Dissipation via particle production in scalar field theories

Abstract

We study the nonequilibrium evolution of the expectation value of a scalar field in the broken and unbroken symmetry cases. We find that the particles produced by parametric amplification give rise to dissipative behavior for this mode. However, a \ensuremath{\Gamma}\ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{} type of term cannot account for the dissipational dynamics. We are able to show clearly that perturbation theory breaks down at late times, so that dissipation in field theories can only be understood nonperturbatively. When Goldstone bosons are present we find infrared divergences that require a nonperturbative resummation to describe the long-time dynamics. We use the Hartree factorization and the large N approximation to the O(N) linear \ensuremath{\sigma} model to numerically as well as analytically understand the long-time behavior of the zero mode as well as that of the produced particles. The O(N) model case is extremely interesting since, in the spontaneously broken case, the radial mode dissipates all of its energy into production of long-wavelength Goldstone modes. The minima of the effective action (determined by the final value of the expectation value of the scalar field) depend on the initial conditions.