The semi-classical ergodic Theorem for discontinuous metrics
Yves Colin de Verdière1
1 Université de Grenoble, Institut Fourier UMR CNRS-UJF 5582 BP 74 38402-Saint Martin d’Hères Cedex (France)
Séminaire de théorie spectrale et géométrie, Volume 31 (2012-2014), pp. 71-89.

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.

DOI: 10.5802/tsg.295
Yves Colin de Verdière 1

1 Université de Grenoble, Institut Fourier UMR CNRS-UJF 5582 BP 74 38402-Saint Martin d’Hères Cedex (France) 
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Yves Colin de Verdière. The semi-classical ergodic Theorem for discontinuous metrics. Séminaire de théorie spectrale et géométrie, Volume 31 (2012-2014), pp. 71-89. doi : 10.5802/tsg.295. https://tsg.centre-mersenne.org/articles/10.5802/tsg.295/

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