Distribution of resonances for open quantum maps

Abstract

We analyze simple models of classical chaotic open systems and of their quantizations (open quantum maps on the torus). Our models are similar to models recently studied in atomic and mesoscopic physics. They provide a numerical confirmation of the fractal Weyl law for the density of quantum resonances of such systems. The exponent in that law is related to the dimension of the classical repeller (or trapped set) of the system. In a simplified model, a rigorous argument gives the full resonance spectrum, which satisfies the fractal Weyl law. For this model, we can also compute a quantity characterizing the fluctuations of conductance through the system, namely the shot noise power: the value we obtain is close to the prediction of random matrix theory.

60 pages, no figures (numerical results are shown in other references)

References in corpus (4)

• Fractal Weyl laws for chaotic open systems
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• The Selberg zeta function for convex co-compact Schottky groups
• Fractal Weyl laws in discrete models of chaotic scattering

Cited by in corpus (23)

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• Upper bound on the density of Ruelle resonances for Anosov flows
• Spectral problems in open quantum chaos
• Fractal Weyl law for quantum fractal eigenstates
• Resonances in open quantum maps
• Truncations of Random Orthogonal Matrices
• Ulam method and fractal Weyl law for Perron--Frobenius operators
• Quantum chaotic resonances from short periodic orbits
• Resonances for open quantum maps and a fractal uncertainty principle
• Google matrix, dynamical attractors and Ulam networks
• From open quantum systems to open quantum maps
• On the resonance eigenstates of an open quantum baker map
• Lieb-Thirring estimates for non self-adjoint Schrödinger operators
• Fractal Weyl law for Linux Kernel Architecture
• Super-sharp resonances in chaotic wave scattering
• Probabilistic Weyl laws for quantized tori
• Some open questions in "wave chaos"
• Google matrix of the citation network of Physical Review
• Resonance spectra for quantum maps of kicked scattering systems by complex scaling
• Almost sure Weyl law for quantized tori
• Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum
• Localization of eigenvectors of non-Hermitian banded noisy Toeplitz matrices
• Eigenstates and spectral projection for quantized baker's map