Distorted plane waves in chaotic scattering - Archive ouverte HAL Access content directly
Journal Articles Analysis & PDE Year : 2017

Distorted plane waves in chaotic scattering

(1)
1

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.

Dates and versions

cea-01185251 , version 1 (19-08-2015)

Identifiers

Cite

Maxime Ingremeau. Distorted plane waves in chaotic scattering. Analysis & PDE, 2017, 10 (4), pp.765-816. ⟨10.2140/apde.2017.10.765⟩. ⟨cea-01185251⟩
50 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More