Quantum Tunneling Rate through an Inverted Parabola with an Oscillating External Field – an Analysis Using the Exact Feynman Kernel –

Abstract

The quantum tunneling rate through an inverted parabola potential in an oscillating external field is studied. The tunneling rate is calculated within quasi-classical accuracy as a function of the frequency of the field. In this calculation, the complex-time path integral method, which has been previously applied to the case of tunneling through static potentials, is used after being appropriately extended for application to the case of tunneling through explicitly time-dependent potentials. Since the Feynman kernel for the case considered in the present paper can be exactly obtained, we are able to calculate the tunneling rate over a considerably wider range of frequencies of the oscillating field than in the case that this quantity is calculated through a perturbative treatment of the external field, as done in the previous studies. The present analysis reveals that the perturbative analysis for the present problem is insufficient even in the region where it has been considered to be appropriate. From t...