 Yes, so thanks everyone. Thanks for organizing and like accepting me to give a talk. I'm Vladimir Hannesian and I'll be talking about the enhancing spin-spin correlators in mixed field icing due to stochastic resetting. So the thing is, I mean, I got curious in the stochastic resetting processes motivated by my collaborators, Petresca and Sandev and I just started kind of learning about this and those are some of the results that we got along the way. Nobody... Go forward, I mean. It's okay, I'll just... Yes, try with the... I'll just try from here. Should be fine, I guess. Yeah, I'll be resetting it all the time to the beginning. Okay, so I'll give kind of like a quick overview on classical and then also quantum resetting. Then I'll introduce the model of mixed field icing. Then I'll also introduce the reset protocol there and I'll be talking about two different resetting functions. One of them is Poisson resetting and the other one is a power low resetting function. Well, so I mean, by now I guess everyone is familiar with the idea of stochastic resetting in classical systems was kind of like introduced in the 2011 and the idea is you have some diffusive process and beside the diffusive kind of like known process you add some constant probability for the particle to return to its initial condition. So this is like a constant probability at every position in space and time. And this is the delta function that is for the resetting to the initial state and this was explained in the first day how it works in classical systems. It gives a rise to a non-equilibrium steady state and also for example, if you kind of like monitor the mean squared displacement, it's fine with resetting, which is not the case if you just have a diffusive process then it diverges. Well, it's obvious that I haven't given like a talk in a long time in front of people. So for quantum systems, it's kind of like a similar idea. It's quite interesting that it was introduced by the same alter of the classical resetting in 2018. So now what we have is some quantum system, the dynamic that's evolving with some Hamiltonian H and you have some initial state psi zero and then you evolve the system unitary, of course, but then at every time point, you give it a constant probability R for the system to go back to its initial state. So you have something like unitary evolution and then a reset can happen to the initial state. And now I won't go into too many details, but what really matters here in this reset is basically how much time has passed since the last reset all the way until TM, which is a measuring time here, like the time where we're interested about the system. And this can be kind of like casting a renewable equation concept where you kind of like get the expression for the density matrix and also for the expectation value of an operator in this form. So kind of to understand quickly what's this, this is kind of like a probability, it's a sum of probabilities. So this is the probability that the system will not be reset all the way until the measurement time where the second part is you're integrating over the resetting to happen at each tau here with a certain probability. So if you have a constant probability R here that gives a rise to a Poissonian resetting function and then I'll introduce later another PDF which will bring some interesting properties in the system. Okay, so here are similar to a classical system. What happens is that you're getting a stationary state for the density matrix. This was also kind of like introducing the 2080 paper of quantum resetting. And the interesting thing is here that you know that if you let the system evolve uniterially at the very late times like if you take the measurement time at infinity you get the diagonal basis. However, here once we have resetting in the system we kind of like get off diagonal terms that lead, I mean that give rise to some kind of like non-trivial correlations in the system and also would manifest that into the expectation values of the operators which is something I'll be talking about. Now the model that we are studying though this was kind of like very optimistic it's the mixed field ising where you have like a chain of spins and you have coupling between neighboring spins in the ZZs and then also you have like a some type of field that's like magnetic field in the X direction and also in the Z direction. Here those capital letters are basically same as the Pauli matrices X and Z but it's just kind of like a condensed version. And like depending on the parameters there are different models. So you can have like the non-interacting which is kind of like a trivially solvable and then you have the interacting model which has a chaotic regime and also transversing model where the HZ is zero. So I mean we plan kind of like to talk about everything but there won't be time for that. So I'll focus mostly on the non-interacting system which even though it's non-interacting it has some interesting properties thanks to a recent paper that was by Matteo Perfetto. Okay, so now the reset protocol is the simplest one that you can have. Like as I said I'm learning about this so we just take the simplest one where we start with the state that it's all up and then it's also the reset state. So we set the system to an all up state and then we let it evolve. I mean how you can kind of like see this if you're setting protocol physically is like you have some pulses, the stochastic pulses or very high magnetic field. So for example if you turn them on regardless of the spin configuration it will tend to kind of like flip all of the spins up. And they're also, I mean also like the resetting is kind of like some special type of measurements where probability one you kind of like measure the system into the initial state. And then for some other reset protocols you can check for example like one of Perfetto's papers. Yes, we said that. Okay, so I said like I'll talk about non-interacting systems here, the magnetic field this is some constant that will appear but just so you know that it's kind of the combination of the magnetic fields and those are the observables that we will be interested in. So it's the one point function of X and Z and also like the two point function of X and Z. Because we don't have interacting system they don't, so this is the time evolution they don't depend on the position. So even, so that's why no I or J appears here. Sorry, I have a conceptual question. What is the meaning of a two point correlation function if the spins are independent? Wait for a second. Okay, wait. Yes, so this is the whole idea. So for example you can compute all of those things and for example you compute the full two point functions and you can analytically compute those things as a function of the magnetic fields and also the resetting rates. So this is already in the stationary state. And then here we have the X, X correlators. Here we have the Z, Z correlators. And we see that kind of like some interesting thing