 So, if there is one word for me to characterize Boris Alter, this is superiorityism. I looked for Google to check for synonymum and it gave me suprematism with referring to Kazibir Khmalevich. And this somehow provoked me to some studies related to the statistics of these meetings. So it's very common now to show photo of people to whom we are referring during the talk. I never did it before. So, since there are so many relative names and faces that I decided to, in fact, to measure them in one photo. So you guess what it is? So, Khmalevich, a black square. Well, you know, Kazibir Khmalevich helped us to enter the object in itself is meaningless. Let's see. Is it true? So we go to limited unification, measuring photos of all co-authors of Boris. Khmalevich, red square, slightly optimistic, but still rather featureless. The ideas of the conscious mind are worthless, so don't worry. Well, so in such a reality, now I'm measuring all Boris photos which have appeared during this presentation. There are many dozens of them and again they match to something not very featureless. Well, you know, maybe it's a bit ambiguous, but once again Khmalevich helped us to come that every reason to view both the mask and the actual face with skepticism since it disputes the reality of the human faces all together. Well, I go on. So now we have to apply some filter, at least trying to extract some information. So I'm trying the filter of the first achievements. So we have something else, believe or not, but Khmalevich called this picture self-portrait in two dimensions, quite relative to our topics. And we see a lot of things. We see apparent 2D localization. We see self-destructive interference. We have apparently a single, at least single, mesoscopic rotation. So Khmalevich's black circle probably hides a hologram of Boris's actual inventions. Well, it looks so. Well, so maybe back to the black square, now applying the filter of most sincere wishes, which can be given to Boris. So we see, we will see the square to rectangle the symmetry breaking today is called nematicity and color symmetry violation yields best wishes, Boris, and thanks for giving the insensitivity for all of us to get together. Thank you. So this relatively long, long introduction was more prestigious present I could give because nothing is more precious than the time left taken from the presentation. So what I'm going to tell today is some recent work after the collaboration with Natasha Kira with the insensitivity power after our visit to Tokyo. More precisely, this is not quite finished work, even if we are a deadline to write for another anniversary for Keldysh, 85 years, we will see who will be writing for Boris 85 years. It will be JTP Boris, or will it be a GTP when people will write for your 85 years? So hands because of Keldysh, they'll be about excitonic insulator, but the concentration of excitons with the path polypollaritones will provide me to the GSMC to speak at these meetings. So all that will be about the science which exists from the beginning of this millennium or century, like, and this is the science of so-called pump-induced phase transitions. It is related to more techniques of pump-pumping probe in optics, which because of particular astonishing progress is now called the femtosecond pump and probe, where people use very short laser, very short pulses to pump up incredible number of excitations, more than 10 percent sometimes maybe up to 50 at the first femtosecond, and then after this pumping people see for the evolution, evolution is obtained by optics and now remarkably more complicated techniques like angle-result for emission, diffraction also becomes time-resolved, shorter than picoseconds, and the goal and advantages of this science is first of all to disentangle very short electronic times from slow 10 to minus 12 picosecond, latest times, which is particularly important for physics of high Tc superconductance and for the mode physics, then provoke dynamic evolution over the wide range of the whole phase diagram, not only near those equilibrium states. And then in the course of this evolution, we may either reach the short-living hidden H states, which are unavailable in thermodynamic approaches, which is what I call hidden, or even what there is a recent success to obtain a truly stable H state with unlimited, at least at low temperature lifetime. So what is going on, usually we have a laser and usually the laser produces high energy electron and whole pairs, which relax remarkably fast in tens up to 100, up to 100 second, so they come to the bottleneck, which may whatever we're interested in, it may be gap, observe the gap in superconductors, in charge density waves, in mod insulators and so on. And since that moment, relatively slow evolution becomes which we trace. I will speak a bit about that, give you one example of this electron hole pumping, but mostly my talk will be about very rare, but unit is still now, this is a sub pump pumping, not to the high energy electron hole pair, but to the bound pairs, which are the excitons. And this is kind of abstract of this original part of the work, is that we at high density and cooled excitons might, with big question mark, to both theory and experiment, formic was a condensate, like it is proved for polaritons, a kind, a special form of excitons. Now the wave function psi of this macroscopic quantum states will evolve, interacting with other degrees of freedom, we have system with a typically broken, symmetry broken state, so it interacts with other degrees of freedom, which are themselves prone to instability. And then because of this interaction, a number of things happen, one of them is psi is subject to self-trapping, acute