Out of equilibrium quantum field dynamics of an initial thermal state after a change in the external field

Abstract

The effects of the initial temperature in the out of equilibrium quantum field dynamics in the presence of a homogeneous external field are investigated. We consider an initial thermal state of temperature $T$ for a constant external field $\stackrel{\ensuremath{\rightarrow}}{J}$. A subsequent sign flip of the external field, $\stackrel{\ensuremath{\rightarrow}}{J}\ensuremath{\rightarrow}\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{J}$, gives rise to an out of equilibrium nonperturbative quantum field dynamics. The dynamics is studied here for the symmetry broken $\ensuremath{\lambda}({\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Phi}}}^{2}{)}^{2}$ scalar $N$ component field theory in the large $N$ limit. We find a dynamical effective potential for the expectation value that helps us to understand the dynamics. The dynamics presents two regimes defined by the presence or absence of a temporal trapping close to the metastable equilibrium position of the potential. The two regimes are separated by a critical value of the external field that depends on the initial temperature. The temporal trapping is shorter for larger initial temperatures or larger external fields. Parametric resonances and spinodal instabilities amplify the quantum fluctuations in the field components transverse to the external field. When there is a temporal trapping, this is the main mechanism that allows the system to escape from the metastable state for large $N$. Subsequently, backreaction stops the growth of the quantum fluctuations and the system enters a quasiperiodic regime.