Quantum-to-classical crossover of quasi-bound states in open quantum systems

TL;DR

This paper investigates the transition from quantum to classical behavior in open quantum systems, revealing how decay modes and state statistics evolve with system parameters, validated through numerical simulations of the open kicked rotator.

Contribution

It introduces a detailed analysis of decay modes in open quantum systems, connecting classical escape dynamics with quantum state statistics and validating the theory numerically.

Findings

Identification of instantaneous decay modes guided by classical escape.

Long-lived states follow renormalized random-matrix statistics.

Validation of the theory using the open kicked rotator model.

Abstract

In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence of instantaneous decay modes guided by classical escape faster than the Ehrenfest time. The decay time of the associated quasi-bound states is smaller than the classical time of flight. The remaining long-lived quasi-bound states obey random-matrix statistics, renormalized in compliance with the recently proposed fractal Weyl law for open systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)]. We validate our theory numerically for a model system, the open kicked rotator.