would like to be here to speak to this Max Conference. And of course we discuss non-equilibrium physics and about how non-equilibrium physics is related to HPC systems. So let me say that to run simulations on HPC systems and to design the code for HPC systems. It's sometimes a thing but it of course offers also the opportunity to do simulations po nemu ječnem izgrednimi. Izgleda je pospedil ta, kaj hom počasem persimulati, v nemojo v nekaj, ki bomo pravoditi včešen. Proto, bomo počasem, da polidoj državce bili nemaželji, če samo je izvalalo na prangentna specija teori. In so bi voživкого načinati v daljih priključanjo, Premaj, da je je koncerto, da se nasenjemo CouldThumb ajdeא nespešnev Medicare, zato skupel je nekrat, že legače z večtina vzela nekaj, kaj je in tudi zamišnev in nekaj, da se se nekaj nekrije obsošenje nespešnev Leahskega obsošenje,其實 nekaj je nekaj nekako obsošenje. is that we can consider to describe from the first principle new physics, and here for new physics I mean out of equilibrium physics, so we can think of running first principle simulations of materials in highly non-equilibru situations, which of course there is a lot of new physics, and these kind of simulations are very demanding, The answer is what I would like to discuss about today. I start with my introduction which I used already a couple of times to explain what is non-equilibrium physics and ultra-fast physics. I start with a picture of the human eye because this is the instrument that we mostly use to try to explore the world which is around us. And it is a very powerful instrument but of course it has limitation both in space and in time resolution. Prvé, da smo pošli problem events in izgledali o domenju. Prvič, da smo izgledali o domenju, je se vzgledali z Galileo, iz 16.09. Zelo se tudi zaeleskop lukov vendom, imeli na stah ni pravdi. Proveso se iglim del配on, zgleda jenje internet, tudi vsega elektrovana mikroskopija, in nekaj nekaj da počekaj tudi vsega latonija, je vsega pukrana grafina v 2011, so nene objevno od ovega. Z njač delno, da pa posebimo zbičaj sej, ovo je napravil nekaj nekaj, da je 10, 6, 10, 7. Zelo, nekaj je začnega? In tukaj počuče sem postavljeni postavljeni v 1791, vzvečenju mnjela na vzveč, ko je vzveč. Vzveč je vzveč, da je vzveč, kako je vzveč na vzveč. Vzveč je tukaj, kako je vzveč vzveč, ker je nekaj vzveč, da je vzveč vzveč, tako, da ne rezovamo v izgledanju, zelo se rovno v početku. If we compare these, with instead the first movie of the history, I would say it was taken in 1878 in Palo Alto, it was indeed a series of 16 pictures of EOS running, and here we see that there is never a moment where the EOS is floating with the legs stretched, so the closest situation to the picture is maybe this one, but the EOS is always touching the ground, and just when the legs are, let's say, not stretched, the EOS is floating over the ground while running. So this is a nice example of taking pictures in sequence, which we can somehow overcome the limitation of our eye. And of course this was the first result, and well, how fast we can go. So I represent a few important moments, so this is the Nobel Prize, which was given in 1967 for the invention of the photolysis method, which was invented some years before, and it enabled the observation of chemical reaction, so 10 to the minus six seconds, or one microsecond. So some years later, another Nobel Prize in 1999, this time, was given for the ability to absorb femtosecond spectroscopy, actually close to picosecond spectroscopy. So we have been able to observe the motion of the atoms. Indeed, if we consider the atoms, and if we consider the typical coulomb interaction between two ions, and the mass of the atom from simple laws of classical physics, which we see that the time in which a atom moves is of the order of 100 femtoseconds. And beyond that, there is the dynamics of the electrons. So the electrons, using the Bohr model, we can see that they move on a time scale, which is close to one femtosecond, a little below. And so this is the kind of physics that we can now try to observe with the modern laser passes. And here in this plot, I represent the time duration of laser passes, which one can imagine to be used to take a picture of the electron dynamics. So here you see the time duration, and this is the period in which the fastest laser pass was created. And in particularly staying in the visible UV range, now we have reached the duration of below 10 femtoseconds. And this is the kind of experiment I would like to describe. So I have to say that if one goes in the X-ray, instead can even have passes below one femtoseconds, but for this presentation I will focus on this kind of physics, so with passes in the visible UV range. And this is the kind of physics which can be described or measured with this kind of passes. And it is, of course, related to electron dynamics. So here is the representation of the duration of the pass, and here of the different kind of processes I would like to model from first principles. And one important observation is that if one tries to model this kind of physics with time-dependent density functional theory, basically one can describe the absorption of photons, the coherent dynamics which follows, but not much more of all these physical processes. And one of the reasons is that for TDF team practicers we know the adiabatic approximation. This is well-established, but we don't know how to use instead the frequency-dependent kernes in the equation of motion. And then it is harder to include all these kind of processes. And instead if we move to many more perturbation theory, we have a way to include all these kind of