Scarring effects on tunneling in chaotic double-well potentials.

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 Planck's over 2 pi 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-Planck's over 2 pi effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.