Quantum ergodicity for restrictions to hypersurfaces

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

References in corpus (1)

• Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes

Cited by in corpus (8)

• The quantum unique ergodicity conjecture for thin sets
• The Quantum Sabine Law for Resonances in Transmission Problems
• Around quantum ergodicity
• Quantum ergodicity and $L^p$ norms of restrictions of eigenfunctions
• Equidistribution of Eisenstein series on geodesic segments
• The $L^2$ Behavior of Eigenfunctions Near the Glancing Set
• Sign changes of the Eisenstein series on the critical line
• Extreme values of geodesic periods on arithmetic hyperbolic surfaces