processes. So here is a picture of a typical pump and probe experiment where you can measure the electron's dynamics. So there is a first short pass which is sent on the sample and then the dynamics is activated. And after some time delay, a second pass which is in this case emitting the electron from the system which is then detected and changing the delay between the pump and the probe, one can try to have a picture of the dynamics of electrons. And here I reported here a couple of papers where this kind of dynamics was measured in bulk silicon. And in particular they pumped near the optical gap of silicon so a direct injecting electron from the top of the valence band to the conduction band and then measuring the intensity of photoemission signal from this point in the Brillouin zone. And here you see the picture of the intensity. And the simple mind interpretation is that electrons are injected here or in this region, in this valley from the pump pass which is here in red. And then electrons cut from here to the minimum of the conduction band so the signal goes down. And this is a simple interpretation and I will show you how we can try to describe that and if this matches with the first principle simulations. Another kind of experiment which is similar in the spirit so there is again a pump pass sent to the material and with a given time delay probe but this time instead of photoemitting an electron what is detected is the reflection of the probe signal. So this is an experiment which has been done for example in these two papers. Again bulk silicon pumping near the optical gap. And in this case I will consider instead of the signal from this paper a signal we got from a collaboration where with Polytechnic of Milano. So this is a typical reflectivity signal it depends on the frequency of the probe pulse and it is represented at fixed delay between the pump of the probe. And of course one could also change the delay and see how this profile changes. And I would like also to outline that pump and probe experiments are nice to see the electron dynamics to see new physics but there is also strong technological interest because if you can control the electron dynamics basically you can control the magnetization dynamics of the system and magnetization is what is used to basically record information. So here in the picture you see the way you can control magnetization and the easiest way is using an external magnetic field but with a laser pulse you can even think about controlling the magnetization on a much shorter time scale. And indeed there have been a lot of work I am just highlighting two papers where the control of magnetization using ultra short laser pulses has been realized so it has been proposed in ultra fast devices where one can read and write information on the fem to second time scale. And even in this case this is taken from this review a proper theoretical framework to describe the ultra fast dynamics remains challenging. So the message is that there are a lot of experiments which can be done with pump and probe setup this is a table top setup and which strongly need a proper theoretical description because it is not easy to describe this kind of experiment in an intuitive way and not only table top experiments but there are also experiments done at large facilities for example at the free electron laser this is a picture of the field which is nearby here in Trieste. So how I would like to do all this from first principles and the idea is that I want to start from a standard ground state calculation where I compute the equilibrium properties so the structure of the system and even the phonons and the electron phonon matrix elements and then I would like to use that to describe the interaction with the pump the scattering mechanism and then eventually also the measurement process. How I do that in practice I want to use many body perturbation theory so I start from DFT and then I want to merge the DFT with many body perturbation theory so I use what we call ab initio many body perturbation theory where the konešan way functions and again energies are used as a zero order theory to construct the green function and then to solve the equation for the many body perturbation theory. Of course it is computationally very demanding and this is why I say that HPC system can be helping that but the nice thing is that it is an approach which is very powerful predictive and parameter free so this is how it works in practice in silicon so here is the starting point representation of the mass structure of silicon I start with a DFT mass structure which is the dashed one and then I compute the quasi particle correction then I also compute the phonons dispersion and then I plug these two ingredients together with the wave functions and electron phonon matrix elements in my equation of motion so what I solved is an equation of motion where there is explicitly the pump pulse there is the equilibrium mass structure and there are the many body correlations and then importantly there are there is this scattering term which takes into account of the scattering processes for example with phonons in the system it is an equation of motion so I need say the equilibrium the starting point which is the starting point of my g lesser which is nothing but the density matrix of the system projected on the Konešan mass structure so these m and k indexes are the indexes of the mass structure I prepared the equation of motion and I can extract different information for example the polarization but mainly what I will use is the occupations on the mass structure as a function of time and this time will be the time delay from the pump