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Abstract: In this article we prove that for a large class of operators, includingSchroedinger operators, with hyperbolic classical flows, the smallness ofdimension of the trapped set implies that there is a gap between the resonancesand the real axis. In other words, the quantum decay rate is bounded from belowif the classical repeller is sufficiently filamentary. The higher dimensionalstatement is given in terms of the topological pressure. Under the sameassumptions we also prove a resolvent estimate with a logarithmic loss comparedto nontrapping estimates.

Author: Stephane Nonnenmacher, Maciej Zworski

Source: https://arxiv.org/

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