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Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations

V. A. Benderskii·E. V. Vetoshkin·E. I. Kats·L. D. Landau·H. P. Trommsdorff
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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.

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V. A. Benderskii, E. V. Vetoshkin, E. I. Kats, L. D. Landau, H. P. Trommsdorff. 2002-09-02. Competing tunneling trajectories in a 2D potential with variable topology as a model for quantum bifurcations. https://doi.org/10.1103/physreve.67.026102

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