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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