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Communications in Mathematical Physics

, Volume 343, Issue 1, pp 311–359 | Cite as

Long Time Quantum Evolution of Observables on Cusp Manifolds

  • Yannick Bonthonneau
Article

Abstract

The Eisenstein functions \({E(s)}\) are some generalized eigenfunctions of the Laplacian on manifolds with cusps. We give a version of Quantum Unique Ergodicity for them, for \({|\mathfrak{I}s| \to \infty}\) and \({\mathfrak{R}s \to d/2}\) with \({\mathfrak{R}s - d/2 \geq \log \log |\mathfrak{I}s| / \log |\mathfrak{I}s|}\). For the purpose of the proof, we build a semi-classical quantization procedure for finite volume manifolds with hyperbolic cusps, adapted to a geometrical class of symbols. We also prove an Egorov Lemma until Ehrenfest times on such manifolds.

Keywords

Manifold Covariant Derivative Pseudodifferential Operator Eisenstein Series Resonant State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.UQÀM, CIRGETQuébecCanada

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