Resonance-assisted tunneling in mixed regular-chaotic systems

TL;DR

This paper develops a detailed theory of resonance-assisted tunneling in quantum systems with mixed phase space, focusing on systems with periodic driving and comparing theoretical predictions with numerical results.

Contribution

It introduces a more precise expression for effective coupling matrix elements and accounts for partial barriers, improving understanding of resonance-assisted tunneling in mixed systems.

Findings

Derived a new formula for coupling matrix elements

Accounted for partial barriers in chaotic regions

Achieved excellent agreement with numerical level splittings

Abstract

We present a comprehensive theory of resonance-assisted tunneling in quantum systems that exhibit a mixed regular-chaotic classical phase space structure. After general considerations, we specifically focus on quantum systems with one degree of freedom that are subject to a periodic sequence of kicks or to a periodic driving. Tunneling takes place between energetically degenerate quasimodes that are localized on symmetric regular islands within the stroboscopic Poincare surface of section. In contrast to previous theoretical descriptions of resonance-assisted tunneling, we derive a more precise expression for the effective coupling matrix elements that induce the resonance-assisted tunneling process, and we take into account the influence of partial barriers within the chaotic part of the phase space. Comparison with numerically computed level splittings of eigenphases within the quantum kicked rotor shows very good agreement.