  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.
