Fractal Weyl Law for Open Chaotic Maps

Details Fractal Weyl Law for Open Chaotic Maps Fractal Weyl Law for Open Chaotic Maps

2005-06-21

arxiv.org/abs/math-ph/0506056v2

Mathematical Physics of Quantum Mechanics, (2006) 435-450

Physics

Mathematical Physics

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

Scientific paper

10.1007/b11573432

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 r\'{e}gime, and show that they satisfy a fractal Weyl law. We can
prove this fractal law in the case of a modified model.

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