Okay, so Alex has the floor is yours. Right?
Thank you very much. My name is Alex asmus allows us and I'm very happy today to talk
about a calibration of problem plasma in small systems. This is based on a series
of works I did with various collaborators. And yesterday, we put a put a review which
discusses the formalization in QC D in in many aspects and I invite you to have a
have a look, I have a lot to talk about a small part of general physics of QC D
optimization in CD. So why we are so interested in Van collisions? It's because
it's probably the only place in the universe where we can study the non
equilibrium accuracy dynamics of dense matter. And one of the very fascinating
features of this matter is nucleons collide and fundamental degrees of
freedoms of parks and lawns are released that the internet so strong lands So fast
but in a very short time system is very short lived and medium is formed which we
call Quark gluon plasma, which behaves like you know, some medium with properties
like a viscosity equation of state. So, it's very interesting how such dynamics
managed to happen in such a short time. And the reason why we believe that there
is such a medium creating head and collisions is from always excellent
experimental results, which were already discussed in the first plenary, which in
Monday that various observables indicate a certain level of conductivity to the
system and familiarization. So, for example, many particles share very similar
flow or collective flow and also a hydrant chemistry appears to be close to that of
thermal system indicating that certain level of formalization is achieved. And
one interesting feature that many of you signals are very smooth functions of
particle a multiplicity is created in the system. And it doesn't matter whether the
system is led collision proton, proton proton, which looks quite different, but
that land verbal signals are very similar. So, to understand how is it possible for a
system to thermalize we need to know you know what drives were crucially matter to
ephemeralization. And, in our review, we looked at various theoretical approaches
to describe non equilibrium risky behavior. And it's also a corresponds to
different stages and have an collisions as two nuclear collide initially, this fast
moving color charges produce strong chromo electrical chromo magnetic fields. So,
description in terms of strong classical fields is appropriate. Later the system is
expanding and as more dilute. So you have to take into account that and quasi
particle descriptions governed by kinetic theory is more appropriate to describe
this describe this phase. Finally, the system is close enough to equilibrium that
you can use a macroscopic hydrodynamic description to describe a system evolution
and later the system goes down and freezes up into particles. So, in this talk I will
focus on this earlier time dynamics was pre cooling room, and in particular how it
is described using to study kinetic theory because it connects with early time
physics in terms of strong fields and late time in terms of hydrodynamics. And
mechanistic theory I'm talking about is effective description of the city at high
temperatures were
the typical nodes have momentum of or the temperature and they score the particles
of quarks and gluons are governed by Boltzmann's equation. So, that
distribution function of quarks and gluons evolve driven by the expansion term, the
longitudinal expansion tries to drive a system more and as a topic and collision
terms. And here we have to do scatterings and one to two process. And I would like
to emphasize that we have the same kind of collision processes, which drive energy
loss of energetic pattern as it moves from problem plasma or emission of photons from
quarks perturbed by the medium. So, um and as I said, basically two types of
scattering processes, elastic processes, and thanks to the medium induced
radiation, you can additionally have wanted to affect one to two processes, as
these are the leading with the processes, and two, we have both forward and backward
processes to guarantee the detailed balance. And once you solve this Boltzmann
equation, you can describe the equilibration in terms of kinetic theory,
and this is a picture or approach to librium so called bottom up
familiarization. So, in this talk, I will you review various consequences of this
picture and the world One of the first things is to was sort of this more broad
understanding in recent years is that if you look at how system equilibrate, and
particularly if you look at energy longer today, more pressure on, you know,
component energy momentum tensor, relative to energy in equilibrium for conformal
gas, you're expected to be one third ratio, but away from equilibrium, this
expansion drives the system away from this equilibrium value. And small deviations
are described by black, which is viscous hydrodynamics. That's a universal
description. However, even at much earlier times, when expansion is very fast. And
there is this emergence of macroscopic description in terms of hydrogen dynamic
attractors, which were discussed by Bill Cohen on His plenary. That means that if
you look at for mu curvatures youngness, kinetic theory simulations and you start
to have great podcasts, which are different initial conditions may collapse
on the same curve which then approaches equilibrium at late times. And this
approach is given in terms of W parameter, which is time measured in units of kinetic
relaxation time power and kinetic relaxation time is given inversely
proportional to temperature. So hot the systems are accelerating faster and she
has a scarcity. So, more strongly the system has smaller shared resources. So,
it also calibrates faster and the fact that many different microscopic theories
behave rather you know, very well parameterised by this variable suggests us
to look how a system you know what is the system's lifetime in this unit, because,
you know, once this time reaches around one, we know that for example, this goes
hydrodynamics should become a good description of microscopic behavior. And
so, in order to estimate with a lifetime in units of a capitalization time.
