Quantum ergodicity for restrictions to hypersurfaces
Analysis of PDEs
2012-11-20 v3 Spectral Theory
Abstract
Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple dynamical condition, the restrictions of eigenstates to N are also quantum ergodic.
Keywords
Cite
@article{arxiv.1204.0284,
title = {Quantum ergodicity for restrictions to hypersurfaces},
author = {Semyon Dyatlov and Maciej Zworski},
journal= {arXiv preprint arXiv:1204.0284},
year = {2012}
}
Comments
22 pages, 1 figure; revised according to referee's comments. To appear in Nonlinearity