Long Time Quantum Evolution of Observables

Abstract

We build a semi-classical quantization procedure for finite volume man- ifolds with hyperbolic cusps, adapted to a geometrical class of symbols. We prove an Egorov Lemma until Ehrenfest times on such manifolds. Then we give a version of Quantum Unique Ergodicity for the Eisenstein series for values of s converging slowly to the unitary axis.

51 pages, 1 figure

References in corpus (2)

• Quantum Limits of Eisenstein Series and Scattering states
• Microlocal limits of Eisenstein functions away from the unitarity axis

Cited by in corpus (1)

• Quantum Ergodicity for Eisenstein functions