Fractal Weyl laws for quantum decay in generic dynamical systems

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.

4 pages, 4 figures

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Cited by in corpus (24)

• Leaking Chaotic Systems
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Generating particle-like scattering states in wave transport
• Wave packet evolution in non-Hermitian quantum systems
• Resonances in open quantum maps
• Weyl asymptotics: From closed to open systems
• Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
• Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems
• Resonance eigenfunction hypothesis for chaotic systems
• Formation and interaction of resonance chains in the open 3-disk system
• Multifractality of open quantum systems
• Husimi dynamics generated by non-Hermitian Hamiltonians
• Semiclassical Husimi distributions for non-Hermitian quantum systems
• Weyl law for open systems with sharply divided mixed phase space
• Semiclassical theory of chaotic quantum resonances
• Local random vector model for semiclassical fractal structure of chaotic resonance states
• Lyapunov exponents and Hamiltonian poles in a non Hermitian dynamics
• Resonance spectra for quantum maps of kicked scattering systems by complex scaling
• Resonance states of the three-disk scattering system
• Semiclassical Limit of Resonance States in Chaotic Scattering
• Weyl law for fat fractals
• Self-Similarity Among Energy Eigenstates
• Weyl law for contractive maps
• A non-Hermitian PT-symmetric kicked top