https://hal-cea.archives-ouvertes.fr/cea-01185251Ingremeau, MaximeMaximeIngremeauIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueDistorted plane waves in chaotic scatteringHAL CCSD2017[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph]De Laborderie, Emmanuelle2015-08-19 15:49:112023-03-24 14:53:012015-08-19 15:49:11enJournal articles10.2140/apde.2017.10.7651We 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.