#### Vol. 10, No. 4, 2017

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Distorted plane waves in chaotic scattering

### Maxime Ingremeau

Vol. 10 (2017), No. 4, 765–816
##### 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, ${e}^{i〈x,\xi 〉∕h}$, 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.

##### Keywords
scattering theory, quantum chaos, semiclassical measures, distorted plane waves
##### Mathematical Subject Classification 2010
Primary: 35P20, 35P25, 81Q50