hydrodynamic instability in the quark-gluon plasma
DESCRIPTION
Hydrodynamic Instability in the Quark-Gluon Plasma. Carlos E. Aguiar Instituto de Física - UFRJ. C.E.A., E.S. Fraga, T. Kodama, nucl-th/0306041. Outline : Introduction; explosive hadronization Thermodynamics of the chiral phase transition Supercooling and spinodal decomposition - PowerPoint PPT PresentationTRANSCRIPT
Hydrodynamic Instabilityin the Quark-Gluon Plasma
Carlos E. AguiarInstituto de Física - UFRJ
C.E.A., E.S. Fraga, T. Kodama, nucl-th/0306041
Outline:
• Introduction; explosive hadronization
• Thermodynamics of the chiral phase transition
• Supercooling and spinodal decomposition
• Hydrodynamics of the chiral phase transition
• Fluid mechanical instability in the QGP
• Comments
Heavy Ion Collisions at High Energies
AuAu
Heavy Ion Collisions at High Energies
SPH calculation
z
t hadrons
10 fm/c
QGP
mixedphase
Explosive Hadronization?
22pair
2side
2out )(VRR
1R/R sideout 0 sudden emission
• HBT radii:
SPSRHIC
___ strong 1st order...... weak 1st order- - - crossover
D. Zschiesche et al. Phys. Rev. C 65 (2002) 064902
The Phase Diagram of Strongly Interacting Matter
T
922 MeV
150 MeV
QGP
Hadrons
crossover
supercooling
Lattice QCD and Freezeout States
Z. Fodor and S. D. Katz, Phys. Lett. B 534 (2002) 87, JHEP 0203 (2002) 014
RHIC
SPS
Thermodynamics of theChiral Phase Transition
Linear sigma model
)(U2
1qigiqL 05
),(,)d,u(q
hv
4)(U
22222
0
fgm,mm
m3mfv,
f2
mm,mfh q22
2222
2
222
3.3g,MeV 600m,MeV 138m,MeV 93f
Partition function
Effective potential
V
0q
3T/1
0
qqLxd)ti(dexpDDqqDTNHexpTrZ
)3/( q
ZlnV
T),T(U PV/U
• mean field approximation: <>
)(T/)E(exp1ln)2(
pdT)(U),,T(U qqq3
3
q0
2q
2 mpE 222222q ggm
Effective Potential
-20 0 20 40 60 80 100 120 (M eV)
-120
-100
-80
-60
-40
-20
U (
Me
V/fm
3 ) T = 105 M eV
118 M eV
130 M eV
= 500 M eV
-20 0 20 40 60 80 100 120 (M eV)
-50
-40
-30
-20
-10
0
U (
MeV
/fm
3 )
T = 41 M eV
49.9 M eV
57 M eV
63.5 M eV
69 M eV
= 800 M eV
crossover1st order
Supercooling and Spinodal Decomposition
-20 0 20 40 60 80 100 120 (M eV)
-120
-100
-80
-60
-40
-20
U (
Me
V/fm
3 ) T = 105 M eV
118 M eV
130 M eV
= 500 M eV
-20 0 20 40 60 80 100 120 (M eV)
-50
-40
-30
-20
-10
0
U (
MeV
/fm
3 )
T = 41 M eV
49.9 M eV
57 M eV
63.5 M eV
69 M eV
= 800 M eV
crossover1st order
Pressure and Chiral Field
4 0 5 0 6 0 7 0tem perature (M eV)
2 0
3 0
4 0
5 0
pre
ssur
e (M
eV
/fm3 )
0 40 80 120 160tem perature (M eV)
0
20
40
60
80
100
sigm
a fi
eld
(M
eV
)
= 800 M eV
sh
sc
First order
Mesons
2
22
2
22 U
m,U
m
0 40 80 120 160T (M eV)
0
200
400
600
800
m
(M
eV)
0 40 80 120 160T (M eV)
0
200
400
600
800
m
(MeV
)
= 800 M eV
First order
Pressure and Chiral FieldCrossover
0 40 80 120 160 200tem perature (M eV)
0
200
400
600
pres
sure
(M
eV/f
m3)
0 40 80 120 160 200tem perature (M eV)
0
20
40
60
80
100
sigm
a fie
ld (
MeV
)
= 500 M eV
Mesons
Crossover
0 40 80 120 160 200T (M eV)
0
200
400
600
800
m
(M
eV)
0 40 80 120 160 200T (M eV)
0
200
400
600
800
m
(MeV
)
= 500 M eV
Chiral Phase Diagram
400 600 800 1000chem ical potentia l (M eV)
0
40
80
120te
mpe
ratu
re (
MeV
)
chiralsymmetry
broken chiralsymmetry
spinodalline
T-n Diagram
0 0.1 0.2 0.3
baryon density (1 /fm 3)
0
40
80
120te
mpe
ratu
re (
MeV
)
spinodal
chiralsymmetry
brokensymmetry
Hydrodynamics of the Chiral Phase Transition
),s,n(2
1xdA 4
nTsUdensityenergy ),s,n(
1uu
0)us(
0)un(
constraints: baryon number conservation entropy conservation flow velocity normalization
Action:
Chiral Hydrodynamics
),,T(UR
Pguu)P(T
R
RT
0)un(
0)us(
Wave Motion
Perturbation ofequilibrium:
k//v1
Linearizedequations:
)k,(K
0
),n/s,(PP
0
),n/s,(RR
101222 vRw
kmk
0mk 1222
1122 RkvkP
xKi10 e)x(
xKi10 euu)x(u
00 )P(w
Chiral and Sound Modes
220
22222 kRwmkkP
Dispersion relation
Long wavelengths
22
202
s km
RwP
22 m
sound waves:
chiral waves:
Hydrodynamic Instability
0m
RwP
2
20
If
then s2 < 0, and the sound modes become
unstable, growing exponentially instead of propagating. This instability occurs before the chiral spinodal line (m
2 = 0) is reached.More importantly, the crossover region (m
2 0) is unstable.
Hydrodynamic Instability in the QGP
0 200 400 600 800 1000chem ical potentia l (M eV)
0
40
80
120
160te
mp
erat
ure
(M
eV)
instabilityline
spinodal
Instability Line in the T-n Plane
0 0.1 0.2 0.3
baryon density (1 /fm 3)
0
40
80
120
160te
mpe
ratu
re (
MeV
)instability
line
In summary:
• The nonequilibrium chiral condensate changes qualitatively the hydrodynamical behavior of the QGP
• Explosive hadronization doesn’t need spinodal decomposition, and can occur even in the crossover region.
Final comments:
• This is a very general effect; it doesn’t depend on specific aspects of the sigma model.
• The instability develops even for very slow cooling, contrary to spinodal decomposition.
• Finite size effects may be important in nuclei: min ~ 5 fm at the critical point
• Implications for the hadronization process in: heavy ion collisions (?) early universe (!)