Quantum ergodicity for restrictions to hypersurfaces
arXiv:1204.0284 · doi:10.1088/0951-7715/26/1/35
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.
22 pages, 1 figure; revised according to referee's comments. To appear in Nonlinearity