Quantum ergodicity for restrictions to hypersurfaces

Author: Dyatlov Semyon   Zworski Maciej  

Publisher: IOP Publishing

ISSN: 0951-7715

Source: Nonlinearity, Vol.26, Iss.1, 2013-01, pp. : 35-52

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Abstract

Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, on 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.