11:31:06 So,
11:31:06 let me introduce you, but it's your faculty from while we have a few.
11:31:17 I think he's university but he said, Yes, yes. Okay. Okay. So, you're gonna start.
11:31:19 So I think he's university but he said, Yes, Yes.
11:31:20 Okay. So, hello, and I would like to thank the organizer for the invitation. And today I would like to present some model that emerges in some strong coupling limit, and the smaller some kind of peculiar property so I think it's gonna be interesting for
11:31:36 for the police conference.
11:31:38 So the setting, and consider is what is now known as winch
11:31:46 winch dynamics, which essentially means that we started the evolution, after in preparing the initial state in some physical internal state and which can be GM state or their mistake.
11:31:58 And then it is to suddenly change some global parameter, like a magnetic field or a capital costs, and the the system that are generally consider are many buddy.
11:32:10 So the typical example has been that the systems are under 50 years. Here I'm focusing on speed up the systems.
11:32:25 Soon particularly means that they look angry space is the final dimension up and they total dimension scales exponential with the new the volume or the system.
11:32:30 Now in this kind of lattice model there is a basic theorem of quantum mechanics that tells us that there is not an acceleration.
11:32:40 And the reason is that the, the energy medicine discreet.
11:32:45 So this means that if you wait sufficient long time your state will be close to your original state. Okay, as you wish.
11:32:52 Now there are ways of circumvent this theorem.
11:32:56 And one possibility is to consider relaxation, on average, which means that you imagine to to consider the state after a long time, random 20, and then you wonder what is expedition value of some or some observable.
11:33:12 And the answer is that it will, there is a high probability that you will be close the particular value that one call that the discretionary additional value of the observer, and can be describing some effective way like diagram ensembles or the mandala,
11:33:28 and samples.
11:33:29 In other possibility in the least the one that I'm considering today is to go to the family family.
11:33:53 This is because in the terms that are mainly meter they deliver space in the game you can stay states become dense energy.
11:33:56 So, this means it is possible to see some broad session properties and in other words if you study expedition might have some observable is gonna relax.
11:34:12 To some, somebody, and it is generally believed the internet system, you will find that you can describe with this stationary battery by means of thermal ensemble, Mel Gibson samples, you just need the one parameter, and instead if you can see the more
11:34:24 symmetric systems like integral.
11:34:26 Then you have to go the more complicated statistic ensemble and they they have been causing this case Jurassic ensemble.
11:34:37 I think the first by Marcus regarding the okay this is about relaxation so about the last nine years. but very often what happens when one study system is that the soap simple simple relax, and shorter times intimate times to Paris which are not consistent
11:34:55 with the stabilization or, relaxation, to keep some some.
11:35:01 So, when this I give you just a few example. One example is a so called Peter monetization. And this happens when the system and the investigation is close to being terrible, despite being generic.
11:35:13 In other words, this means that there are not really exact controversial laws, but there are operator which are classic concept.
11:35:19 So what one observed is that there are a very long thing scale it we see the observer seemed to be stationary.
11:35:33 And in order to see the reactor mouth immunization when it's with a very long time. Okay, and it's furniture at lunchtime.
11:35:40 So, this was no in a generic system then but essentially the same.
11:35:43 But the they, they're like the they relax to the wrong expedition model.
11:35:46 The same situation up in full swing into a global system, which are by definition more symmetric engineering systems.
11:35:54 The difference now is that instead of being close to an integrated point with mark on submission lows, one should be close to some, some supersymmetric one so when I should have even more controversial laws, then in any legal system.
11:36:09 So this means that you should have even more considerations that they want you need to characterize a complete set of, I guess, of the model.
11:36:17 And in the past they studied too simple possibilities. One was then we can be living in apartments by model.
11:36:26 Because in the when there is no magnetic field this model becomes indeed not a big an internal super intelligent. And then, because of these when the magnetic field is more one realize that there is this intimate time dynamics, which is not described
11:36:38 by a GG, a commercial energy, but ok now I'm more interested in the other example, which is this one, and he's a strong couple Leeming of the Zi center model, which is an interesting model and it's, as we see in a moment and show them the tone is it doesn't
11:36:55 mean that a mother.
