Multi-dimensional WKB treatment of first passage time

The problem of first passage time is mathematically equivalent to the tunnelling of a particle out of a potential well and hence can be treated by the multi-dimensional WKB technique. In general, the most probable tunnelling path (MPTP) is curved and is difficult to determine. The authors discuss a model potential for which the curved MPTP can be solved analytically. It is shown that the rate of tunnelling calculated along the straight path as usually assumed is unreliable. Numerical results of the mean switching time for the bistable two-mode laser and comparison with experiments and other theories are also discussed.