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Scarring Effects on Tunneling in Chaotic Double-Well Potentials

W. E. Bies·L. Kaplan·E. J. Heller
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Abstract

The connection between scarring and tunneling in chaotic double-well potentials is studied in detail through the distribution of level splittings. The mean level splitting is found to have oscillations as a function of energy, as expected if scarring plays a role in determining the size of the splittings, and the spacing between peaks is observed to be periodic of period {$2π\hbar$} in action. Moreover, the size of the oscillations is directly correlated with the strength of scarring. These results are interpreted within the theoretical framework of Creagh and Whelan. The semiclassical limit and finite-{$\hbar$} effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.

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W. E. Bies, L. Kaplan, E. J. Heller. 2000-07-25. Scarring Effects on Tunneling in Chaotic Double-Well Potentials. https://doi.org/10.1103/physreve.64.016204

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