Mish UstinNon-equilibrium phase transitions

8/13/2019 Mish UstinNon-equilibrium phase transitions

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Igor Mishustin*)

Frankfurt Institute for Advanced Studies,J.W. Goethe Universitt, Frankfurt am Main

National Research Centre, Kurchatov Institute

Moscow

Non-equilibrium Dynamics, Hersonissos, Crete, 25-30 June, 2012

NonNon--equilibrium phase transitionsequilibrium phase transitions

in expanding matterin expanding matter

*)

in collaboration with Marlene Nahrgang and Marcus Bleicher


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QCDCD hase diagramhase diagram

Marlene


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Contentsontents

Introduction: Effects of fast dynamics

Fluctuations of the order parameter

Chiral fluid dynamics with damping and noise

Critical slowing down and supercooling

Observable signatures

Conclusions

This talk is based on recent works:M. Nahrgang, M. Bleicher, S. Leupold and I. Mishustin, The impact of dissipation and

noise on fluctuations in chiral fluid dynamics, arXiv:1105.1962 [nucl-th];

M. Nahrgang, I.Mishustin, M. Bleicher, Dynamical domain formation in expanding

chiral fluid underegoing 1

st

order phase transition, in preparation


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Effects of fast dynamics

T

0ad

iabat1

23

C

spinoidallines

critical line

4

0

2 4 60( ; , ) ( , )

2 4 6a b cT T

Effective thermodynamic potential for a 1st order transition

In rapidly expanding system 1-st order transition is delayed until the barrier

between two competing phases disappears - spinodal decompositionI.N. Mishustin, Ph s. Rev. Lett. 82 1999 4779; Nucl. Ph s. A681 2001 56

a,b,c are functions of

andT

0 ( )eqP

crossover cp

1-st order

Equilibrium is determined by


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Equilibrium fluctuations of order parameter in1st

rder phase transition

P()T>Tc

P()T


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Evolution of equilibrium fluctuations

in 2nd order phase transition

T>Tc

0

T


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rel 1( ) , 2c

TT T

Critical slowing down in the 2nd order

phase transition

0

T=0

T>Tc

T=Tc

B

In the vicinity of the critical pointthe relaxation time for the order

parameter diverges -

no restoring force

(Landau&Lifshitz, vol. X,Physical kinetics)

rel

ddt

Rolling down from the top of the potentialis similar to spinodal decomposition(Csernai&Mishustin 1995)

eff( )U

f

Fluctuations of the order parameterevolve according to the equation


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Critical slowing down 2B. Berdnikov, K. Rajagopal, Phys. Rec. D61 (2000)

Critical fluctuations have not enough time to build up. One can expect only a factor 2enhancement in the correlation length (even for slow cooling rate, dT/dt=10 MeV/fm).


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Dynamical model of chiral phase transition

Linear sigma model (LM) with constituent quarks

Thermodynamics of LM on the mean-field level was studied inScavenius, Mocsy, Mishustin&Rischke, Phys. Rev. C64 (2001) 045202

Effective thermodynamic potential:

CO, 2nd and 1st order chiral transitionsare obtained in T- plane.

5

2

2 2 2 2 2vac

1[ ( )] [ ] ( , ),

2

( , ) ( ) , < >4

L q i g i q U

U v H f H f m

eff

2 2 2

( ; , ) ( , ( ; , )

( )

qU T U m T

m g


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Effective thermodynamic potential

Here we consider =0 system but tune the order of thechiral phase transition by changing the coupling g.

2 23

f-( ; , ) ln 1 exp ( ) , =2

q q cm pdm T T N N

T

3p(2 )


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Order parameter field vs T

g=4.5g=3.3

crossover 1-st order

unstable states at 122 MeV


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Chiral fluid dynamics (CFD)

Fluid is formed by constituent quarks and antiquarks which

interact with the chiral field via quark effective mass

CFD equations are obtained from the energy momentum

conservation for the coupled system fluid+field

I.N. Mishustin, O. Scavenius, Phys. Rev. Lett. 83 (1999) 3134

K. Paech, H. Stocker and A. Dumitru, Phys. Rev. C 68 (2003) 044907

m g

fluid field fluid field

2 eff

( ) 0

( ) ( )s t

T T T T S

US g

We solve generalized e. o. m. with friction () and noise ():

Langevin equation

for the order parameter

(f

efft

Ug qq

' ' ' '1( , ) 0, ( , ) ( , ) ( ) ( )coth2mt r t r t r m t t r r

V T


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Calculation of damping termCalculation of damping termT.Biro and C. Greiner, PRL, 79. 3138 (1997)

