PMID: 11909222Mar 23, 2002Paper

Coherent oscillations and incoherent tunneling in a one-dimensional asymmetric double-well potential

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
V A Benderskii, E I Kats

Abstract

For a model one-dimensional asymmetric double-well potential we calculated the so-called survival probability (i.e., the probability for a particle initially localized in one well to remain there). We use a semiclassical (WKB) solution of the Schrödinger equation. It is shown that behavior essentially depends on transition probability, and on a dimensionless parameter Lambda that is a ratio of characteristic frequencies for low-energy nonlinear in-well oscillations and interwell tunneling. For the potential describing a finite motion (double-well) one has always a regular behavior. For Lambda<1, there are well defined resonance pairs of levels and the survival probability has coherent oscillations related to resonance splitting. However, for Lambda>1 there are no oscillations at all for the survival probability, and there is almost an exponential decay with the characteristic time determined by Fermi golden rule. In this case, one may not restrict himself to only resonance pair levels. The number of levels perturbed by tunneling grows proportionally to square root of [Lambda] (in other words, instead of isolated pairs there appear the resonance regions containing the sets of strongly coupled levels). In the region of intermedia...Continue Reading

References

Jun 1, 1986·Physical Review A: General Physics·T ZimmermannL S Cederbaum
Jul 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S Tomsovic, D Ullmo
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·L Kaplan, E J Heller

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