 in-person events or hybrid, but with a lot of in-person participants. So before we start with the scientific program, we just wanted to give you some practical information and give you an overview over the program. So let me introduce the organizers, so Andrea Gambassi and Benjamin Walter and Ed Garoldan and my name is Sarah Los. And this is the email address of the secretaries. Whenever you have some issues, you can email this email address and they will try to help you. Okay, so and this is an overview over the program. So we have longer talks in the morning and then the second talks here in orange are a bit shorter and then there come the contributed talks who are even a bit shorter. If you want to go online, you can also see the program here and you can click onto the abstract here to see the abstract of the invited talks and I explain this because it's a bit complicated. To see the booklet of the contributed talks, you have to download it as a separate PDF and you have also a printout of the invited talks and the contributed talks separately here. So the talks start every day at 9.15. We have the keynote talks which are in total 45 minutes and invited talks are in total 30 minutes and contributed talks 20 and we will take like 5 minutes for discussion. Then very importantly, we have the lunch and discussion break. So please use that time also to have discussions with each other. Then importantly, the lunch is at the ICTP main building which is not this building but it is a building at the main campus of ICTP and it's about a 15-minute walk but there will be lunch shuttles so you can also take the shuttle to go there. Tonight we have a welcome reception in this building starting at 6 where you are all welcome to join. Tomorrow it's 12.20 so after the morning session we will take a conference photo so please everybody join that and we also have the poster session tomorrow at 4.30. So yeah, this is a snapshot of how the poster session is going to look like for all of you who haven't used Gather Town before and I think Benjamin wants to say some things about that. Yeah, good morning also from my side and welcome here to GS. It's nice to be in a room full of offline participants but we also have over 40 online participants and so in order to make the exchange with them possible we have a poster session tomorrow from 4.30 to 6pm and the online session is going to take place in Gather Town which is an arcade style online platform. Many of you will be familiar with it. You have received the link, I hope, in an email. Okay, wonderful. So just log in there, you choose your avatar, you walk around in this 2D world, you can interact with people, please use it. So this room is actually open throughout the conference for up to 25 participants at a time so especially for those who are attending online. In the coffee breaks you can explore the posters, meet other people, get in touch. And tomorrow, so all of Thursday, we have 125 licenses so all of us can spend as much time as you like in that space, meet with people that couldn't come for various reasons and I would like to encourage all of you to make use of this, in particular the online crew, just have a walk, stroll around and get in touch with other people. Thank you. So maybe I can add something. So those of you who are... So one complaint about Gather Town that I heard in the past was, ah, I cannot find somebody with whom I would like to talk. There is a search option in Gather Town which allows you to really, you know, stalker your colleagues so you can really follow. So if he's moving, your avatar is following him. So use it, it's very useful to stalk people. We are not encouraging to stalk people. No, no, we are not encouraging stalking people. But it's very easy to use, very fun and it's a way also to connect to people which is online. It's also a sort of Pac-Man video game on the page. Fella. Okay. Yeah, so lastly, maybe we should mention that doing the talks for the online participants, doing the talks, you will be muted and you cannot unmute yourself to ask a question. But you can write us in the chat and we can unmute you. And then after the talks, you will be unmuted and you can also ask questions in the chat, hopefully. Yeah, and okay, this is just an overview over this building so that you know where are the restrooms and this is the lecture hall that we are currently in. And this is the map of the ICTP campus. So we are right now in this building but the lunch is going to be in this building. So we can all walk together. Don't worry, you will not get lost. But just so you know that this is a different building and in between is this big park. And there's also the shuttle. So, yeah, I think this is all that we wanted to say. I don't know if you'd want to add something. Reed? Ah, okay. So yeah, so we just wanted to put here a very nice paper that maybe some of you already know from a fund company who made a very nice summary of why it is important to look at non-Macovian processes and a very important remark that he made his first remark, non-Macovian is the rule and Markov is the exception. And on that note, I think we can turn on to the scientific program. And I hope you all enjoy this conference. Thank you. Okay, do you hear me? Yes, very good. Good morning. Welcome everyone. I have been volunteered to be your chair for this morning. There is the agreement that questions should be asked during the talks if someone has an urgent question. Letizia, are you fine with that? Sorry? If someone asks questions during the talk, very good. Yeah, yeah, please, stop me, yeah. I will not be very strict on tracking time. I trust that all the speakers will keep their slots. I'm optimistic. Good, so the first speaker is Letizia Cugliandolo from Paris. And she will talk about non-Macovian effects in many body systems. Please. Okay, thank you. Thank you very much. It's always a pleasure to come to Trieste, so thank the organizers for inviting me. What I planned is to make a sort of introduction on non-Macovian effects, and I will pick three cases or three broad subjects, which are actually the subjects of the three days of the conference. So these names, which appear here, people with whom I collaborated in