Quantum ergodicity for restrictions to hypersurfaces

Details Quantum ergodicity for restrictions to hypersurfaces Quantum ergodicity for restrictions to hypersurfaces

2012-04-02

arxiv.org/abs/1204.0284v1

Mathematics

Analysis of PDEs

16 pages, 1 figure

Scientific paper

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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