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Okay, so Alex has the floor is yours.
Right?

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Thank you very much. My name is Alex asmus
allows us and I'm very happy today to talk

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about a calibration of problem plasma in
small systems. This is based on a series

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of works I did with various collaborators.
And yesterday, we put a put a review which

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discusses the formalization in QC D in in
many aspects and I invite you to have a

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have a look, I have a lot to talk about a
small part of general physics of QC D

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optimization in CD. So why we are so
interested in Van collisions? It's because

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it's probably the only place in the
universe where we can study the non

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equilibrium accuracy dynamics of dense
matter. And one of the very fascinating

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features of this matter is nucleons
collide and fundamental degrees of

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freedoms of parks and lawns are released
that the internet so strong lands So fast

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but in a very short time system is very
short lived and medium is formed which we

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call Quark gluon plasma, which behaves
like you know, some medium with properties

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like a viscosity equation of state. So,
it's very interesting how such dynamics

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managed to happen in such a short time.
And the reason why we believe that there

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is such a medium creating head and
collisions is from always excellent

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experimental results, which were already
discussed in the first plenary, which in

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Monday that various observables indicate a
certain level of conductivity to the

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system and familiarization. So, for
example, many particles share very similar

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flow or collective flow and also a hydrant
chemistry appears to be close to that of

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thermal system indicating that certain
level of formalization is achieved. And

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one interesting feature that many of you
signals are very smooth functions of

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particle a multiplicity is created in the
system. And it doesn't matter whether the

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system is led collision proton, proton
proton, which looks quite different, but

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that land verbal signals are very similar.
So, to understand how is it possible for a

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system to thermalize we need to know you
know what drives were crucially matter to

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ephemeralization. And, in our review, we
looked at various theoretical approaches

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to describe non equilibrium risky
behavior. And it's also a corresponds to

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different stages and have an collisions as
two nuclear collide initially, this fast

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moving color charges produce strong chromo
electrical chromo magnetic fields. So,

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description in terms of strong classical
fields is appropriate. Later the system is

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expanding and as more dilute. So you have
to take into account that and quasi

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particle descriptions governed by kinetic
theory is more appropriate to describe

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this describe this phase. Finally, the
system is close enough to equilibrium that

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you can use a macroscopic hydrodynamic
description to describe a system evolution

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and later the system goes down and freezes
up into particles. So, in this talk I will

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focus on this earlier time dynamics was
pre cooling room, and in particular how it

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is described using to study kinetic theory
because it connects with early time

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physics in terms of strong fields and late
time in terms of hydrodynamics. And

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mechanistic theory I'm talking about is
effective description of the city at high

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temperatures were

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the typical nodes have momentum of or the
temperature and they score the particles

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of quarks and gluons are governed by
Boltzmann's equation. So, that

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distribution function of quarks and gluons
evolve driven by the expansion term, the

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longitudinal expansion tries to drive a
system more and as a topic and collision

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terms. And here we have to do scatterings
and one to two process. And I would like

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to emphasize that we have the same kind of
collision processes, which drive energy

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loss of energetic pattern as it moves from
problem plasma or emission of photons from

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quarks perturbed by the medium. So, um and
as I said, basically two types of

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scattering processes, elastic processes,
and thanks to the medium induced

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radiation, you can additionally have
wanted to affect one to two processes, as

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these are the leading with the processes,
and two, we have both forward and backward

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processes to guarantee the detailed
balance. And once you solve this Boltzmann

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equation, you can describe the
equilibration in terms of kinetic theory,

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and this is a picture or approach to
librium so called bottom up

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familiarization. So, in this talk, I will
you review various consequences of this

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picture and the world One of the first
things is to was sort of this more broad

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understanding in recent years is that if
you look at how system equilibrate, and

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particularly if you look at energy longer
today, more pressure on, you know,

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component energy momentum tensor, relative
to energy in equilibrium for conformal

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gas, you're expected to be one third
ratio, but away from equilibrium, this

