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Thermal features far from equilibrium: Prethermalization

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;

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Thermal features far from equilibrium: Prethermalization

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  1. Thermal featuresfar 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

  2. ideal hydro equations of motion: LTE in heavy ion collisions? How can the local equilibrium established? Present estimates for thermalization tLTE > 2-3 fm/c t0 = 0.6 fm/c Hirano,Nara 2004 Kolb et al

  3. 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

  4. 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

  5. Damping Thermalization Prethermalization Levels of equilibration

  6. Damping time • Initial relaxation of propagatorstime-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

  7. Define n(t) at the peak of the spectral function Express n(t) as a function of the peak location If this relation holds for close-to-the-peak frequencies as well, a Boltzmann equation may be derived from the 2PI gap equation. Nonequilibrium KMS condition Equilibrium (KMS condition): Out of equilibrium (generalized KMS): F and r are the outcome of the dynamics. Initially they were independent variables. The particle distribution is established on the damping time scale

  8. 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

  9. coupling independent! “Dephasing” Loss of phase information Loss of coherence tpt * Temperature = 2..2.5 Equation of state Prethermalization is a universal far-from-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 Sz.B, Patkós, Sexty 2003

  10. Inhomogeneous ensemble? Prethermalization: • Very early evolution • Far-from-equilibrium • High occupation numbers • Weak sensitivity to interaction details O(4) model, withrealistic mass scales: tPretherm < 0.5 fm/c We find: After tPretherm pressure(h,t)/energy(h,t) is h and t independent.

  11. 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 tpt¼ 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!

  12. 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

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