to self-focusing of light. And also the local intensity can trigger transformation even if the mean density is below the global threshold. All what I'm going to say, but now let's go. So actually I have been baptized half a decade ago to this field, very close from here, my Jordan River is only one hour drive in Slovenia, in Ljubljana, in principle this extremely advanced science, it almost totally monopolized by Germany and Japan, with some special facilities in the United States. But there is a group in Ljubljana, in such a small country, which actually in some respects is superior to at least in terms of originality to many other things. And all together we have done all together, I mean some participation from me as a theorist, we have already put some four articles published in Nature and Science type of journals. And these are, in the title, there are some keywords, like coherent dynamics, dynamical symmetry breaking transition, ultrafast switching to stable human quantum states, metastable human quantum states, and switching between microscopic charge-ordering quantum state, not only by optics, but also by charge injection. And I will speak a bit about only one of them, my eldest and beloved work. So what is going on? Suppose that you are dealing with something, actually this was an example of charge density wave, it could be a superconductor, we have a system which has spontaneous symmetry breaking, so it has some degeneracy, actually this is maybe cross-section of the Mexican head potential, if the other parameter is complex. So originally the system was in the symmetry broken state, then we applied the last laser pulse, electronic temperature becomes very high, and this minimum, this minimum in energy disappears, the minimum now is at the trivial state or the parameter is zero, like in high temperatures, but the system is prepared at high energy, so it starts to oscillate across the whole interval of the parameter, and it oscillates, meanwhile the electronic temperature decreases, particularly combined, so the new minimum starts to reappear, and then at some moment this oscillation bump into the barrier, and the system is strapped again, this is a dynamic phase transition. And actually depending on odd or even number of half oscillation that the system may do, it may end up either in this state or in another state, and it gives also an interesting aspect of inhomogeneity, because the system is inhomogeneous, particularly in this experiment, the intensity of light is different in depth of the sample, so the system at different parts of the sample may have different parity in number of oscillations, so either in one state or in another state, so the domain walls appear, and these domain walls annihilate in time, and then we have a theory, rather elementary theory and the modeling, and this is, I think from my point of view, it's quite interesting, encouraging comparison between the theory and the experiment. So what we have here, we have here appearance of this amplitude mode of the order parameter, this is actually this kind of modeling of the Higgs modern, and then we have the dynamic phase transitions, and later we have some anomalies, and these anomalies are earthquakes coming from annihilation of domain walls. So this is a short introduction to the cases of electronic pumping, now to my main goal, pumping to the excitons. By now, this is only one example, but extremely intensively studied, and in number of examples it's numerous, because practically any system close to the phase transition, which is non-metallic, have some excitons to which we may pump, and these are so-called neutral ionic phase transitions, which happen in the donor-accepted chains, and this donor-accepted chain has a double phase transition, or the first order phase transition, where two other parameters appear. One is no symmetry breaking, this is that the charge transfer, which already is present because these molecules are different, the charge transfer jump from one value to another one, because it's from neutral to observe the neutral to observe the ionic state. This is effect of strong correlations, because actually it happens only because the system, the correlations of molecules are such that it prefers single electron. Molecules want to have spin one-half, and then, since somehow the states, even if we have not reached them, but somehow the system already knows that it's going towards chain of spin one-half, it also offers us the spin-pire transition, the demyelization instability, and this is symmetry breaking instability. So we have this double instability in our system, so this is more or less the sketch, and what is wonderful is that this material offers us two types of excitons. One is the intramolecular excitons at a very high energy, this is its shape, and this is the probe, for example, we may probe, but we also may pump, there are experiments with both pumping to these excitons, and then there is a charge transfer exciton, which, okay, this chemistry-oriented science, called the molecular science, calls charge transfer, for us this is more, one year more exciton, the bound state of the electron, and of the electron core, they are rather broad, so they have pretty small effective mass, so they are just maybe quite collective particles, so the laser may pump, this is a laser profile, this is the profile of the exciton. Well, so this is, we can write an elementary modeling, this is exciton energy multiplied with concentration plus repulsion of excitons, plus we will need it in the interaction of the third order of three excitons, and here we have the demerization, and this demerization gives you to ask where changes when q exceeds some critical value, so if