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expansion drives the system away from this
equilibrium value. And small deviations

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are described by black, which is viscous
hydrodynamics. That's a universal

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description. However, even at much earlier
times, when expansion is very fast. And

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there is this emergence of macroscopic
description in terms of hydrogen dynamic

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attractors, which were discussed by Bill
Cohen on His plenary. That means that if

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you look at for mu curvatures youngness,
kinetic theory simulations and you start

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to have great podcasts, which are
different initial conditions may collapse

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on the same curve which then approaches
equilibrium at late times. And this

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approach is given in terms of W parameter,
which is time measured in units of kinetic

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relaxation time power and kinetic
relaxation time is given inversely

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proportional to temperature. So hot the
systems are accelerating faster and she

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has a scarcity. So, more strongly the
system has smaller shared resources. So,

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it also calibrates faster and the fact
that many different microscopic theories

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behave rather you know, very well
parameterised by this variable suggests us

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to look how a system you know what is the
system's lifetime in this unit, because,

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you know, once this time reaches around
one, we know that for example, this goes

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hydrodynamics should become a good
description of microscopic behavior. And

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so, in order to estimate with a lifetime
in units of a capitalization time.

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Firstly, note that produce particle
multiplicity is responsible for entropy in

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the system, which is expressed in this way
in terms of temperature. And of course, if

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you have the same particle multiplicity
coming from a large system, it will be

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spread over a larger area than from a
small system. So, a smaller system will be

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hotter higher temperature means it's
equilibrates faster. However, the system

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which is larger has also more time to
equilibrate or to evolve because initially

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for small times the system is only
expanding in one day in one dimensionally

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and the temperatures falling very slowly,
but at late times, once a system starts

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expanding in three dimensions, expansion
is very fast. So, we can estimate that you

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know, system lifetime typically is of
order of radius. So, that means, that if

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you put a radius in this formula and try
to calculate, what is the ratio on in your

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in units of power Find the system lifetime
in this unit is given completely in terms

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of a particle multiplicity and independent
of its radius r. So, that is one way why

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systems is a similar multiplicity looks so
similar because they have the same

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lifetime in units in of kinetic relaxation
time, although we don't have the same

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lifetime in

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physical units.

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So, moving on, as I said the kinetic
theory is a is a good description which

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allows us to connect with initial
classical field descriptions we're in have

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an collisions systems are very unusual and
it's a tropic pressures are very strongly

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separated and multi dimensional in transit
directions. Well in a hydrodynamic

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description, you would expect them to be
close to each other. And in our work we

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showed how kinetic theory indeed can
connect with ln late time behavior and

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they they have a smooth overlap in this
region where both descriptions are, you

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know, valid, and we can use the condition
for this validity to find small systems

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would also approach hydrodynamics. So I
said if the system as we saw before, but

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if the system lifetime is larger than one
in units of kinetic relaxation time,

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there'll be enough time for viscous
hydrodynamics to be applicable. So, yeah,

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I it's plotted the particle multiplicity
and ether overs on this axis and you plot

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with this ratio. So, for large systems
like lead collisions with enough particle

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multiplicity or a system is large enough
that the system will reach this

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hydrodynamic phase and live rather long in
that phase for a long time, while for

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small multiplicities this ratio is much
smaller and that means that system is

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barely reaching this hydrodynamic
behavior. Of course, it depends on the

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exact properties of of it over But it does
indicate that small systems have very

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little time to really evolve in this
classical hydrodynamics. So we need to

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00:10:07,470 --> 00:10:12,360
think whether some of these observables
are come already in equilibrium dynamics.

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Another interesting feature of
equilibration is production of fermions.

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Because in this recoupling picture, the
initial state is completely dominated by

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gluons, all energies is in terms of ones
while in equilibrium when you try to use

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for lattice equation of state, you have
more Quark degrees of freedom than once.

