Fractal Weyl laws for quantum decay in generic dynamical systems

TL;DR

This paper demonstrates that in generic open quantum systems, the distribution of resonances follows a fractal Weyl law, revealing new insights into quantum decay and quantum-classical correspondence even with mixed classical dynamics.

Contribution

It introduces a modified fractal Weyl law applicable to systems with mixed classical dynamics, extending the understanding beyond fully chaotic systems.

Findings

Resonances follow a fractal Weyl law in generic systems.

Provides insight into quantum decay in mixed dynamical systems.

Enhances understanding of quantum-to-classical correspondence.

Abstract

Weyl's law approximates the number of states in a quantum system by partitioning the energetically accessible phase-space volume into Planck cells. Here we show that typical resonances in generic open quantum systems follow a modified, fractal Weyl law, even though their classical dynamics is not globally chaotic but also contains domains of regular motion. Besides the obvious ramifications for quantum decay, this delivers detailed insight into quantum-to-classical correspondence, a phenomenon which is poorly understood for generic quantum-dynamical systems.