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2017 Distorted plane waves in chaotic scattering
Maxime Ingremeau
Anal. PDE 10(4): 765-816 (2017). DOI: 10.2140/apde.2017.10.765

Abstract

We provide a precise description of distorted plane waves for semiclassical Schrödinger operators under the assumption that the classical trapped set is hyperbolic and that a certain topological pressure (a quantity defined using thermodynamical formalism) is negative. Distorted plane waves are generalized eigenfunctions of the Schrödinger operator which differ from free plane waves, eix,ξh, by an outgoing term. Under our assumptions we show that they can be written as a convergent sum of Lagrangian states. That provides a description of their semiclassical defect measures in the spirit of quantum ergodicity and extends results of Guillarmou and Naud obtained for hyperbolic quotients to our setting.

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Maxime Ingremeau. "Distorted plane waves in chaotic scattering." Anal. PDE 10 (4) 765 - 816, 2017. https://doi.org/10.2140/apde.2017.10.765

Information

Received: 7 January 2016; Revised: 19 November 2016; Accepted: 7 March 2017; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 1365.35100
MathSciNet: MR3649368
Digital Object Identifier: 10.2140/apde.2017.10.765

Subjects:
Primary: 35P20, 35P25, 81Q50

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 4 • 2017
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