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So you have more energy in quarks and
gluons. So, he needs to describe how a

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system produce fermions and kinetic theory
is, is well suited for that there are

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processes which produce quarks from once
and you see that in the simulation, there

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were a number of energy in terms of muons
rather quickly or overtake ones and

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fermions are becoming dominating in terms
of energy at a reasonably short time. So

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that justifies me. application of his
thermodynamic, you know thermal equation

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of states from lack of scarcity.

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And the

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Another feature of you know, thermal
chemical equilibrium is the fact that, you

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know, we can in fact indirectly from a
thermal equilibrium of hadrons that is

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also thermal equilibrium of one lone
plasma and perhaps vice versa. So, in

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these simulations using similar arguments
as I said before, we estimated that if a

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system has at least 100 units of charged
particles per rapidity, IT system lives

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long enough to reach a sufficient chemical
equilibration in terms of bogland plasma

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of quarks and gluons. So, this perhaps
could mean that we also would see chemical

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equilibration in terms of hadrons even
though we don't describe how the

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realization and that would mean that you
know, at very high multiplicity, pp

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collisions, which may be accessed at
Future rants are for let's see, we could

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00:12:03,360 --> 00:12:13,170
see the separation of strange strangeness
even in a small system. So, now moving on,

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on the last part, I wanted to say that
with this knowledge of hydrodynamic

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attractors, we can describe the system
evolution from very early times far from

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equilibrium state to equilibrium. And that
allows us to solve the equations of

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motions for energy density. So, in the in
the early stages, when the system is still

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one dimensional expanding the we can use
the pressure from a hydrodynamic attractor

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to solve this equation. And that allows us
to calculate what is the energy density at

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later times, when the system is close to
thermal equilibrium. And from that energy

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we can calculate the entropy and entropy
is proportional to produce particle

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multiplicity and have an collisions. So
using that inverse paper, we were able to

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derive an exact formula which connects
initial state energy deposition. It's very

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00:13:02,670 --> 00:13:08,310
early times when a system is very far from
equilibrium to produce particle

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multiplicities at late times, or what
would be measured afterwards. And we found

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00:13:14,070 --> 00:13:20,580
that with proper transport properties of a
medium like Seamus, Casa De Anza, some are

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00:13:20,580 --> 00:13:28,890
known coefficients. So, this is, you know,
very nice formula and makes allows us to

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make some predictions. In particular, if
you can, you know, come up with a model

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for initial state deposition, and there
are some models which habit, and they are

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in general dependent on the overlap of two
nuclei when they collide. So we have

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impact dependence that allows to get a
centrality dependence of initial state

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00:13:47,430 --> 00:13:52,680
energy and plugging into this formula, we
get the particle multiplicity, so we get a

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00:13:52,740 --> 00:13:59,580
party impact or centrality dependence of
particle multiplicities. And in this work,

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00:13:59,580 --> 00:14:03,840
we just use single point in centrality in
support of multiplicities versus

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00:14:03,840 --> 00:14:10,020
centrality to fix the normalization at one
point. And when this is the green curve,

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00:14:10,050 --> 00:14:15,240
our best prediction has a good and
positive prediction for particle

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multiplicities. And when that allows us
also to know what was the initial state

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00:14:20,490 --> 00:14:26,610
energy, which is plotted here, in these
great bands, in comparison to the

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experimental and measured points.

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00:14:28,950 --> 00:14:29,940
So you see that

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00:14:29,999 --> 00:14:34,169
initially, the energy in the system is
much larger, because there's work being

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00:14:34,199 --> 00:14:39,329
done during the expansion. And there's
uncertainty in this energy because it

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00:14:39,329 --> 00:14:43,889
depends on what kind of transport
coefficients you use in your system of

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00:14:43,889 --> 00:14:48,239
illusion. And one interesting feature is
that it's very peripheral collisions are

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00:14:48,239 --> 00:14:52,499
some of the energy estimates fall below
the experimental measurement point, which