the charge transfer by pumping of some evolution exceeds qc, then we have also the symmetry breaking transition, so we have a kind of iso, we have trivial minimum, and we have the minimum at final q more than qc, and two opposite values of h of demerization, and this is the energy profile, and the derivative of the energy over the concentration q, so we kind of, v is the kind of chemical potential of exciton, instantaneous energy of excitons, so we see four intervals, repulsion of excitons, then we have attraction of excitons, then we have the region of stability of negative energy of excitons, where they will be spontaneously created, and then again the stable, so we have, I have maybe original phase, which is quasi-neutral phase, and other stable phase is this quasi-ionic phase. Well, so now, now we are discussing these things, so charge transfer excitons, pump in a media, prone to also charge transfer instability, so it means actually that both the exciton and the charge ordering are built from the same processes of electron transfer between donors and molecules, so the thermodynamic or the parameter and intensity of pump excitons are of the same origin, let me just literally call them, call them, call them undistinguishable. Okay, so, so, so I have, I have, not distinguish from the thermodynamic or the parameter, so how can we treat it all together? Both the excitons pumping, which probably by the condensation and the thermodynamic phase transition, it can be done maybe the only way at least more efficient way, recalling the very old concepts of external instability introduced by a number of people in 60s, and more recently, it is called quite frequently in interpretation of experiments and some theory appears. So actually what this theory tells literally in application of semiconductors, commercial semiconductors is that suppose I have the particle gap, EG, I have the bonding energy of the electron, and then since they can be manipulated by pressure, by some other field independently, why not EB to become as large so that the total energy of X becomes negative? So that time it was very exotic thing, and I'm not sure that it really, really exists in the conventional semiconductors, but we understand today that there is nothing but a quantum phase transition, a kind of quantum phase transition. It's at zero temperature, energy of some excitation becomes zero. Well, so, so this, but this concept is too, is too, is too general for us. It covers practically all, at least non-metallic quantum phase transitions. So we distinguish it in a way, narrow it in a way that it was originally suggested for semiconductors when, when the total number of exciton is approximately conserved. Not exactly, but, but at least, at least, change, change slowly. And then, and then just recall that microscopic theories, if we recall theories of Keldyshkapayev, of, of Korn, with Jerome, and Rice, and other people who actually give this, this, this nickname, excitonic insulator, then, then these two, two, two, two, the theories of, of pump excitons, and the theories of excitonic insulator, they are theoretically almost the same, just we have different control parameters, either chemical potential or, or, or, or the concentration. And that will help us to build, to build the theory. Now, we face immediately some, some interesting question. This enigma, because thermodynamic charge transfer, the distribution of charge density is a single, general speaking non-conserved field. And if I decide phenomenologically to write some equation of motion, guiding dynamics of the system, I would just write something with second derivative of Q is variation of the, of the, of the omega, omega over Q. And this is, this is, so, so, so, and this is Q is not conserved, so Q may move as, as, as much as we see, just as we, as we saw in, in, in the, in the, in the first example of charge density, which I showed in the beginning. But now if I am saying that this Q is model psi squared, then model psi will be, naturally, we will see it, will be described by another, first order differential equation, which is kind of generalized growth PTIFK equation. And it conserves the number of particles. So it means that within this theory, I will not be able to change the number of excitons. It also will not be able to change dynamically the, the, the, the, the, the, the other parameter. When I do thermodynamics, I don't care about the times. Time, time, time is infinite. The system will always pass, find some path. But, but, but, but, but, but, but, but in, in dynamics, I will, I will not see, see, see, see this path. Now the resolution actually exists if we notice one quite passing by work of Keldshek and Kozlov in the end of, of this, of the whole story of excitonic insulator. And they notice the following thing. When, when I decompose my particles in the semiconductor, the wave, the wave functional operator in, in terms of electrons and holes and, and, and, and, and right the total, the original total Coulomb interaction, I find not, not, not, not, not, not, not, not, not, not, not, not, not only, only, only directly scattering like electron goes to electron holes and holes. So which, which actually after I, I declare this, this thing to be average in the face of the excitonic insulator or both the, both the condensate that will give me psi, that may give me psi, psi star. There are also some other processes. We do not conserve the number of particles because here two electrons go to, to holes. Normally these are virtual processes. They don't conserve the energy, but if the system has a condensate, then they give me immediately psi squared plus psi star squared. Certainly there is some phase, but I will