the past on some of the results that I will show you, but I will not be very specific about the problems themselves. It's more like a global introduction that I will make. So this is the way in which I organize this introduction. So at the beginning I will talk about classical systems, give some definitions and properties and the physical origin of non-Macovian effects in the kind of equations that we use in physics. And then I will talk about some biological applications at the single particle level, many body effects, glassiness, how these appear in the description of glassy problems, and specifically explicitly non-equilibrium problem which is the field of active matter. And then, well, depending a little bit on time, I will give you some ideas about non-equilibrium effects on quantum systems. So I also picked this article from Fankampen to start with my talk. So as it was said, non-Macov is the rule. This is the point that is here? No, okay, I don't know which is the point. Anyway, so non-Macovian is the rule, it's not the exception, and it's just not proper to treat non-Macovian processes as just little modifications of Markovian ones. So there is more flesh into them, let's say. So let me pick a definition. Imagine that you have a stochastic process, you have time, you discretize this time, so you have three other times, T1, T2, and T3, and say that the stochastic process is this X of T taking values at these times that are selected. So the joint probability distribution of these three values of X at the three times, which is this capital P3 that I wrote over there, well, it satisfies the fact that it's the product of the probability of the joint probability distribution of the variables at the two first times and then times this conditional probability of going from these values at the two previous times to the value at the third time here. So for a Markovian process, which is special, is that this thing here just becomes, this conditional probability just depends on the next variable to the one you're focusing on. Okay, so this dependence here disappears and this depends only on the just previous one. This is a special feature of Markovian processes and normal Markovian processes are those that don't satisfy this property. So one can generalize what I have just said and consider the values of this stochastic process at n times, or there's in the same way as before, then you have the joint probability distribution of the values of the variable at all these times and using what I have just said previously and extending it to the n variable case, what it turns out is that this joint probability distribution is just the product of these transition probabilities or conditional probabilities defined before, but just depending on the two nearest times considered and times the probability of the initial value. So this is very practical for calculations of course, if you can factorize in this way, but for non-Markovian processes you cannot. So this is sort of the mathematical setting, you can find it in a very similar description in Fankampens' radio article. So what are the effects, the simplest effects of these non-Markovianity? So on the left, I just picked from Barkema's book, a realization of a random walk. So in the left panel, the random walk is not constrained, so at each step in the evolution, the walker can go to any of the nearest neighbors on the lattice with equal probability and in particular, he can come back to a point which was already visited with no restriction, so it can overlap in the way it's sketched over there. So this is the Markovian case, is not constrained at all in the evolution. While on the right side, there is a self-evolving walk, so it's a walk that remembers everything that happened before and it remembers it in the way that it cannot overlap, it cannot go twice on the same site and if you have a look at it, it's well, a little bit more expanded, no? I mean, not really in this picture, but what will happen in the end is that because of the fact that it cannot go back to points which were already visited, it will expand a little bit. And this is what is shown in this figure here, which I took, well, okay, I didn't take it from there, but it's an example that you can see in Doi and Eduard's book on polymer dynamics. So if you allow for overlapping of the random walk and this is just a modeling of a polymer, what it can do, if it can go on top of itself, the radius of duration, so roughly, how much big it is, will scale with a number of monomers with one half power, like in a normal random walk, in a sense, while here, in the self-avoiding case, while the power is different, is higher, so this is the expanding feature that I was mentioning. So they are visual and, you know, consequences, visual effects and consequences of these constraints that are imposed with the normal covianity in this example here. I don't know, maybe for the ones who ask questions online, I reply only later, right? This is the idea, yeah, okay. Yeah, so maybe it's better if I do it later for the ones who are not here, because it will take time to read and, no, yeah, I guess. Sorry? But there is a raise hand over there. Yeah, if, I mean, can he talk? No, okay, so then. So then I'll do it later. So here I just, I did an example about what happens with an exponentially correlated problem. I will jump over this one, it's not very important what I want to say, I prefer to spend more time in the physical origin in particular of these non-marcovianity. So imagine now that instead of thinking about this random walk problems I told you about before, let me try to give an idea of where these memory can come from in a problem described at the Langevin, okay? So the idea is that I will think about, I have some system and this system, I will couple to some environments and it will interact with the environment in some way. So I will model the system in the simplest possible way. I will think of it as a particle, just a particle characterized by a position and a momentum, the x and the p over there. And then I will model as well the environment in some way, simplest as possible and I will model it with the harmonic oscillators, you will see, which are also