pulse which can be obtained from the diagonal elements and I can even use these occupations to construct the the unequilibrium linear response of the system and then for example the absorption so I came back to the experiment I was showing a few slides ago these pump and probe experiments on silicon and I tried to to simulate this experiment and the first thing we realized is that if I apply a laser pulse to the system to the mass structure of the system this pulse is linearly polarized and it will break some of the symmetries in the Brillouin zone so what happens here is that the polarization of the electric field is directed along a precise direction and then in particular the L points in the Brillouin zone of bike silicon they will not be all equivalents anymore so here is a representation in need of the band structure with both L and L prime so the bands are the same but what happens is that the pulse is mainly injecting electron around L and not at L prime because for selection so we use the excitations of electron at L prime are forbidden so after that one can imagine what happens there are two degenerate levels one which is occupied and the other not and there is a very fast transfer of electrons from L to L prime so we did the simulation and with that we were able to reproduce very nicely the time decay of the experiment and just after there is disequilibration then the electrons scatter to the minimum of the conduction band and then eventually they cool and connected to that I would like to discuss also an interesting concept which is related to the lifetime of a level so here we were describing experimentally they were measuring the time it takes to an electron to go from in out of equilibrium state L to relax to the minimum and we are used to think that the lifetime is related in many body perturbation theory to the imaginary part of the self energy which in photoemission is related to the width of a photoemission peak so what I would like to compare is how this lifetime is connected with the simulation I did and in particular if I think that the lifetime is connected to the width I am thinking that the population of a specific level will decay in time with this specific lifetime which means here this lifetime this level the population in this level is dictated by an equation of motion like this one but indeed during the theory in the matter what once obtained is an equation of motion like this one and you see the difference here so here the population is reduced in time by the electronic lifetime and this describes what are called the out processes but there is also another term which is zero equilibrium which describes the processes of electron jumping in the level because there can be electrons in other points of the bus structure so if I want something which matches this idea I can simply divide and multiply by the electronic occupation and write an effective equation with this lifetime which now has this form and it will be time dependent so what I do is to compare this effective lifetime of the equilibrium lifetime during my simulation and here is a plot so this is the equilibrium lifetime and this is the effective lifetime at L and we see that at the beginning of the simulation they are very close so the pump is pumping electron just here and so the electron can scatter mostly everywhere in the Brillouin zone and so the lifetime is the equilibrium concept but then after some time this channel is closed and it is closed because electrons can still jump here but there will be also electron jumping back all the lifetime and so there is a fast drop of the lifetime in energy so it becomes much longer in time ok, another nice thing that I can do is I can take my population and I plot them as a function of the energy at different time step and this is what is pictured here so here is the population in the conduction band at equilibrium I have no electrons, it is 0 and then the pump pass starts to inject electrons in the conduction band and in particular also here I see that the occupation of the L level is much higher than the occupation of the L prime level and then since there are electron phonons scattering process the electrons spread everywhere in the mass structure and this is what is happening here so the L and L prime levels are the same now and then they go towards the minimum and they start to form a fermilike distribution with a temperature which is then decreasing because my system is giving energy to the lattice so the electrons are cooling at the beginning the temperature is very high and for the moment in the simulation the temperature of the lattice is kept fixed at equilibrium and so you see that the system is cooling and cooling and then if I go on with the simulation it will eventually reach the temperature of the lattice ok, maybe I can stop here I had also the other experiment but I think I will not have time so I would like to mention that all these results are part of a a collaboration so I am working with André Marini at the Cienar ISM and we are doing both theory and code developing with the Yambo code we have a collaboration with Enrico Perfetto and Gianluca Stefanucci which also are using non-equilibrium functions and they also have their own code which is called CHIRS which is meant for models or isolated systems and recently we have interfaced the two codes and then that we are also using the coding collaboration with a group in Modena who is now left science now but did part of the simulations in other material which I didn't discuss today and Aléandro Molina Sanchez in Spain is also using the the code for doing simulation and that's it thank you and a list of references