11:36:57 And what one finds and which is kind of unexpected. For example, when you consider this larger strong ability meeting 90 anisotropy is that the transition environment is not restored.
11:37:07 So you have a very long sometimes you have a very long time window were observed was that what are the table I was still the special depends on whether the status even world, okay.
11:37:19 It's okay to be interesting to understand how can we capture these kind of dynamics in effective way.
11:37:26 So we have to understand how to treat this model in this trunk upper limit.
11:37:31 And, okay. These are just some basic observations of strong cabling is that when you ever, a Hamiltonian recollecting space like a CEO plus some perturbation major one, and let's assume this promotion is very large.
11:37:46 so more than ever to mention is kind of the opposite.
11:37:49 So, it's important to understand that when k Kappa here goes to zero, it doesn't mean that that we can neglect HTC room. But actually, it is very important in the time evolution.
11:38:06 Indeed, what happens especially is being changed is that the the part of the demolition related to this Hai is kind of trivia generally is like a rotation or some space or something like that, instead of this little dynamic is is presented by something
11:38:18 related to hcu, and so on question is, how can we, How can we capture this dynamics. And then, okay. The what what we need. So, inspired by a an old war by McDonald's.
11:38:42 seems to be possible in kind of generic spin chains to to represent the quantum
11:38:53 And in such a way that the period of time about periodically, and the Peter is proportional to this parameter Kappa instead of the state to tell me about this we can affect you and historian, which is them independent.
11:39:03 Okay.
11:39:04 And, if in case of the amygdala that can be read in this form, which okay he could appear kind of weird, but it's very general need enough, you can you and this kind of expansion in almost every model if you can imagine that's been changed.
11:39:19 The only difference that is number two changes, but in a moment when you write in this form, then it's possible to to compute this effective Amazon and order my order.
11:39:29 Okay, number two, by the way. Yeah, just to give an example I show you the result the forum Q equal to.
11:39:34 And these are the first order of the expansion which can be retained as of this operator, essentially that you identify in the Hamiltonian, and for to equal to means for example this there is a possible model is the easy model in transfers energy within
11:39:48 our feet, where you identify hf equal to the regular the text model. And then these two are very nice one NF to.
11:39:58 Okay, so we this machinery, so that we can somehow replace our original amygdala with this effect on with Donna, if when we take this kind of a strong, strong community meet.
11:40:13 And we would like to apply this to my favorite model now which is the XXZ spin one off chain that I mentioned before, this is the Smithsonian. So what I was saying before the any sort of is late to this parameter, delta.
11:40:26 So the idea is to see what happens when you increase them. Okay, when you increase delta and you apply this kind of folded feature, then you find that that is an American Cemetery generated by this operator.
11:40:39 You want scenery and then you end up with this effective Amazon. Okay, this is a for me Tony will arrange for. So it's not.
11:40:49 Yeah.
11:40:51 What if you issue like us, referred to, to work with a shorter range Amazon it's more convenient to to market to something different. In particular, we realized that there is a different interest formation, which is very similar to the one, the number,
11:41:07 the sorting to order operators, which brings this Hamiltonian this form, which now was already arranged three. Okay. And we call this one for the taxi model.
11:41:16 I mentioned that this Amazon is correspond to a special point of delivery of model, which is studied 30 years ago, a general form is anything about model, and a sold by the answers to these kind of a complicated model.
11:41:33 So, it's kind of a complicated model. But this is a very special symmetric point of the model and.
11:41:37 And so let's see let's see what the, what is summertime, what the, the summertime does.
11:41:43 So the action on on a state, which is retained turnovers peanuts attractions very seem so simple these moves has been up when it's possible, and because three is that they should be to spin down close to the spin out.
11:41:57 Okay. It is coming to Burma this guy, kind of a simple action, introducing two species of particles. I will call this a particle glass, and with this kind of triangle.
11:42:08 This particular orientation, and this triangle means that there is a spin up on an event.
