Remarks on quantum ergodicity

Gabriel Riviere (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We prove a generalized version of the Quantum Ergodicity Theorem on smooth compact Riemannian manifolds without boundary. We apply it to prove some asymptotic properties on the distribution of typical eigenfunctions of the Laplacian in geometric situations where the Liouville measure is not (or not known to be) ergodic.

Mots clés: eigenfunctions of the Laplacian; quantum ergodicity; nonuniform hyperbolicity

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]; Systèmes dynamiques [math.DS]

Gabriel Riviere. Remarks on quantum ergodicity. Journal of modern dynamics, 2013, 7 (1), pp.119-133. ⟨10.3934/jmd.2013.7.119⟩. ⟨hal-00732742v3⟩