Firstly, note that produce particle multiplicity is responsible for entropy in
the system, which is expressed in this way in terms of temperature. And of course, if
you have the same particle multiplicity coming from a large system, it will be
spread over a larger area than from a small system. So, a smaller system will be
hotter higher temperature means it's equilibrates faster. However, the system
which is larger has also more time to equilibrate or to evolve because initially
for small times the system is only expanding in one day in one dimensionally
and the temperatures falling very slowly, but at late times, once a system starts
expanding in three dimensions, expansion is very fast. So, we can estimate that you
know, system lifetime typically is of order of radius. So, that means, that if
you put a radius in this formula and try to calculate, what is the ratio on in your
in units of power Find the system lifetime in this unit is given completely in terms
of a particle multiplicity and independent of its radius r. So, that is one way why
systems is a similar multiplicity looks so similar because they have the same
lifetime in units in of kinetic relaxation time, although we don't have the same
lifetime in
physical units.
So, moving on, as I said the kinetic theory is a is a good description which
allows us to connect with initial classical field descriptions we're in have
an collisions systems are very unusual and it's a tropic pressures are very strongly
separated and multi dimensional in transit directions. Well in a hydrodynamic
description, you would expect them to be close to each other. And in our work we
showed how kinetic theory indeed can connect with ln late time behavior and
they they have a smooth overlap in this region where both descriptions are, you
know, valid, and we can use the condition for this validity to find small systems
would also approach hydrodynamics. So I said if the system as we saw before, but
if the system lifetime is larger than one in units of kinetic relaxation time,
there'll be enough time for viscous hydrodynamics to be applicable. So, yeah,
I it's plotted the particle multiplicity and ether overs on this axis and you plot
with this ratio. So, for large systems like lead collisions with enough particle
multiplicity or a system is large enough that the system will reach this
hydrodynamic phase and live rather long in that phase for a long time, while for
small multiplicities this ratio is much smaller and that means that system is
barely reaching this hydrodynamic behavior. Of course, it depends on the
exact properties of of it over But it does indicate that small systems have very
little time to really evolve in this classical hydrodynamics. So we need to
think whether some of these observables are come already in equilibrium dynamics.
Another interesting feature of equilibration is production of fermions.
Because in this recoupling picture, the initial state is completely dominated by
gluons, all energies is in terms of ones while in equilibrium when you try to use
for lattice equation of state, you have more Quark degrees of freedom than once.
So you have more energy in quarks and gluons. So, he needs to describe how a
system produce fermions and kinetic theory is, is well suited for that there are
processes which produce quarks from once and you see that in the simulation, there
were a number of energy in terms of muons rather quickly or overtake ones and
fermions are becoming dominating in terms of energy at a reasonably short time. So
that justifies me. application of his thermodynamic, you know thermal equation
of states from lack of scarcity.
