Scarring Effects on Tunneling in Chaotic Double-Well Potentials

Details Scarring Effects on Tunneling in Chaotic Double-Well Potentials Scarring Effects on Tunneling in Chaotic Double-Well Potentials

2000-07-25

arxiv.org/abs/nlin/0007037v1

Phys. Rev. E 64, 016204 (2001)

Nonlinear Sciences

Chaotic Dynamics

22 pages, including 11 figures

Scientific paper

10.1103/PhysRevE.64.016204

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 {$2\pi\hbar$} 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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