characterized by positions and momentum. And the A is an index that labels how many harmonic oscillators you have and I don't put arrows nor bowls because I think in one dimension because it's simple. So one can ask the questions, what are the static and the dynamical behavior of the reduced system? So what do I mean by the reduced system? Well I have the coupled system but I will like to integrate out, so get rid with a calculation of the explicit dependence on the environment and the interaction but then this will imply necessarily some change in what the system will feel and I want to characterize this change and I want to understand how much it influences the equilibrium behavior of the system, the dynamics of the system and later on I will say a couple of words about the quantum extensions of that. So as I said, the simplest possible modeling is to consider, well harmonic oscillators at the back, I will have to give initial conditions to my system, I will have to give initial conditions to the oscillators. When I focus on the system, of course the energy of the system is not conserved, but the energy of the full coupled system plus environment ensemble is conserved because I consider it isolated from the rest of the world and in the modeling one also considers that the system is small compared to the environment because if you model an environment above, you imagine that it's a huge object with a lot of degrees of freedom. So this is a sketch of what I'm thinking about, I have my particle perhaps subject to some potential and coupled to all these oscillators, many of them that consist, that make the bath, that are the elements of the bath. So then one can give a modelization, say how one's going to describe the coupling between the system and the bath. I said that bath were oscillators, I know which is the Hamiltonian of the oscillators, it's very simple, it's quadratic thing and then I have to choose the coupling. So the simplest possible coupling is one given over there, so X is the position of the particle, QA is at the positions if you wish of the oscillators with respect to their equilibrium positions and then you see that here what I have is a bilinear coupling of X and QA because if I expand the squared, I have a double product, right? So this is a simplest modeling of environment interaction and it was already considered by Feynman in the quantum context in the 50s and other people which Kawasaki, Swansea, a bit late. So if you want to solve this problem, what do we have to do? I have to consider the coupled Newton equations of the particle and the oscillators. The equations for the oscillators will be linear because I'm working with oscillators because this is the reason why I chose them to make the calculation feasible. I can integrate these Newton equations of the oscillators. They will depend the solution on the position of the particle because they are coupled. I inject the solution of the Newton equations of the oscillators in the equations of the particle and then I get a final equation for the particle alone. Alone in the sense that only the variables of the particle appear but the influence of the oscillators will be there in that equation. Now if you assume, because everything I said up to now is completely deterministic, it's just Newton's equations and solving Newton's equations, if you assume that the initial distribution of the oscillator variables is of Gibbs Boltzmann kind with some interest temperature put by hand in this calculation there, then what you will find is a cooler launch of an equation. So a launch of an equation with memory and noise which is correlated in the classical case or in the quantum case, something a little bit more complicated what is called a reduced dynamic generating functional. If I have time, I will come to that at the end of my talk. But just focus on the classical case for the moment. Something happened here. Ah, the connection is lost. This is the zoom or my computer, I don't know. No, connection lost. Connection lost. But the internet is on. Yeah, you're on. I think it's just slow. The car sharing again? But the, oh there it is, no? Yeah, okay, well. So why don't we worry about this in classical equilibrium? I mean, nobody told you about this in classical equilibrium, right? You just have a system, you say it's coupled to a bath and you do the Gibbs Boltzmann measure with no problem. So the thing is that if I do the same calculation at the level of the partition function, so if I think about the partition function as a sum over environmental and system degrees of freedom and I integrate over the environment degrees of freedom which are the quadratic, I can do it, then what you will get is some reduced partition function which is modified with respect to the original one by this term over here. But because of the coupling that I chose between the system and the environment, there is also a contribution that is exactly the same as this one. You cancel them and you get that the reduced partition function is equal to the systems one. So at the level of the calculation of the partition function, the effect of these coupling to the environment for these environment I chose goes away. This appears. So then you can think about what we usually do. We never think about what is the environment at the classical level and at the equilibrium level, right? We always say, okay, we just write the partition function and that's it. But at the level of the dynamics, no, at the level of the dynamics, if I do the procedure that I mentioned with words before, sorry, then what I get, oh, sorry, then what I get is a generalized launch of an equation of this kind where there is a kernel here which is the friction kernel that depends on times and all the times that have been run since the initial time of the evolution and there is a noise over there which is correlated with this same kernel, the same one here and there, if you chose initial conditions for your environmental variables which are in equilibrium at beta and this is the inverse of beta which appears here. So the assumption of equilibration of the bath leads to a delayed launch of an equation with color noise but with a relation between the friction kernel and