Quantum decay rates in chaotic scattering

Details Quantum decay rates in chaotic scattering Quantum decay rates in chaotic scattering

2007-06-22

arxiv.org/abs/0706.3242v2

Physics

Mathematical Physics

73 pages, 5 figures

Scientific paper

In this article we prove that for a large class of operators, including Schroedinger operators, with hyperbolic classical flows, the smallness of dimension of the trapped set implies that there is a gap between the resonances and the real axis. In other words, the quantum decay rate is bounded from below if the classical repeller is sufficiently filamentary. The higher dimensional statement is given in terms of the topological pressure. Under the same assumptions we also prove a resolvent estimate with a logarithmic loss compared to nontrapping estimates.

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