Semyon Dyatlov, Maciej Zworski
Published 2012-04-02, updated 2012-10-17Version 3
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.
Comments: 22 pages, 1 figure; revised according to referee's comments. To appear in Nonlinearity
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Fourier coefficients of restrictions of eigenfunctions
Quantum ergodicity and $L^p$ norms of restrictions of eigenfunctions
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