11:42:14 Instead of a spin up is no position on us this other representation equal this minus, why I'm doing this because now if you know let's assume that we are just the initial stage right this of this point is a sequence of spins.
11:42:27 And then let's see what happens whenever the amygdala. So this pin could move here.
11:42:33 Sorry. Yeah. And so this means that this plus particle move here, or otherwise could move on the other side, and this is what happens.
11:42:46 Okay, or not they can move on the other side. It's been announced he could move their body can't move on the other side is being can move here, but it can move on the other side, and so on. Okay, so this means that there are just two species.
11:42:56 So the solution descriptors visual freebie moving impenetrable particles. Okay.
11:43:02 Anybody well we can from here we can immediately realize that they.
11:43:08 The second sequence of species concept by the Amazon. And this is an emergency medicine, because if you can see the original model. The model is not, this doesn't, this doesn't happen.
11:43:19 Okay.
11:43:22 So, from this picture here we can also immediately identify not interrupting sectors of the model. And this corresponds to when they save that are already partings have a single species.
11:43:33 Indeed, one can be easier to realize that the demolition is equivalent to a demolition of the overlapping Amazonian the objects amygdala which is not interrupted, is not.
11:43:42 So, the question is Where is interactive there is interaction still in this limit, because of these limits over lunch that is usually called easing limit.
11:43:50 Neglecting may be that there is a part of the amygdala which is interactive.
11:43:54 So there was a, is there any interaction or not. Now, okay, well, let's see compare Clearly, we need to consider two species of particles because we know that with a single species is not interacting.
11:44:04 Now we see that in this configuration nothing changes with respect to the before. Now if I consider a particle plus in this configuration can move he can move they're not nothing different from the contract in case something start being different, if
11:44:21 I put this kind of sequence, because this, the possibility to move department say Microsoft is possible only if I have to speak some particle.
11:44:30 And then this worries interaction, and indeed the one who can. This is manifesting the scattering matrix, which is non trivial, only if there is a political minus before a particle plus, when I say three years, I mean I went through your means that they
11:44:45 just the fermion it free fermion skeptic method which is a minus one.
11:44:51 Otherwise, as you can see, for me it means that instead of being managed one becomes a face. Okay. Nevertheless, this is probably one of the simplest thing terrible models that you can imagine.
11:45:16 And you can solve it by code the ultimate answer so what you have to do essentially to fix the configuration of particles which is an environment, then you can parameter eyes, the state and by set the momentum or abilities, and the state are superposition
11:45:18 playing waves. Okay. And the only subtlety is that the the position of the particle is not given by the side, but by the macro side, because each particle years is associated to two speeds.
11:45:32 Okay.
11:45:33 Okay then.
11:45:54 the.
11:45:56 The question that describes the tri state.
11:46:11 Now, it is not the important, they, they kind of surprising part is that I can write down solution to this equation.
11:46:12 The question such that the the the should be satisfied by the session I state Parliament cries by this moment or abilities. Okay.
11:46:19 And you see, these are.
11:46:21 So these are the day the hour unknown, the momentum that can be expressed in terms of quantum numbers J.
11:46:30 Like in an interesting case in their interesting case the quantum numbers are just integer. Okay. Yeah, what do you have is that they are not really integer, they are just shifted integer, because they are fresh on number.
11:46:42 And that is where interaction is ok so this is kind of very simple incredible systems.
11:46:48 So essentially I'm representing these numbers, so this could be a representation of a stationary state where these are the quantum number present in the state.
11:47:03 Is it customary to call moment of the particles, they wanted to see the with with quantum numbers present in the state, and it pulls the one that I'm impressed.
11:47:06 Okay, why am tell you this because when you go into the terminal me limit you change the presentation, and instead of expressing everything does over rapidity you express everything does have the density of happiness in the, in the corresponding space.
11:47:22 So, with this I mean, for example, that when you have Sam over there a piece of a function, you are in the tournament I mean it you replace the somebody integral and unifying the density as the weight of this integral.
11:47:37 And now if you use this gathering metrics are there they probably know the system you can write, almost immediately in any question that relates the density of particles with the density of all okay which we could call first.
