Whether KPMG sets because of own collapse or legacy is not important to do favorite feeling.
11:26:08 I mean, I think, If you have okay you could have an interoperable field theory that would have, I think, super diffusion if it had the right properties so I don't know that it's directly connected them government here here's my rough picture of what's
11:26:22 happening with the lender liquid picture if you like so you start off and you know you can usually analyze the leading behavior of perturbations to the lender liquid and get estimate of conductivity from like memory matrix and things like that but there's
11:26:34 is an assumption, when you, when you do that so I mean, this is something that I had assumed that I've committed but I I knew that it was applicable in some cases so it wasn't two biggest thing.
11:26:44 You know you ask well I've got a current that would live forever in the lunch or liquid limit and I say okay well here's a perturbation you know what preservation is for example, for a sucky and Matt Vega is probably the classic paper on this or at least
11:26:55 one classic paper, you ask, you know, what is the leading process that would cause this current to scatter, and then I assume that gives rise to an exponential decay and I think in in systems that are not interoperable.
11:27:07 That is the right picture that the corrections to the ledger liquid, give you, unusual power laws and conductivity so you get kind of activities that blow up you know with the eighth power of temperature for example or, you know, some power of how far
11:27:20 you were duped or whatever. And so I'm glad can often be the leading perturbation that causes scattering the current.
11:27:28 But the main point here is that picture of what the scattering does is not really correct in the integral model because it doesn't take you all the way to just gives ensemble, there are limitations on what the scattering can do only because of interoperability.
11:27:42 So if you like what's breaking down as the sort of memory function idea that you can just assume that once you've got a rate you can make that a exponential decay.
11:27:52 So that made sense I think that's, you know, that saying that there still is a timescale for these perturbations to kick in and you can kind of calculate you know when does the lunch or liquid behavior, start to stop, it's because of those I'm claps and
11:28:05 other things.
11:28:07 Although yet, but the ultimate fate from having unclogged is different than the integral model because unclothed can't thermal eyes you fully. Well if you had a, you know, if you had a couple of other perturbations and you destroy the interoperability,
11:28:19 then you would get the correct and so in other words I think it's fairly special cases where this is the right physics, but there is physics where all the unclip and other things that are not in the ledger liquid, they break the ledger liquid but they
11:28:34 give you KPZ instead of diffusion.
11:28:35 What does a search on serving doing it.
11:28:38 Based getting the latest or not.
11:28:42 You know, for for longer but that is what was your feeling well okay let me see me move by not having back and I need an ok so i would say if I have an integral role model with a non and billion cemetery, I can get KPZ and their models like that that
11:29:05 even have a less so in that sense I don't need a lattice and I don't need to get KPZ is the short answer is it. Should we should move on. Yeah, yeah, sorry. You're better, but I enjoyed it. Thanks a lot, a lot of interesting things or maybe something
11:29:16 I mean there's another you know nice model we can implement which is saying one which is much more linked to this table and half physics which has all this stuff a logic to patients as a gap and something like that.
11:29:28 to some of the other experiments you do which I don't I'm not gonna talk about afterwards. So the questions that you know You talk a lot about Latin to liquid.
11:29:35 And it's also we can tune basically Bq need to be extremely strongly correlated in the in the experiment.
11:29:44 And, you know, could you map that onto, onto a sanguine like model because many of these thin chain, things can be mapped the sanguine into into into single leg.
11:29:57 That's right, I think, I think the design Gordon model has is integral and it will have this range of behaviors and if you could get to just the right point where it has the SU to cemetery.
11:30:06 There is such a point, I believe, then you will get this kind of physics, I mean, the only the advantage of doing it in solids I'll put it that way is the fact that the solid is cubic has sort of put you at the isotopic point, naturally, so you so you
11:30:19 all you've done by going to a solid is remove one tuning tuning parameter that you need another hand you've added lots of Decaux hearing things, so I think it'd be fantastic to have a realization of this point with Adams I think there would be some advantages
11:30:34 to the atomic case if you can pull it on it. Because I mean we observed something that looks like in hydrodynamic in a very very strongly correlated very far off equilibrium sanguine model, which looks like really time local equilibrium.
11:30:45 Now we are completely lost in how to describe that.
11:30:49 Yeah, but it might be some you know maybe we should talk about maybe some, some of your hydrogen me see approximations.
11:30:59 Middle observations. Yeah.
11:31:01 And there are different things that happened and give you nonlinear behavior, and sometimes you can get continuously variable exponents like if you have a, there's certain things in enlightened or liquid certain ways of driving it that the few of us worked
11:31:11 on that will give you other ways to get power loss, so I don't really know which is the right one for your experiment like yeah I mean,
11:31:18 if you can see the unusual scaling and just linear response correlate, then it's probably something like what I talked about today. If it looks more like strongly driven nonlinear thing than it would be another thing that we should still talk about.
11:31:32 Yeah, yeah, no, no questions that we have to do the Linda responses sermons now. That's true.
11:31:39 The questions that we have to do the linear response experiments now. That's true. Yeah, because I think you can divide up, you can divide up the cases where you got unusual parallels there somewhere. It's really a linear response phenomena like here and there, others were at linear response, it would be defensive but because it's strongly
11:31:52 driven, you get something else. Yeah, so we shall we. Okay, thanks for us the word to me.
11:31:55 Then I'm, are you there.
11:31:58 Thank you Joe for the nice stop, very brief question. Do you see any prospect of a two dimensional system that could show dynamics like the two DK PC.
11:32:11 Yes.
11:32:11 Um, I don't immediately.
11:32:15 I do think it would be very nice to take some two dimensional crystals and analyze their neutron scattering in this way and just look for collective spin dynamics but I could be in other words I don't think people have ever thought very much about this
11:32:26 regime of low frequency high temperature, it's usually the opposite. But I do not know a case. Maybe someone else on the call does but I don't know the case that would naturally be two plus one DKPZ would be great to have one.
11:32:40 Thank you.
11:32:41 Can I can ask a small question, and present, there is this all this enormous literature of mapping.
11:32:50 Starting from the supersymmetric young males and then calculating expectation of products of operators and then mapping this onto a spin chain, which is usually integral and usually with larger groups, I mean on a billion.
11:33:07 What does the KPZ have to save anything about your regional model doesn't this shouldn't this tell you something about the model you started from.
11:33:18 Yes, it tells you something about correlate or is that high temperature in these models with non a billion symmetries but I don't think people had really thought to, to look at it but if you like that a leaf ski at all paper I think is kind of the place
11:33:31 I might start.
11:33:32 Okay.
11:33:34 Okay.
11:33:35 Thank you very much. If there are no more questions, yours. It's your turn.