PATH-INTEGRAL DERIVATION FOR THE RATE OF STATIONARY DIFFUSION OVER A MULTIDIMENSIONAL BARRIER

We give a path-integral derivation for the rate of stationary diffusion over a multidimensional barrier which reduces to Kramers formula in the classical limit. As an example we show within a two-dimensional model for nuclear fission that the classical-rate formula yields a stationary flow in close agreement with a more accurate Langevin calculation in which stationarity is reached after a transient time. We also calculate quantal corrections to the classical rate as function of the temperature, and discuss differences between the one-and two-dimensional treatments of the fission process.