11:47:50 That will not be but the answer the question this is very general nothing new.
11:47:53 And then okay in general, this is not enough to characterize our, our market space, because we have to establish the lead a relation between the density and the state itself.
11:48:05 And this is usually done by minimizing the free energy, if one is interesting in terms of state or generous keeps on sample.
11:48:15 But in emergency situations like the one of them more interesting that you are to replace this kind of second step which is a standard one with what is now known as generalized agronomic wish.
11:48:27 So what do they mean with this. So, well, in anything more modern you have infinitely many controversial laws.
11:48:35 Okay, and in particular with a proceeding people system that you can easily you can express the simple form. Okay, this is a very old herself so that they will have the charges written like a sample function of their abilities.
11:48:49 This is a very new result. Okay, and it's about the special value of the currents, but nevertheless Okay, now it's possible to express both of them in terms of therapies, and then it becomes easy to take the time with me leaving.
11:49:05 So he already told you that we have to replace some with integrals. We can do the same here and modifying that the current and I was written so far into the wrong hands, feet and you were a Q is depends on the, on the controversial laws that you are considered
11:49:19 these are just expressions that they can be can be derived in the simple model that I'm considering the this function, associated with the charges are very simple, or just cosine and sine me so well.
11:49:33 This means that the issue of the establishment of charges exhibition below currents, you can write the continued equation, they have to satisfy charged by charge.
11:49:41 Now since every charge to satisfy this equation and qR a complete set it compete basis next to them. This is also the Integra should satisfy this equation.
11:49:52 And this is more or less what is called the generator ground equation.
11:49:57 Okay, in our case it's there is something more. And this is related to the fact that if we impose it also the roof, the density of home exhibition should satisfy the same equation then we have a, an additional question.
11:50:12 Which, which is any question for this out zero parameter MRM, which appears in this effective but last. Okay.
11:50:21 And then, okay, this is just a special example of economic equation question that they're being used recently to for the last few years to characterize this can leave it in the present you know more genetics.
11:50:30 So what happens in, in particular in our, in our model.
11:50:34 So, this is a very simple example when we can see that the junction of to thermal state, and instead of transport, so the the energy and the I'm, I'm blocking the energies of financial position at different times.
11:50:47 So what you can see is that the larger is the time, and the more this point, move to a function of the, the racial equity. Okay, so it becomes a function of activity.
11:51:04 And, and you can see other than the numerical data and in agreement with this with our GHD prediction. Now what this picture of the model is okay this happens in a very integral systems in general you find some smooth curve.
11:51:21 Well this peculiar the model is that the discontinuities and.
11:51:25 But that you don't have this continues on kind of special operators, energy or particular conservation laws, you have been discontinued for any local examples.
11:51:36 Okay, this is related to the fact that we have this parameter Mr. And we service by a special equation and okay so here in this case you see that this is very small, it's almost imperceptible, but you can play a bit with initial state and you can emphasize
11:51:52 this guy knows these continued.
11:51:57 So in general, what does it mean to be discontinued in this limit means that there should be some. The transport is not only ballistic, but it should be maybe some defusing
11:52:08 The abusive contribution or.
11:52:25 What I want to emphasize is that the generally these results are independent. Are you prepared interested I will join the initial state, so they are independent of the details in the middle of the junctions.
11:52:37 And this is able to kind of general because when you were to block her estate and then you wait a long time, generator is definitely expected this perturbation fades away.
11:52:46 Okay, so I won't be able to see.
11:52:51 Late in time.
11:52:52 In fact, in this model you can you can see you You have the counter example of this general belief.
11:52:59 And in order to see the counter example I want to briefly introduce a big sector of the modern which is consequences of Gen state with the jumps data means that there are particles that are stuck together and they can make you can realize here you can
11:53:11 move anything.
11:53:14 Okay, fine.
11:53:16 A very big. So if you can see the set of Jim state, the wish if you want to should satisfy this condition. this model is important. And then the issue now imagine to perform a local measured on the on the state.
