Nonequilibrium evolution and symmetry structure of the large-N $\Phi^4$ model at finite temperature

We consider the large-N $\Phi^4$ theory with spontaneously broken symmetry at finite temperature. We study, in the large-N limit, quantum states which are characterized by a time dependent, spatially homogenous expectation value of one of the field components, $\phi_N(t)$, and by quantum fluctuations of the other $N-1$ components, that evolve in the background of the classical field. Investigating such systems out of equilibrium has recently been shown to display several interesting features. We extend here this type of investigations to finite temperature systems. Essentially the novel features observed at T=0 carry over to finite temperature. This is not unexpected, as the main mechanisms that determine the late-time behavior remain the same. We extend two empirical - presumably exact - relations for the late-time behavior to finite temperature and use them to define the boundaries between the region of different asymptotic regimes. This results in a phase diagram with the temperature and the initial value of the classical field as parameters, the phases being characterized by spontaneous symmetry breaking resp. symmetry restoration. The time evolution is computed numerically and agrees very well with the expectations.