# Weyl Laws for Partially Open Quantum Maps

@article{Schenck2008WeylLF, title={Weyl Laws for Partially Open Quantum Maps}, author={Emmanuel Schenck}, journal={Annales Henri Poincar{\'e}}, year={2008}, volume={10}, pages={711-747} }

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 dynamics is chaotic…

## 10 Citations

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This work reexamine and substantially extend the results of a short paper published earlier and finds that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared.

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There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can…

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In the high-frequency limit, the distribution of (quantum) decay rates is shown to cluster near a "typical" value, which is larger than the classical decay rate of the corresponding damped ray dynamics.

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For a general class of unitary quantum maps, whose underlying classical phase space is divided into several invariant domains of positive measure, we establish analogues of Weyl's law for the…

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