Nonperturbative evaluation of the diffusion rate in field theory at high temperatures

TL;DR

This paper extends Kramer's approach to field theory, numerically evaluating the diffusion rate in the 1+1D Sine-Gordon model at various temperatures and friction levels, revealing a crossover from semiclassical to high-temperature behavior.

Contribution

It provides a nonperturbative numerical evaluation of the diffusion rate in a field theory, confirming classical predictions and exploring temperature and friction effects.

Findings

Observed crossover from semiclassical to high-temperature regime.

Determined kink mass matches classical value.

Diffusion rate aligns with Green function measurements at zero friction.

Abstract

Kramer's approach to the rate of the thermally activated escape from a metastable state is extended to field theory. Diffusion rate in the 1+1-dimensional Sine-Gordon model as a function of temperature and friction coefficient is evaluated numerically by solving the Langevin equation in real time. A clear crossover from the semiclassical to the high temperature domain is observed. The temperature behaviour of the diffusion rate allows one to determine the kink mass which is found equal to the corresponding classical value. The Kramer's predictions for the dependence on viscosity are qualitatively valid in this multidimensional case. In the limit of vanishing friction the diffusion rate is shown to coincide with the one obtained from the direct measurements of the conventional classical real-time Green function at finite temperature.