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

The Kramers approach to the rate of thermally activated escape from a metastable state is extended to field theory. The 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 behavior of the diffusion rate allows one to determine the kink mass which is found equal to the corresponding classical value. Kramers 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 direct measurements of the conventional classical real-time Green's function at finite temperature.