11:53:30 For example, this is a gem state and providing here and now you can see a local measurement donors, you know. Okay. And I imagined that they some blind measurements, so I don't know the unknown, but these are the, the outcome, or the measurement.
11:53:43 So in the end of the the statement will collapse to what columns to do a density matrix and the spin will be either down or up the position, the upper part is just the same initial stay the same status, before the gym, nothing happens.
11:53:57 Based on this is these are the non three of them evolution. So what happens if I started the the evolution. Well, what happens is that, again,
11:54:09 what happens is that I find the disposition value of the observable are non premium on Microsoft microscopic case so on.
11:54:19 If you plot this is a function of the distance from the measure over the time, then you still find a incredible profile, despite the measurement being locker locker part of the system.
11:54:30 Okay so, since it's late I I stopped here, so I just presented a particular a strong couple limits of opening terrible system and we'll see discarded bit of peculiar feature that one can can arise in this land.
11:54:47 Thank you for your attention.
11:54:50 Thank you very much.
11:54:52 So now it's time for questions.
11:54:55 Does anybody have any.
11:55:02 Go ahead.
11:55:05 Hey, can you hear me. Yes. Yeah, thanks for the nice talk.
11:55:10 So you mentioned, towards the end, this result that you have for the energy currents, where you say that it's ballistic with some sort of disconnected continuity but, I mean, if I remember correctly and I've done a little bit of work on this from the,
11:55:24 from the open systems perspective I mean the results by Marcos literature on boundary driving in the, in the kind of delta greater than one limits for the spin for the spin transport is interesting because the spin transport is diffuse diffuse of right
11:55:38 with coefficient, which goes like one over delta is this consistent with the, with the theory I mean okay what happens here okay thanks for the, for the question, because indeed what I want to stress is that the properties of this model is strong coupling
11:55:52 fast very different from the properties of back sexy.
11:56:03 bother for that Roger one should be using this continuity of the screen. Yeah. Is that what you see is that you have this continuous you are completely independent obviously is a completely new.
11:56:07 In particular, okay for that particular one we did you have a very strange behavior, and it's not even
11:56:16 Thanks a lot man. Cheers.
11:56:24 Because it's right to difference image. I said, America is in the limit. So they are very empty, they are not related.
11:56:28 Okay, any other comment or question.
11:56:40 Yeah, Marcus, please.
11:56:42 Okay so yeah maybe we can ask a question here. I want the time is scarce I mean this is this is very interesting right that when you you you take that aspirational environment, more than right and you you make the feel very strong, you have in homogeneous
11:56:57 survive right kind of smells like like MBA and I would say so. So the question that I wanted to ask yourself all the time is scale. So, I mean, essentially, can you prove that so long as you have, hoping you will equilibrate and then there is some very
11:57:15 long time to scale.
11:57:18 So we are talking about x and z. Now, we are.
11:57:23 That's correct. That's correct. The new that the can, I can ask, I can answer you.
11:57:29 Without doubt if for a particular initial state, which I consider it wasn't done arise the mushroom the gosh state, because in this case indeed the US, this kind of the picture that I showed you at the beginning, you have a look like that the symbolism
11:57:46 for stored. But then if you wait. In fact, you can see that is restored and the time scale is order, a femoral wrong this one of our data. Sorry, is that no not one of them.
11:57:57 So you have a day the Thanksgiving which you have this kind of a breaking of a similarly, or they have an hour to death of a giant or not okay to be the major wrong but OK, OK, Ok.
11:58:13 And, but after that they should they should relax.
11:58:15 I mean he likes this really you can see it a simple way to do that is to decrease that.
11:58:22 Because when that is very large, it's kind of difficult to see because okay the limitation of the American population, But the crazy thing becomes clear.
11:58:32 I see so there is no pressure you can prove there is no pressure for for no I don't think there is education. Now I come.
11:58:41 That said, we can prove that but I don't think that there is a fresh.
11:58:44 Okay. Thanks.
11:58:49 Okay, so if there are no more questions.
11:58:53 So let's thank you for your talk, and move to our next speaker.