Fractal Weyl Law for Open Chaotic Maps

Stéphane Nonnenmacher (1)

1 SPhT - Service de Physique Théorique

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.

Mots clés: quantum chaotic scattering; resonances; fractal Weyl law

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Stéphane Nonnenmacher. Fractal Weyl Law for Open Chaotic Maps. Mathematical Physics of Quantum Mechanics (QMath9), Sep 2004, Giens, France. pp.435-450, ⟨10.1007/b11573432⟩. ⟨hal-00005509v2⟩