the noise kernel which is just proportional to KBT and this is, well, what is a representation of the fluctuation dissipation of relation that tells you that the environment is in equilibrium. So these are the references I mentioned and if you want to see them, these calculations down in detail, this book here presents them. Again, is it moving? Hmm, there's again the same problem here. Is it moving now? Yeah. Okay, so the familiar white noise limit is obtained when this sigma that was appearing here becomes the delta function proportional to the friction coefficient and then also you have the delta correlation of the noise that you know for white noise launch of an equations. As I mentioned, the constraint on the kernels, the fact that I am assuming that they are, the environment was in equilibrium, constrain this sigma in the friction to be the same as the sigma in the correlation noise but in other problems you can have non-equilibrium baths and then don't respect this relation. Now, what is the effect of the different choices of oscillators? You can choose oscillators of different kinds. You can choose ensembles of oscillators with their own frequencies being distributed in some different ways, right? So, according to how these oscillators are chosen, you choose this function i of omega which is there which is the spectral function of the bath and you can get different baths. So, this black thing here is a white bath but then you can have colored baths, colored noises that will give you, you know, i of omegas which have different dependencies on the frequencies. And, okay, this I took from some radio article over there and the names omic is usually associated with white noise but then you can have super-omic or sub-omic depending on how these i of omegas depend on omega at large values of omega, whether they, how they decrease with omega or whether they increase with omega and so on. There is a case, a special case that will appear later in the active matter context which is the case of having this kernel sigma be of exponential form, so be an exponential function. Although it's not a delta and you could imagine that this leads to a non-Marcovian process, this problem in the usual cases can be disentangled, let's say by introducing an auxiliary variable or by considering this xi to be given by another launch of an equation, this one with a white noise and this is the Orson-Ulenbeck well-known process that is actually when you open it up and you include this as a dynamical variable itself, the xi, you realize that, okay, you just have two equations coupled together but you don't see the memory any longer. So the exponential correlated noise is a little bit special. But then whatever else you can have, you have power load the case which corresponds to the power loss of the i of omega that I mentioned beforehand, well then you have proper long-term memory in the characterizations of the path. Okay, this one I can jump. Now, okay, from the point of view of the calculations you know that when you have a launch of an equation with a white noise and with no inertia so where you drop the second time derivative there are lots of peculiarities of those equations that have to be taken with care, the discretization that you use to consider them has to be considered in great detail especially if you have what is called multiplicative noise, so on and so forth. These things are smooth, are, you know, often let's say these problems are sort of avoided if you have correlated noise. So from the point of view of discretization issues having correlated noise is helpfully simpler. You don't have to worry about those problems. But okay, then there are other problems that appear which is linked to the fact that those equations are more difficult to solve. So there is, you know, again and a loss in considering correlated noise and problems with memory. Then I just want to mention very briefly that there are certain generic results of non-equilibrium and equilibrium systems that evolve with these launch of unprocesses that can be proven like for example the fluctuation dissipation relations in and out of equilibrium. Those can be proven in very similar ways if you have memory and correlated noise like this. So all these things remain. The fluctuation theorems and fluctuation theorems out of equilibrium are still valid for processes with memory and correlated noise if those are in equilibrium. Okay, so now what else can I say? Well, what I can say is that the effects of these non-marcovianity appear at all levels. So for example, the simplest possible problem you can imagine is a particle moving in a harmonic potential coupled to a bath. So if I couple this problem to a bath power-low correlations in time like the ones I mentioned before and you consider for example the measurement of the correlations of the position of this particle at different times, well, for a white noise you would find an exponential decay. For a correlated noise you have an ugly function there which has a name and that has some serious representation which is not exponential. So the decay of these correlations is very different in the sense that it depends on the time differences but it depends on the time differences in a complicated manner and the characteristics of the bath are encoded here in this alpha which is the alpha that characterizes the decay of the power-low correlations in time and that will give you different functions here. So the bath has an explicit effect on the dynamics of the particle even in this very simple problem. This has been used by these people for example who were doing experiments on some proteins and they were looking at something similar like the correlation function I mentioned before. So experimentally they measure this correlation function and they see some decay as a function of time difference so this t here is time difference and this decay is not exponential it's something that looks asymptotically like a power-low but has some functional form which is more or less complicated and what they do is they fit this mithasic lefter function that I mentioned before and from there they extract the alpha of the bath. So what they want to do in these experiments is to