come, come, consider it to be to, to be zero. So I have, I have, I have, and this is the source of, for conservation of, of, of, of, of a number of particles. Recall that, that when Valeriy Pokrovsky a few days ago spoke about theory of spin, of spin, of spin waves or of basic condensate in, in magnons, he also noticed and played with, with these terms which not can, can, can contain, conserve the total number of magnons. Well, so what I have now, I have now, will have now the, the kind of the, of the generalized Gross-Petaevsky equation, which is generalized because Hamiltonian will be variation. It may not be just simple psi to the fourth, not, not originate from simple repulsion psi to the fourth. It's a variation of, of, of, of q of its total energy which can sense also interaction with the same, with, with other parameters. And this, and this, this, this psi star is, is, is coming, is coming from, from, from, from, from non-conservation, from the generation of pairs of electrons from vacuum, pairs, pairs of excitons from, from, from the vacuum. Now we have gamma here. Well, this is attenuation, attenuation parameter and in, in the, in the theory of, of, of, of, in, in the theory of of polariton that Natasha Berloff reported here today. Actually it, it appears it's important and, and well, well, well discussed quantity. But what, what, what, what, what, what we know about, about, about that. So certainly we know that gamma is, we need now in, in wide interval as a function of q. Well, in, in principle there is a finite, finite lifetime of single exciton. But for us, for me, vanishing concentration will be still a microscopic concentration. So, so gamma will be, it is, gamma will be proportional to q. This is just spontaneous. Okay. Because, because, because, because, because, because, because, because of the, of, of, of the buzzer statistics. But what is important I claim that actually when, when we reach the minimum here there is no, there is no channel to decay once again. So gamma must, must, must become here zero. So if I, if I would walk without, without this, this, this particular term I would write that gamma is proportional to V, V is the derivative of, of the, of the, of the energy curve. So it is, it is zero, it is zero in the, in the, in the static phase which cannot be fed. You can, the, the very complicated multi-process, multi-particle process because certainly metastable state should decay somehow. But it's not, that doesn't decay, decay, decay in a, in a, in a, in a simple way. Gamma, yes, I claim that the gamma should vanish here, yes. No, here, here, here, here gamma proportional to Q. Actually, actually, there will be some finite value for gamma because even the single exciton can decay. But for me small Q equals standing to zero is still a microscopic concentration of exciton. So, so I, I write this spontaneous, spontaneous emission. Okay. So, so, but then actually this minimum is more complicated because we live not only in, in, in the, in the amplitude Q but also in, in the phase now. So my claim is that, that, that actually this, this condition is generalized as that, as that this gamma will be proportional d phi over dt. So when, when, when there is no more time dependence then no, no more, no more decay. The system reached thermodynamic stable, stable, stable state. So if I now write it in, without, without, without, okay, I will, I will not speak much, much about, about, about space dependence. So suppose I'm in a kind of quantum dot or homogenous, in, in, in enforce the homogenous regime, which is not quite so. And then, then, then, then, then I have, I have, I have a system of couple equations. Now if I actually, there is also done, done by dependence on this another symmetry breaking parameter for which I have, I have, I have another equation. Well, so, and then, so, so this term gives me either if, if I'm very close somehow, very close to zero, I'm close, close to metastable state, then it gives me look, look, looking, looking over the face. If not, it gives me oscillations. So now let me do the following thing. Let me, let me make the, the toy model for simplicity, where I do not, I do not, I do not have, I do not have this latest demerization. So because this demerization brings, because, because, because, because of its, of its, of its fringes, it will bring, bring, bring, bring its, its, its, its own oscillations. So what we see, what we see here, I had, I had here in the beginning, I had the excitonic insulator. I now, I pump it, I dev, I dev, I dev, I deviate it from, from, from the equilibrium. And since I pump, I pump it with Q exceeding the lock-in transition, then for a while, my face goes, goes almost linearly, which means that I have given energy of elementary excitation. Phi dot, this time derivative of face is, is, is the energy. So I have the energy, but then, but, but, but, but then, then, then I have, have, have, have, have a lock-in. So the smallest, the, the, the, the face, the face space, the, the, how to say, the plot, polar, polar plot Q of function, we see how we go from one regime, unlocked regime to, to the locked one. Well, so now, now, once, once again, once again, the, once again, the generic model. So now, now I am just, just, just up, just above, above, above the threshold transition. So I have a long waiting time because I, I just, I put myself close, close to the, close, close to the threshold, but after, artificially, but, especially, but, but after, after, after, after the threshold, we see that the system, which, so, so original system was instead Q equals 0. So it was, it was neutral phase. And here, final Q is the excitonic insulator state. So, so, so, so original, I was Q 0, then I pumped it up