Remarks on quantum ergodicity
Spectral Theory
2013-01-29 v3 Mathematical Physics
Dynamical Systems
math.MP
Abstract
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.
Cite
@article{arxiv.1209.3576,
title = {Remarks on quantum ergodicity},
author = {Gabriel Riviere},
journal= {arXiv preprint arXiv:1209.3576},
year = {2013}
}
Comments
12 pages. Compared with previous version, some details added and presentation improved