characterize the environment where these proteins are moving and they do it by just doing the same calculation or applying the result of the same calculation I gave you before and like this they characterize the bath. Similar problems were treated recently by Andrea and collaborators of the Venturelli student so for example this is a very similar situation where you have a particle moving in a harmonic potential which is this term here but it's coupled to an environment which for example can represent a surface on which this particle is moving and this surface is rough or this surface is characterized by a field here is the field and here is the coupling between the particle and the field and then you have a problem where this is the particle you want to characterize and this is interaction so it's very similar to what I was just saying if you want more details you can see WS poster. Now how these things at the level of single particle that I mentioned just before generalize to a more complicated situation where you have for example many particles in interaction competition and then slow dynamics and glassiness can this be used that I just learned to say something about this more complicated problem and here what I want to tell you is about some old ideas actually from like 20 years ago and the idea is let me think in the same terms I have done it but now consider that I have a particle coupled to two baths they still have a particle with some potential which can be a harmonic potential but then it's coupled to two baths which are different so one is white and the other one is exponentially correlated this makes my calculation simple it's not necessary to choose this but this makes calculations easy and not only the kernels are different the temperatures are different so imagine that one has T1 the other one has T2 so my particle is explicitly set out of equilibrium by this coupling to these baths which are different evolving different scales so this problem of course can be solved analytically it's very simple if I put a potential which is again harmonic and what turns out is that the correlation functions of the positions of the particle under these two baths become relatively complex so there are two time scales that develop when I choose the tool that characterizes the exponential decay of the bath to be very large and set my baths to be very different to evolve in different scales so there is a short time scale here which is controlled by the white bath and there is a long time scale here which is controlled by the color bath the exponentially correlated one and this is the sort of things that are seen in glasses so in glasses you see this separation of time scales itself induced by the interactions of the particles among them here I'm just considering one particle and there is another feature that can be solved completely in this simple problem which is to have a look at fluctuation dissipation relations for the particle so for those of you who don't know it don't worry so much there is a relation between linear response and correlation functions that in perfect equilibrium is completely controlled by the temperature of the bath if you have only one bath but here I have two at different temperatures and what I see is that I have a regime here white bath, another regime controlled by the color bath and this regime here corresponds to short time delays this corresponds to long time delays so this is the explicit solution of the equations that I showed you before now compared to what happens in glasses and you see it's very similar these are simulations of a Leonard Jones system with these two timescales developing here when you increase waiting time but you can also do it in the same way when you get close to the glass transition just look at this and this is very similar look at that and that is also very similar so I have induced the very features of out of equilibrium glassy dynamics in a trivial problem of a particle coupled to two baths so the idea is that what is going on in a glass well there is an effective description of all these many body problems which consists in saying okay I will pick some relevant variable this relevant variable will follow some effective dynamics of course I cannot solve analytically for these dynamics I cannot show, prove in all details which these dynamics will be but I can make a guess and in certain cases like large dimensionality, mean field model and so on I can do this calculation analytically and the thing that turns out is that what you get is that for this selected variable you get an effective launch of an equation with delayed friction and with noise which is correlated and in out of equilibrium situations like the ones you have in glasses this delayed friction and this correlated noise are not linked by the usual fluctuation dissipation relation of an equilibrium bath because this effective bath is the system itself and the system itself in glasses is out of equilibrium so the relation between these two a priori you don't know it but in practice is the one that is characterizing this fluctuation dissipation relations I showed you before in the previous slide so what you have to keep in mind here is that there is a way in certain cases to prove in other cases to guess an effective launch of an equation for the relevant variable that describes it's by construction it has memory and it has correlated noise okay this one I can jump it's just the details of what I said and this is the summary of going back to the same figures I showed you before and giving this explanation for them now active matter well you know what active matter is perhaps is just an ensemble of objects but with consumption of energy at the level of the individuals so the injection of energy is made at the level of each agent in interaction and then you can have birds, you can have artificial things you can have grains have many scales and many many realizations of this idea of inputting energy at different levels at the microscopic level in these interacting problems and typically what this introduction of energy is doing is that the level of the single particle is changing its motion so this just is the motion that you would have with