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American Journal of Physics

Quick and easy escape from a metastable state

Anupam Garg

Published Mar 26, 2014• 2 citations
Publisher

Abstract

An elementary but complete calculation of metastable state decay from a piecewise-constant one-dimensional potential well is presented that does not invoke the concept of an attempt frequency or require a knowledge of the Wentzel-Kramers-Brillouin method. Connection is made with scattering resonances for advanced readers.
DOI
10.1119/1.4856655

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The WKB approach to quantum tunneling from a metastable well is generalized to include a weak oscillatory force. Both one-dimensional decay and multidimensional decay, appropriate for a system coupled to a dissipative environment, are considered. In both cases, general expressions are derived for the enhancement of the decay rate linear in the applied force. The enhancement is expressed exclusively in terms of the instanton trajectories of the unperturbed system. For a cubic potential with no damping, the decay rate exhibits sharp resonances when the applied frequency coincides with the energy spacing between the ground and excited states in the metastable well. In the strong-damping limit, this resonance structure is completely suppressed.