M. Nahrgang, S. Leupold, C. Herold, M. Bleicher, PRC 84, 024912 (2011)

The damping is associated with the processes:

It has been calculated using 2PI effective action

Around Tc the damping is due to the pion modes, =2.2/fm

,qq 3/ 22

2 2

21 2

2 4q

F q

m mg n m

m


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Dynamic simulations: Bjorken-like expansion

Initial state: cylinder of length L in z direction, with ellipsoidal crosssection in x-y direction

x

2At 0 : ( ) 0.2 , - ; v 0; 160

2 2

y

z L Lt v z c z v T MeV

L

In the vicinity of the c.p. sigma shows pronounced oscillations

since damping term vanishesSupercooling and reheating effects are clearly seen in the 1-st

order transition.

( 2 )qm m


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Dynamical evolution of chiral fluid1st

order transition (g=5.5)

Reheating

2-nd order transition (g=3.63)


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Dynamical evolution of sigma fluctuations2-nd order transition (g=3.63) 1st

order transition (g=5.5)


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Latest developments

Realistic initial conditions are obtained fromUrQMD simulations; Correlations of noise variables in neighboringcells are introduced by averaging over V=1fm3;

Dynamical domain formation studied

Tc

100

110

120

130

140

150

160

170

180

0 2 4 6 8 10 1220

30

40

50

60

70

80

90

100

T

[MeV]

[Me

V]

t [fm]

T


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t= 3.4 fm t= 5.0 fm t= 6.6 fm

z = 0.4 fm

z = 0 fm

z = 0.4 fm

[MeV]

x [fm]

y

[fm]

-10 -5 0 5 10 -10 -5 0 5 10 -10 -5 0 5 10

-10

-5

0

5

10-10

-5

0

5

10-10

-5

0

5

10

0

10

20

30

40

50

60

70

80

90

Tomographic visualization of domains

Domains of restored phase are embedded into a chirally-broken background


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Tomography of the system at t=4 fm/c

z= 1.6 fm z= 1.2 fm z= 0.8 fm

z= 0.4 fm z= 0 fm z= 0.4 fm

z= 0.8 fm z= 1.2 fm z= 1.6 fm

t=

4.

0 fm/c

[MeV]

x [fm]

y

[fm]

-8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8

-8

-4

0

4

8-8

-4

0

4

8-8

-4

0

4

8

0

10

2030

40

50

60

70

80

90

One can clearly see a big domain in the central region (r


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Tomography of the system at t=5 fm/c

Smaller domains have been formed in the bigger region (r


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Domains (droplets) are spred over the large region (r


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Strength of sigma fluctuations transitionStrength of sigma fluctuations transition

eq

2.

2 2 2 2 2 2 eff3 3 21 1 [ | | | | ], ,(2 ) 2

k k k k

k

dN Um k md k

Fluctuations are rather weak, effective number of sigmas is small

Crossover transition (g-3.3)


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Second order transition with criticalSecond order transition with critical

point (g=3.63)point (g=3.63)

Fluctuations are stronger, but no traces of divergence are seen


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Strong first order transition (g=5.5)Strong first order transition (g=5.5)

Strong supercooling and reheating effects are clearly seen.

Sharp rise of fluctuations after 6 fm/c, when the barrier

in thermodynamic potential disappears. Effective number of

sigmas increases by two orders of magnitude!


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Rapid expansion should lead to dynamicalfragmentation of QGP

In the course of fast expansion the system enters spinodal instability when

Q phase becomes unstable and splits into QGP droplets/hadron resonances

Csernai&Mishustin 1995, Mishustin 1999, Rafelski et al. 2000, Koch&Randrup, 2003

Extreme possibility - direct transition from quarks to hadrons without mixed phase


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Ultrarelativistic A+A collisionsUltrarelativistic A+A collisions

Au+Au, Pb+Pb,

RHIC (STAR) LHC (ALICE)Charged particles tracks

one of these tracks could be an antinucleus


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Experimental signal of droplets in therapidity-azimuthal angle plane

Look for event-by-event distributions of hadron multiplicities in

momentum space associated with emission from QGP droplets.Such measurements should be done in the broad energy range!

Select hadrons in different pt

interwals


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ConclusionsConclusions

Phase transitions in relativistic heavy-ion collisions willmost likely proceed out of equilibrium

2nd order phase transitions with CEP) are too weak toproduce significant observable effects

Non-equilibrium effects in a1st order transition spinodaldecomposition, dynamical domain formation) may helpto identify the phase transition

If large QGP domains are produced in the 1-st orderphase transition they will show up in large non-statisticalmultiplicity fluctuations in single events

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Mish UstinNon-equilibrium phase transitions