to, this Q is, is in number, number of excitons. I pumped it up to this level, which is slightly super, super critical. The system stays here, and then it loses. It, it has very, very, very strong oscillations until, until it, until it experiences the dynamic phase transition to another, to, to, to another phase. And now, and now, let me go, go to more complicated picture. Actually, the real picture for this material, when I have also, also the lattice, and the lattice has its own oscillations. So here, S equals 0, so I don't have here any oscillations, which I have said before from microscopic interference for small s, they will, and then, and then, so, so, what happens? I have, I have a dynamic phase transition. Phase is more or less, you know, more or less goes linearly in time. So I am in, in the, in the state with the, with the given energy of exciton. Actually, this is the time derivative. I have, I see, I see some, some, some oscillations. And then, since I'm a subcritical pumping, in spite of some strong initial oscillations, Q finally vanes. So my exciton, this, this, this, this, disappear. Now, the, almost the same, the same from, if I introduce S, but only oscillations appear. I have this quantum interference between the, actually, between the bose condensate of excitons and the, and the ground state of the extraneous oscillator. And then, and then I go, I go, I go to, I go to the supercritical pumping. If I am, it, it, it, it, it, it, it, it's short time, time, time, I see that, okay, in the beginning Q decreases, but not sufficiently, then it is, it, it is, it is, it, it is picked up, picked up and, and the, the exciton energy somehow starts to oscillate between positive and negative parts. So in, in this part, in this part excitons are emitted from the vacuum. Here they, here, here, exciton is, is negative. They are, they are, they are emitted from the vacuum. And we see some tendency of the phase in the original, if I do, it was more than, it was given energy of the exciton and now it, it's, it's, it, it, it tends, tends, tends to, to, to, to level, to zero. So then finally, finally maybe the last, the last, at, at, at long times, at long times, what we have, what we have now, if, if there is no, this, this term, no, no, no, no, no, no, no, no phase locking terms, then the system will grow and they come, we are at the supercritical pumping to the new state. This is a equilibrium, metastable equilibrium state of the excitonic insulator. And, and the exciton, the, the phase is finally locked. We pass through the energy, through the region of negative, positive excitonic energy to unstable region of the negative, of negative excitonic energies and then again, again, back, back, back, back to the stability and, but it's locked, but it's locked at arbitrary value. The drug may be dependent on the initial condition and so on, but as soon, as soon as, as, as, as, as I introduce at least small, small phase, phase locking term, then instead of this smooth, smooth transition here, I have abrupt, abrupt lock, lock, lock in transition which generates for me new, new series of, of, of, of, of, of acceptations. Well, so it was more or less conditional that I impose more or less, more or less homogeneous conditions, so at least the sample is not, is not quite, is not, is not, is not too big. Now what happens, what happens if I, if I, if I take into account some initial fluctuations? So now this is modeling not only in time, but in time and space. And what I do recall that the latest demerization was a symmetry breaking parameter because it can have either positive or negative values. So we introduce here the extremely small 10 to minus 12 initial, initial perturbation of different sites into half of the sample. Actually it will better, better to study, to study the disorder system, but it has not been done yet. And then, and, and, and then, then we see that the two domains appear, one with opposite, opposite equivalent signs and then one of them wins in other vanishes. And then the one which wins, if it is initially small, it starts to make oscillations around, around, around the middle of the sample. If I'm close to them, yeah. Okay, I'm very close. So I have not, I have not spoken here at all about, about, about, about the case which is slightly more complicated because we have more fields but conceptually much more simple. The case I have mentioned of so-called intramolecular excitons where the excitonic density and the other parameter are different fields. So we just, we just simply, simply now, now, without much philosophy, write and solve the, the couple system of equations. So we see here some, a number of interesting things which, which, which we have done here for. So at, at, at short times we see a regeneration of the, there is no, there is no seeding here anymore. No seeding for the symmetry breaking. So the system itself experiences the self, self-focusing and then, and then in two different points and then they, then they measure, start oscillating and this is even before the regeneration appears. It's a, it's, it's a moment maybe because of measuring of different domains. The, the amplitude becomes sufficient to large to provoke, to provoke the symmetry breaking phase transitions. And if I go now to high times then, then with time now the, the, the, the concentration of excitons may even, even disappear but the system keeps, keeps the persistent domain. So it's practically all, all what I wanted to say. So one cannot witness against himself at least without presence of the advocate. But still I want to say that what, about some regrets and cues about, about some suggestions or incomplete studies that we have done. Thank you. Thank you very much.