happens that depend on the resetting rate. I mean it's kind of like not difficult to see that. Like here initially the state when, when magnetic field X is kind of like zero the spins are really just all up and the reset rate it also brings them to all up so nothing happens. But here you get kind of like an interplay of scales because you have this reset rate which is kind of like a very strong magnetic field along the Z direction but then also you have this magnetic field along the X direction which is a transverse one and that's why you are getting those kind of like bumps. But this is the full one. This is the full one and now we didn't even pay attention because we thought like it's not interacting systems so like why considering the connected part because there won't be a connected correlator. And then there was like Mateos and Perfetto's paper and some of their other collaborators and basically a very recent paper. It's a very interesting one. So they realized basically that if you compute the connected part in the stationary state there is kind of like an emergence of correlation of connected correlators. So they were studying this part. They were studying the ZZ correlators and they're also kind of like interesting but then they saturate and that's because like there you don't see the interplay between the X, the X. And then because before we were thinking about the XX correlators in an interacting system we thought okay let's see what happens here. And then what you can realize is that basically here some maximum of correlations happen and they depend on the reset rate. So we thought okay let's see like how is the dependence of this maximum. I mean the maximum of the fields where this maximum happens and also like the maximum of the correlators as functions of the reset rate are. And then an interesting thing, I mean it's just the derivative to zero and it's interesting that it's kind of like you get some optimal reset rate at which the field for maximal correlations happens but also even more interesting you get kind of like maximal correlations at the given reset rate here. So this is some row star. Okay so like this is kind of like the dependence of the maximum of the peak on the reset rate and you see that there is kind of like enhancement of those correlators at some reset rate. Good so here is kind of like in an interacting system but they won't present this it's on the right side and you see it kind of like you get like much richer structure when you turn on interaction because there is another energy scales that appears and that gives kind of like rise to some interesting things but that will be for some other conference I guess. And now as I said because this is kind of like a non-mercovian processes conference we will be talking about another probability for the reset to happen and that's a power law. And in order to analyze that we need to use kind of like I mean we were using methods from the review paper by Majumdar of 2020 and that we can extend it to operators and this is again like thanks to Perfetto which pointed it out to me. And the idea is here that this p star is basically the survival probability. The survival probability means that the state won't be resetted all the way until time t. And now for this to get like a stationary state the only requirement is for this integral to not diverge. And then also you're getting kind of like expectation value of those operators. And now why we are interested in this is because like in classical systems there were some research studies of the power law function which is this one and this is the survival probability. And even more recent study kind of of one of my collaborators sounded so they explore kind of like what's the dependence of the diffusive classical process on this parameter gamma. And they saw some different interesting regimes when you monitor the mean square displacement. So basically if gamma is smaller than zero then you get kind of like some diffusive process and that diverges but then for example if you have other extreme gamma larger than two then you get like a stationary state. And now the idea was like just to see how this manifests in quantum systems. This is a computation that we can do for quantum systems and then we realize basically that due to the divergence of this integral for gamma smaller zero also in quantum system sorry here it's one. So it's gamma smaller than one or zero then we have like it's not defined the stationary state is not defined. And then we can do the whole thing for the correlators. For example with this power law it's expressed by the tritium conflict hypergram metric function. And then we can again like study what are the maximum correlations as a function of the reset rate but now also this gamma. And here we see and this compared to the exponential behavior and then the interesting thing is we see for example if you go to larger resetting rates for example the exponential one you have kind of like this maximum decreases it's kind of like logical because if you reset the system with a higher rate that means that it will be aligned more and more in the Z direction so you lose the correlators in the XX operators. But here for the power law it seems it kind of like either go ups or it saturates or and we are still not sure what happens even at higher things and that's something to be checked. Well, I maybe went a bit too fast but thanks a lot and you've seen this like a couple of times but anyways, take some attention. Thank you very much for the talk. Are there questions here? No, there is nothing. Oh. Sorry, I have no, no, you need to have the microphone. Sorry. So I have one curiosity about the last thing that you presented. Is it possible to cure up the regime gamma smaller than one to introduce some sort of cuts in normalization in the resetting protocol such that this regime is well defined the steady state is well defined? Because when I think about the easy model for instance if I have long range interactions if I have gamma smaller than one then I put the cuts in normalization and then the energy becomes. Gamma larger than one? Smaller than one. Smaller than one, you mean in the power? Yes, in your case is it possible at all or is it just curiosity, huh? I really don't know, like I really can't say because this is something that. You try, you put that in normalization and you check. This is something that's quite fresh, right? I mean it's like maybe a week. Yesterday night, you know, I did it. I mean to be fair, like some of the results were like two days ago after I talked with Perfetto and Mancetta. I see, okay. So add the normalization and check. That's why it's very useful to have this like kind of like in person conference and I really appreciate that. I don't know, but I mean, okay. So then given also, we are running way too late. I think let's thank you all. We thank you again for the talk and we go towards the last. Yeah, what is this? Oh, okay, okay, so we have a, I don't know, bread, I don't know.