Coherent oscillations and incoherent tunneling in a onedimensional asymmetric doublewell potential
Abstract
For a model onedimensional asymmetric doublewell potential we calculated the socalled 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 Λ that is a ratio of characteristic frequencies for lowenergy nonlinear inwell oscillations and interwell tunneling. For the potential describing a finite motion (doublewell) one has always a regular behavior. For Λ<<1, there are well defined resonance pairs of levels and the survival probability has coherent oscillations related to resonance splitting. However, for Λ>>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 (Λ) (in other words, instead of isolated pairs there appear the resonance regions containing the sets of strongly coupled levels). In the region of intermediate values of Λ one has a crossover between both limiting cases, namely, the exponential decay with subsequent long period recurrent behavior.
 Publication:

Physical Review E
 Pub Date:
 March 2002
 DOI:
 10.1103/PhysRevE.65.036217
 arXiv:
 arXiv:condmat/0107495
 Bibcode:
 2002PhRvE..65c6217B
 Keywords:

 05.45.a;
 03.65.Sq;
 Nonlinear dynamics and chaos;
 Semiclassical theories and applications;
 Condensed Matter  Statistical Mechanics
 EPrint:
 19 pages, 7 figures, Revtex, revised version. Accepted to Phys. Rev. E