Mish UstinNon-equilibrium phase transitions
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Transcript of 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