Coherent oscillations and incoherent tunneling in a one-dimensional asymmetric double-well potential
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 Λ 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 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:cond-mat/0107495
- Bibcode:
- 2002PhRvE..65c6217B
- Keywords:
-
- 05.45.-a;
- 03.65.Sq;
- Nonlinear dynamics and chaos;
- Semiclassical theories and applications;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 19 pages, 7 figures, Revtex, revised version. Accepted to Phys. Rev. E