Quantized open chaotic systems
St\'ephane Nonnenmacher (IPHT)
TL;DR
This paper explores the analysis of wave chaotic systems with complex eigenvalues using semiclassical methods, deriving bounds on resonance density and criteria for spectral gaps.
Contribution
It introduces a unified semiclassical approach to analyze wave chaotic systems with complex eigenvalues, providing new bounds and criteria for spectral properties.
Findings
Fractal Weyl upper bounds for resonance density
Classical dynamical criterion for spectral gap
Unified semiclassical analysis of wave chaotic systems
Abstract
Two different "wave chaotic" systems, involving complex eigenvalues or resonances, can be analyzed using common semiclassical methods. In particular, one obtains fractal Weyl upper bounds for the density of resonances/eigenvalues near the real axis, and a classical dynamical criterion for a spectral gap.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Spectral Theory in Mathematical Physics · Quantum Mechanics and Non-Hermitian Physics