Simple approach to computing tunneling time: Test cases

摘要

We suggest a recipe for calculating the time taken by a particle to tunnel out from an initially localized state in one of the wells of symmetrical double-well potential into the other well. We calculate average velocity <(ν) over bar > of the tunneling particle by solving the Schrodinger equation numerically for Psi(x, t), then estimating = (d/dt) and time-averaging it. The time taken to tunnel is measured by calculating tau(anu) = l(0)/<(ν) over bar > where l(0) is an idealized estimate of the barrier width. We suggest an approximate partitioning of tau(anu) into an intrinsic decay time (tau(d)) and a barrier crossing time (tau(b)), tau(d) being obtained from energy spread of the packet. tau(anu) - tau(d) is shown to be close to the Wentzel-Brillouin-Kramers estimate of barrier crossing time tau(sc). The response of tau(anu) to an external driving field and nonzero temperatures are tested. We also apply the method to a purely barrier penetration problem as well as to the problem of tunneling through a fluctuating barrier. (C) 2003 Wiley Periodicals, Inc. [References: 29]