And the
Another feature of you know, thermal chemical equilibrium is the fact that, you
know, we can in fact indirectly from a thermal equilibrium of hadrons that is
also thermal equilibrium of one lone plasma and perhaps vice versa. So, in
these simulations using similar arguments as I said before, we estimated that if a
system has at least 100 units of charged particles per rapidity, IT system lives
long enough to reach a sufficient chemical equilibration in terms of bogland plasma
of quarks and gluons. So, this perhaps could mean that we also would see chemical
equilibration in terms of hadrons even though we don't describe how the
realization and that would mean that you know, at very high multiplicity, pp
collisions, which may be accessed at Future rants are for let's see, we could
see the separation of strange strangeness even in a small system. So, now moving on,
on the last part, I wanted to say that with this knowledge of hydrodynamic
attractors, we can describe the system evolution from very early times far from
equilibrium state to equilibrium. And that allows us to solve the equations of
motions for energy density. So, in the in the early stages, when the system is still
one dimensional expanding the we can use the pressure from a hydrodynamic attractor
to solve this equation. And that allows us to calculate what is the energy density at
later times, when the system is close to thermal equilibrium. And from that energy
we can calculate the entropy and entropy is proportional to produce particle
multiplicity and have an collisions. So using that inverse paper, we were able to
derive an exact formula which connects initial state energy deposition. It's very
early times when a system is very far from equilibrium to produce particle
multiplicities at late times, or what would be measured afterwards. And we found
that with proper transport properties of a medium like Seamus, Casa De Anza, some are
known coefficients. So, this is, you know, very nice formula and makes allows us to
make some predictions. In particular, if you can, you know, come up with a model
for initial state deposition, and there are some models which habit, and they are
in general dependent on the overlap of two nuclei when they collide. So we have
impact dependence that allows to get a centrality dependence of initial state
energy and plugging into this formula, we get the particle multiplicity, so we get a
party impact or centrality dependence of particle multiplicities. And in this work,
we just use single point in centrality in support of multiplicities versus
centrality to fix the normalization at one point. And when this is the green curve,
our best prediction has a good and positive prediction for particle
multiplicities. And when that allows us also to know what was the initial state
energy, which is plotted here, in these great bands, in comparison to the
experimental and measured points.
So you see that
initially, the energy in the system is much larger, because there's work being
done during the expansion. And there's uncertainty in this energy because it
depends on what kind of transport coefficients you use in your system of
illusion. And one interesting feature is that it's very peripheral collisions are
some of the energy estimates fall below the experimental measurement point, which
is not possible. So that means even risk of transport coefficients are ruled out of
a system is not reaching for On the librium, as assumed in our calculation, so
that's another in ID identification that these peripheral conditions are not
probably not really reaching thermal equilibrium. And I'm just about to finish
that. In order to understand these peripheral collisions better, it's very
exciting to have an opportunity in the next run of a short run of oxygen oxygen
collisions, because if you look in terms of number of patterns and a number of
participants in the collision and number of binary collisions, you can see that
peripheral lead collisions are very close to their minimum bias, oxygen oxygen
collisions, which would be much more easier, or it has more free of biases,
both experimentally and in terms of modeling. So I look forward to these
measurements. So um, let me summarize that I think we have a very improved
understanding of our system equilibrium. And this allows us to have some
predictions on terms of basic calibration can happen also in small systems. But of
course, we need to investigate in more detail of the actual transit expansion is
changing the picture for and make more quantitative predictions. And we need that
because we will have more data and and even use more systems in upcoming policy
runs.
Thank you.
Thank you very much for this very interesting presentation. So now we have
time for one or maybe two questions. If you have a question, please press the
right hand button.
Okay, so we I see one question from Michael. Michael, you can unmute yourself,
Alexis very nice talk on talked about DND ADA. In certain systems you can have a
range of very restricted say two factor systems. You can have a larger pool of the
gap, and then only a certain multiplicity in his hernia, all your most pressing is
concentrated in one narrow region of liquidity. So according to your picture,
you if you were looking at the fact of collisions, you wouldn't compare them with
the same multiplicity to regular questions. But in the end, Ada said that
in this case, I always had the in mind, or it's based on the boost invariant systems
where this end was in at mid rapidity. So here I'm talking mid rapidity at the end.
Of course, it doesn't apply to Universal to all systems. You know, without any
better for mid mid rapidity. Yeah, that's that's the multiplicity I was referring
to.
Okay, okay. Perfect. If you could just think about what because there is quite a
bit of data coming on to factor systems and, and what model might look at in that.
Thank you so much. Thank you.
Okay, thank you. I think we have to move on. Thank you, Alexander.