no injection of energy when you have some injection of energy what typically will happen is that this energy will be used to this place to move in space and you will have long runs before turning and making some kind of random motion but it's like a persistent random motion in the sense that it goes straight in one direction or almost straight in one direction before turning and making its motion so this can be modelled for example by adding a local force on each of the particles which has zero mean but has some correlation in time because you have this, it's not changing matterly over relatively long periods of time and typically what is done is that it's chosen active forces of this kind which are correlated with some exponential decay so typically this f is chosen to be exponential with some pre-factor that gives you an idea of how strong this force is so at the level of the Langevan modelization what is used is something like this so you have inertia, you have a white bath you just consider the normal bath to be white so delta correlated and this is the usual friction term then you have some external potential or some interacting potential between the particles you have these active forces and you have the normal noise associated to this fraction so these two are in normal relation with the delta correlation here as the delta that appears there but this one doesn't have an associated friction term so if you think about this one as a noise it's a noise without friction so it's a noise that doesn't respect the fluctuation dissipation between noise and friction so it's a non-equilibrium explicitly non-equilibrium noise and then although these correlations for effect are usually taken to be exponential as I said in time you cannot play the game of the Ulambic process and disentangle these correlations for two reasons one is that now you have two baths so it's a little bit like the example of the two baths with different temperatures that I mentioned before and different time scales that I mentioned before but also because there is no associated friction with that so there is some missing object and then you cannot do this kind of disentangling and then the system is explicitly out of equilibrium because of this non-equilibrium force that is acting on the particles now these problems are very rich because now you have lots of possibilities depending on the strength of this non-equilibrium force which I'm characterizing here by this Peclet if I move in this direction I'm injecting more energy in the system if I go in this limit I go to the passive case but then in the vertical direction I have the packing fractions so the density, global density of the system here I'm like a gas over there I'm like a solid I have a lot of particles so there is also the temperature of the bath that I could have included as a third axis but I'm fixing it in already this plane of a phase diagram that I'm building here there are many phases with lots of interesting properties but in particular here there is a phase which is called motility induced phase separation where the system likes to phase separate regions in space and typically what you see if you look at configuration is that there is kind of a ball let's say this is two-dimensional simulations so you have regions which are very dense regions which are very dilute you have bubbles within the dense regions you have a lot of structure over there this is what happens in that region grey region of the phase diagram the reason why the system likes to phase separate is basically because of the collisions between the particles that are pushed by this active force and when they collide they start colliding like this and they aggregate because another one comes and it's also pushing in the same direction like it's sketched here and this grows and makes these big dense regions but then the particles turn and then they want to open up and strange things happen now what are we trying to do with the people in body is we are trying to get an effective description of the motion of these clusters because there are a lot of nice things that can be observed in numerics and also in experiments about the motion of these clusters they break up they recombinate let's say there are lots of interesting things so what is the effective motion of these clusters can I write an effective launch of an equation for the centre of mass motion of these objects this is the question we are trying to answer and it's sort of a difficult question we don't still have an answer but we are working on that but just to give you an idea of what we are doing we are trying to characterize for example the total force felt by a cluster so we just sum over all the local individual forces depending on each of the particles I sum over them and I have the total force and how is this total force correlated turns out that it's correlated exponentially in time, or D correlates exponentially in time I can extract a typical characteristic time I can extract the pre-factor I can see how the pre-factor depends on the mass of the cluster and well it depends linearly on the mass of the cluster I can do these sort of things effective force acting on the cluster and then I can say how do the clusters move I can look at the diffusion coefficient of the clusters how they depend on the active force how they depend on the mass of the cluster and try to see which is the launch of an equation that I have to write to reproduce that so this is the sort of things we are doing as I said it's not finished because there are certain things we don't understand yet but ok it's working in progress in the direction of finding the effective launch of an equation for one variable the center of mass of the cluster there are alternative studies that go in the direction of mean field models infinite dimensional settings and there are many people who work on that we did in the past a very old paper where we were considering asymmetric exchanges and then these were the we were injecting force in the system ok there are more recent papers more focus on the active problems themselves and now last thing you know quantum very quickly just for Friday's introduction so I said at the classical level that at