Transcript original talk

Thermal features
far from equilibrium:
Prethermalization
Szabolcs Borsányi
University of Heidelberg
different levels of equilibration is reached
at different time scales;
some equilbrium features appear earlier,
some appear later;
prethermalization: bulk observables settle
close to the final value
in collaboration with
J. Berges, C. Wetterich
LTE in heavy ion collisions?
How can the local equilibrium established?
Present estimates for thermalization
tLTE > 2-3 fm/c
ideal hydro equations of motion:
Hirano,Nara 2004
Kolb et al
t0 = 0.6 fm/c
Theoretical description
Classical approximation (wave dynamics)
• only low-momentum physics, nonrenormalizable,
nonperturbative, off-shell
• classical equilibrium ≠ quantum equlibrium !
Kinetic theories (incoherent particle/parton dynamics)
• elastic or inelastic scattering, perturbative, on-shell
• problems at early times: coherence, gradient expansion
• E.g. pQCD, parton cascade shower simulations
Resummed expansion scheme: 2PI
• Inclusion of off-shell processes
• applicable both for early and late times
2PI resummed chiral model
• Chiral quark model in 3+1 dimensions
(two quark, four scalar degree of freedom, symmetric phase)
• We solve the nonequilibrium gap equation:
momentum
space
coordinate
space
Levels of equilibration
Damping
Prethermalization
Thermalization
Damping time
• Initial relaxation of propagators
time-local G(t1,t2=t1,p)
non-local G(t1,t2=0,p)
• With of the spectral function
(Im )
• No substantial evolution
• Physical meaning:
– signal loss
• signal on top of
equilibrium ensemble:
• compare decay rate to
Im(p) ! they agree
– shorter than thermalization
Berges, Sz.B, Serreau 2003
Sz.B, Szép 2000
Nonequilibrium KMS condition
Equilibrium (KMS condition):
Out of equilibrium (generalized KMS):
Define n(t) at the peak of the spectral function
Express n(t) as a function of the peak location
F and r are the outcome
of the dynamics.
Initially they were
independent variables.
If this relation holds for close-to-the-peak
frequencies as well, a Boltzmann equation
may be derived from the 2PI gap equation.
The particle distribution is established on the damping time scale
Even earlier: prethermalization
• Kinetic energy ! kinetic temperature
Virial theorem
(for weakly coupled fields)
if local equilibrium
then
kinetic energy ¼
gradient energy
+ potential energy
This behavior has been also seen in classical field theory
Equation of state
Prethermalization is a universal farfrom-equilibrium phenomenon which
describes a very rapid establishment
of an almost constant equation of
state as well as kinetic temperature.
similar behavior in
Classical Field Theory
(reheating after cosmological inflation)
Sz.B, Patkós, Sexty 2003
coupling independent! “Dephasing”
Loss of phase information
Loss of coherence
tpt * Temperature = 2..2.5
Sz.B, Patkós, Sexty 2003
Inhomogeneous ensemble?
Prethermalization:
• Very early evolution
• Far-from-equilibrium
• High occupation numbers
• Weak sensitivity to
interaction details
O(4) model, with
realistic mass scales:
tPretherm < 0.5 fm/c
We find: After tPretherm pressure(h,t)/energy(h,t) is h and t independent.
What can we say for
heavy ion physics?
• Assume: Qs sets only the relevant scale of the early dynamics
• Prethermalization time is coupling independent (2-2.5 T-1)
inserting Qs for temperature scale and using a prefactor of 3
tpt ¼ 0.6 fm/c
• After this time: stable equation of state / kinetic temperature
• If we start our model with larger Yukawa coupling ¼ 3
Damping time ! Prethermalization time
Even if equilibrium is reached later
• fluctuation dissipation (KMS) relation
• slowly evolving spectra
• equation of state
Even Hydrodynamics may work!
Summary
• Equilibration can be splitted to different steps:
prethermalization / damping / thermalization
• One of the scales is insensitive to coupling:
prethermalization
– generic phenomenon, present in various scenarios
• After damping time: nonequilibrium KMS relation
• Damping and prethermalization may coincide for
heavy ion collisions, it gives about ¼ 0.6 fm/c
• This can be an ingredient to understand the
success of hydrodynamic description