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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.

Keywords

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

R2 v1 2026-06-21T22:06:05.881Z