Fractal Weyl Law for Open Chaotic Maps
St\'ephane Nonnenmacher (SPhT)
TL;DR
This paper investigates the distribution of resonances in open quantum chaotic maps, demonstrating that they follow a fractal Weyl law, with proofs provided for a modified model, advancing understanding of quantum chaos.
Contribution
It establishes the fractal Weyl law for open quantum chaotic maps and proves it for a modified model, linking quantum resonances to fractal geometry.
Findings
Resonances follow a fractal Weyl law in the semiclassical regime
The law is proven for a modified model of the system
Results connect quantum resonances with fractal structures in phase space
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 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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