Tunneling through a time-dependent barrier - a numerical study

We present a numerical investigation of quantum mechanical tunneling proces s in a double well potential with fluctuating barrier. The tunneling probab ility and rate are calculated for two cases in which (i) the height of the barrier is undergoing harmonic oscillation with frequency omega and (ii) th e height of the barrier is undergoing random fluctuation with frequency ome ga. It is observed that in both cases, the quantum mechanical tunneling pro bability and rate exhibit a maximum as a function of the fluctuation freque ncy. The optimal frequency i.e. the frequency at which rate exhibits a maxi mum shows a strong isotopic mass effect.