the level of the partition function you don't have to worry but what happens at the quantum level if I look at the equivalent let's say of the partition function there could be the density matrix if I redo this calculation of integrating away the oscillators in the quantum problem I end up with something that has also a quadratic dependence on the axis as appeared in the classical case but with the kernel within which depends on times this is much about a time I'm in equilibrium ok I go fast here there is no way to kill this with a counter term in my problem even at the level of the equilibrium properties of the problem I have an effect strong effect of the bath and how does this make influences the behavior of the system so one of the things that it does is that it changes the phase transitions of these problems so imagine I have a quantum problem coupled with some bath say it's anomic bath of oscillators as the ones I had before this is the parameter that controls the phase the strength of the quantum fluctuations compared to the thermal ones so this is like the quantum parameter and then you see that depending on how strong the bath is the transition of this problem which is represented by this jump here in the susceptibility occurs at different values of the gamma so the stronger the bath the more extent you have of the low gamma phase so imagine that this is a ferromagnetic phase let's say and this is a paramagnetic phase and moving the transition of the ferromagnetic phase with the coupling to the bath this is very strange right at the classical level we don't have that in equilibrium at the quantum case you do so these are things which are used in the context of quantum systems now to impose something on a system via the coupling to the bath and there are also effects dynamical effects you can change the dynamics of the system by coupling two different baths ok this I can jump over so what did I do ok I gave you just an introduction a bit fast perhaps on some non-Marcovian effects on many body systems I gave you examples some are unfinished as you saw but ok the idea is that you can manipulate the bath in many situations to impose something on the system and you can also try to imagine that parts of your system are like a bath acting on selected variables and then try to consider how this environment which is the system itself influences the behavior of the selected variable this is what I did in the glassy problem ok three areas of the conference we will talk about this in the presentation again thanks Laetitia for this very nice and extended overview and essentially very excellent introduction into the conference first are the questions in the room so real person questions everyone is still shy then I will ask one I know that you explicitly said that you will not talk about it but what happens if you are coupling between the bath on quadratic you can go ahead and this will give you multiplicative noise so if you choose something like I was calling x the system and qa the oscillators so if you couple this via some qa, ca some over a and here you put a function of x then it's ok because this one is linear and you can do the same calculations I have done and this will appear something that depends on this will appear multiplying the noise if the q is nonlinear you cannot do explicit calculations but then you can do some approximations for example the quantum people do does the qualitative physics change appreciably if you do that it may yes because everything depends on the characteristics of the bath if you change the characteristic the memory term then becomes a function it's not a product of the kernel and the q value then it can be much more complicated then the question becomes nonlinear so then you can do some for example perturbation so when you have fermionic baths people usually do some perturbation and approximation on the fermions to get some explicit equations but it's approximated so there is still room for people the younger generations to start working on non-marcopere there was a question there first you can because in the example I showed which was a bath which was white and a bath which was exponentially correlated with t-minus t prime there you don't because everything is stationary but if you choose a bath which has correlations with the kernel the sigma of the bath which has a sigma that depends on the two times separately then you can get aging as well even for the oscillator under this bath you can get it because you do if you choose a sigma b of t on t prime which is some function of t prime of a t for example then you impose it on the behavior of the particle yeah so yeah I don't see it I don't see it either yeah sure but usually what you assume is that the bath is so big that the system doesn't influence the bath but of course this is not necessarily true you can have a couple system where your focus is on something smaller but the other one is not in the thermodynamic limit so then you have to take care then it's getting very complicated yeah in the meantime are there any other questions here otherwise we will start with the chat if we can I don't know if I see it yeah it's here are there known results if the bath particles themselves are non-equilibrium well it's a bit like here the answer to that question is all of the single particle coupled to two baths if I choose the bath to be characterized by a sigma like that when this is non-stationary so then it's out of equilibrium and then I can set the system itself out of equilibrium even in a case where I can consider a particle moving in harmonic potential which is very simple and one would naively expect equilibrium dynamics but if you couple to something like this you will keep it out of equilibrium good but there the generalized Langevin equation still satisfies FDT but no no because when I put these two baths with different characteristics different time scales and different temperatures there is no single temperature characterization neither of the Langevin equation nor of the motion of the particle any other questions should be addressed later you can write them I guess in an email if there are any additional ones and then let's thank Letitia once again thank you