Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations
Abstract
We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is therefore realized either along one trajectory or along two equivalent paths. Zero point fluctuations smear out the sharp transition between these two regimes and lead to a certain crossover behavior. When the two saddle points are inequivalent one can also have a first order transition related to the fact that one of the two trajectories becomes unstable. We illustrate these results by numerical investigations. Even though a specific model is investigated here, the approach is quite general and has potential applicability for various systems in physics and chemistry exhibiting multi-stability and tunneling phenomena.
Keywords
Cite
@article{arxiv.cond-mat/0209030,
title = {Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations},
author = {V. A. Benderskii and E. V. Vetoshkin and E. I. Kats and L. D. Landau and H. P. Trommsdorff},
journal= {arXiv preprint arXiv:cond-mat/0209030},
year = {2009}
}
Comments
11 pages, 8 eps figures, Revtex-4