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arXiv · 1204.0284

Quantum ergodicity for restrictions to hypersurfaces

Semyon Dyatlov·Maciej Zworski
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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.

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Semyon Dyatlov, Maciej Zworski. 2012-10-17. Quantum ergodicity for restrictions to hypersurfaces. https://doi.org/10.1088/0951-7715%2F26%2F1%2F35

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