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Journal of Physics C Solid State Physics

The influence of dissipation on the quantal transition state tunnelling rate

E. Freidkin, Peter S. Riseborough, Peter Hänggi A

Published Mar 20, 1988• 6 citations
Publisher

Abstract

The authors calculate the rate of quantum mechanical tunnelling through a potential barrier. The tunnelling rate is calculated with the WKB approximation. The influence of the dissipation appears both in the leading term of the WKB approximation and in the next leading term. They calculate these corrections exactly and discuss the regions of validity of the results.

DOI
10.1088/0022-3719/21/8/027

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The authors calculate the rate of quantum mechanical tunnelling through a potential barrier. The tunnelling rate is calculated with the WKB approximation. The influence of the dissipation appears both in the leading term of the WKB approximation and in the next leading term. They calculate these corrections exactly and discuss the regions of validity of the results.
A phenomenological approach to dissipative tunneling, originally put forth by Pollak [Phys. Rev. A 33, 4244 (1986)], is discussed and contrasted with the bounce formalism. This phenomenological approach is based on the WKB theory for parabolic barrier tunneling. It is quite simple and readily evaluated. We study the results for the leading exponential dissipative decay rate in metastable potentials and contrast them with previous instanton-type (bounce-technique) calculations. In doing so, we compare the zero-temperature decay rate in various metastable potentials, different dissipation mechanisms, and also consider the rate enhancement at very low temperatures. One finds between the two methods unexpected good agreement at weak to moderate dissipation strength; the accuracy decreases with increasing dissipation strength and increasing deviation from a harmonic barrier shape.