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Nonnenmacher, Stéphane; Zworski, Maciej

Quantum decay rates in chaotic scattering. (English) Zbl 1226.35061

Acta Math. 203, No. 2, 149-233 (2009).
This long and rather technical paper starts with a section in which the authors have formulated their principal results in the form of five theorems. Their proofs are scattered within the next eight sections and the appendix.
The main subject of their studies is the distribution of quantum resonances associated with hyperbolic classical flows in two and higher dimensions.
The main result is that there exist gaps between the resonances and the real axis. In dimension higher than two the proof relies on the notion of topological pressure associated with the classical hyperbolic flow.
Reviewer: Ivailo Mladenov (Sofia)

Cited in 1 Review
Cited in 65 Documents

MSC:

35P25 Scattering theory for PDEs
35B34 Resonance in context of PDEs
35B45 A priori estimates in context of PDEs

Keywords:

hyperbolic flow; scattering; resonances; topological pressure
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References:

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