Weyl laws for partially open quantum maps

Abstract

We study a toy model for "partially open" wave-mechanical system, like for instance a dielectric micro-cavity, in the semiclassical limit where ray dynamics is applicable. Our model is a quantized map on the 2-dimensional torus, with an additional damping at each time step, resulting in a subunitary propagator, or "damped quantum map". We obtain analogues of Weyl's laws for such maps in the semiclassical limit, and draw some more precise estimates when the classical dynamic is chaotic.

35 pages, 5 figures. Corrected typos. Some proofs clarified

References in corpus (2)

• A model for chaotic dielectric microresonators
• Resonance distribution in open quantum chaotic systems

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• Counting statistics of chaotic resonances at optical frequencies: theory and experiments
• Particle Trajectories for Quantum Maps
• Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation