Fractal Weyl Law for Open Chaotic Maps

Abstract

This contribution summarizes our work with M.Zworski on open quantum open chaoticmaps (math-ph/0505034). For a simple chaotic scattering system (the open quantum baker's map), we compute the "long-living resonances" in the semiclassical régime, and show that they satisfy a fractal Weyl law. We can prove this fractal law in the case of a modified model.

Contribution to the Proceedings of the conference QMath9, Mathematical Physics of Quantum Mechanics, September 12th-16th 2004, Giens, France

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