Multidimensional WKB approximation and the lifetime calculation - art. no.042101

A Wentzel-Kramers-Brillouin (WKB) approach for calculating the lifetime of the ground state of two coupled oscillators with the most probable escape p ath along one of the coordinate axes is suggested. The WKB approximation of the wave function in the neighborhood of this path is obtained by scaling the corresponding variable. An analytic formula for the lifetime is derived and numerically verified. The method is applied to the Henon-Heiles potent ials. It is shown that the WKB method can be, in contrast to the numerical ones, easily extended to the problems of an arbitrary number of spatial dim ensions.