Prethermalization

Prethermalization of the equation of state and the kinetic temperature to their equilibrium values occurs on time scales dramatically shorter than the thermal equilibration time. This is a crucial ingredient for the understanding of collisions of heavy nuclei or other nonequilibrium phenomena in complex quantum and classical many body systems. We also compare the chemical equilibration time with other characteristic time scales.

Figure 1

Fermion occupation number $n^{(f)}(t;p)$ for three different momentum modes as a function of time. The evolution is shown for two different initial conditions with the same energy density. The long-time behavior is shown on a logarithmic scale for $t\ge 30{\mathrm{m}}^{-1}$.

Figure 2

Fermion and scalar mode temperatures $T_p^{(f,s)}(t)$ as a function of momentum $p$ for various times.

Figure 3

The ratio of pressure over energy density $w$ as a function of time. The inset shows the early stages for two different couplings and demonstrates that the prethermalization time is independent of the interaction details.

Figure 4

Chemical temperatures for scalars (upper curves) and fermions (lower curves) for different values of the coupling $h$ and $T_{\mathrm{e}\mathrm{q}}$. We also show the kinetic temperature $T_{\mathrm{k}\mathrm{i}\mathrm{n}}(t)$ (solid line), which prethermalizes on a very short time scale as compared to chemical equilibration.