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00:14:52,499 --> 00:14:58,019
is not possible. So that means even risk
of transport coefficients are ruled out of

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a system is not reaching for On the
librium, as assumed in our calculation, so

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00:15:03,419 --> 00:15:10,709
that's another in ID identification that
these peripheral conditions are not

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00:15:10,739 --> 00:15:16,709
probably not really reaching thermal
equilibrium. And I'm just about to finish

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that. In order to understand these
peripheral collisions better, it's very

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exciting to have an opportunity in the
next run of a short run of oxygen oxygen

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collisions, because if you look in terms
of number of patterns and a number of

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00:15:32,459 --> 00:15:37,169
participants in the collision and number
of binary collisions, you can see that

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00:15:37,169 --> 00:15:41,759
peripheral lead collisions are very close
to their minimum bias, oxygen oxygen

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00:15:41,759 --> 00:15:49,529
collisions, which would be much more
easier, or it has more free of biases,

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00:15:49,529 --> 00:15:53,279
both experimentally and in terms of
modeling. So I look forward to these

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00:15:53,279 --> 00:15:57,959
measurements. So um, let me summarize that
I think we have a very improved

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00:15:57,959 --> 00:16:03,179
understanding of our system equilibrium.
And this allows us to have some

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00:16:03,179 --> 00:16:08,099
predictions on terms of basic calibration
can happen also in small systems. But of

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00:16:08,099 --> 00:16:13,949
course, we need to investigate in more
detail of the actual transit expansion is

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00:16:13,949 --> 00:16:18,149
changing the picture for and make more
quantitative predictions. And we need that

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00:16:18,149 --> 00:16:23,069
because we will have more data and and
even use more systems in upcoming policy

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00:16:23,069 --> 00:16:23,459
runs.

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00:16:23,999 --> 00:16:24,599
Thank you.

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00:16:26,370 --> 00:16:30,840
Thank you very much for this very
interesting presentation. So now we have

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00:16:30,840 --> 00:16:37,260
time for one or maybe two questions. If
you have a question, please press the

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00:16:38,850 --> 00:16:40,050
right hand button.

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00:16:41,940 --> 00:16:47,520
Okay, so we I see one question from
Michael. Michael, you can unmute yourself,

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00:16:47,700 --> 00:16:56,760
Alexis very nice talk on talked about DND
ADA. In certain systems you can have a

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00:16:56,760 --> 00:17:01,800
range of very restricted say two factor
systems. You can have a larger pool of the

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00:17:01,800 --> 00:17:07,200
gap, and then only a certain multiplicity
in his hernia, all your most pressing is

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00:17:07,200 --> 00:17:13,350
concentrated in one narrow region of
liquidity. So according to your picture,

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00:17:14,880 --> 00:17:18,960
you if you were looking at the fact of
collisions, you wouldn't compare them with

200
00:17:18,960 --> 00:17:26,760
the same multiplicity to regular
questions. But in the end, Ada said that

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00:17:28,230 --> 00:17:35,490
in this case, I always had the in mind, or
it's based on the boost invariant systems

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00:17:35,490 --> 00:17:42,480
where this end was in at mid rapidity. So
here I'm talking mid rapidity at the end.

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00:17:43,980 --> 00:17:50,790
Of course, it doesn't apply to Universal
to all systems. You know, without any

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00:17:50,790 --> 00:17:57,540
better for mid mid rapidity. Yeah, that's
that's the multiplicity I was referring

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00:17:57,540 --> 00:17:57,750
to.

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00:17:59,040 --> 00:18:03,060
Okay, okay. Perfect. If you could just
think about what because there is quite a

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00:18:03,060 --> 00:18:09,000
bit of data coming on to factor systems
and, and what model might look at in that.

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00:18:09,300 --> 00:18:11,040
Thank you so much. Thank you.

209
00:18:12,719 --> 00:18:15,989
Okay, thank you. I think we have to move
on. Thank you, Alexander.