Scarring Effects on Tunneling in Chaotic Double-Well Potentials

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 {$2\pi \hslash$} 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-{$\hslash$} effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.

22 pages, including 11 figures

Cited by in corpus (9)

• Eigenstate Structure in Graphs and Disordered Lattices
• Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring
• Observation of anomalous information scrambling in a Rydberg atom array
• Scarring and the statistics of tunnelling
• Phase space structure and escape time dynamics in a Van der Waals model for exothermic reactions
• Classical approach to collision complexes in ultracold chemical reactions
• A realistic example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields
• Schrodinger cat animated on a quantum computer
• Regularization of Tunneling Rates with Quantum Chaos