The semi-classical ergodic Theorem for discontinuous metrics | Zendy

Yves Colin de Verdìère | Zendy

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The semi-classical ergodic Theorem for discontinuous metrics

Author(s) -

Yves Colin de Verdìère

Publication year - 2014

Publication title -

séminaire de théorie spectrale et géométrie

Language(s) - English

Resource type - Journals

eISSN - 2118-9242

pISSN - 1624-5458

DOI - 10.5802/tsg.295

Subject(s) - geodesic , ergodicity , ergodic theory , extension (predicate logic) , euclidean geometry , flow (mathematics) , geodesic flow , mathematics , pure mathematics , markov chain , computer science , mathematical analysis , geometry , statistics , programming language

— In this paper, we present an extension of the classical Quantum ergodicity Theorem, due to Shnirelman, to the case of Laplacians with discontinous metrics along interfaces. The “geodesic flow” is then no more a flow, but a Markov process due to the fact that rays can by reflected or refracted at the interfaces. We give also an example build by gluing together two flat Euclidean disks.

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