The quantum variance of the modular surface

P. Sarnak; P. Zhao; M. Woodbury

doi:10.24033/asens.2406

The quantum variance of the modular surface

P. Sarnak, P. Zhao, M. Woodbury

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The variance of observables of quantum states of the Laplacian on the modular surface is calculated in the semiclassical limit. It is shown that this hermitian form is diagonalized by the irreducible representations of the modular quotient and on each of these it is equal to the classical variance of the geodesic flow after the insertion of a subtle arithmetical special value of the corresponding L-function.

Original language	English (US)
Pages (from-to)	1155-1200
Number of pages	46
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	52
Issue number	5
DOIs	https://doi.org/10.24033/asens.2406
State	Published - 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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10.24033/asens.2406

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AB - The variance of observables of quantum states of the Laplacian on the modular surface is calculated in the semiclassical limit. It is shown that this hermitian form is diagonalized by the irreducible representations of the modular quotient and on each of these it is equal to the classical variance of the geodesic flow after the insertion of a subtle arithmetical special value of the corresponding L-function.

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The quantum variance of the modular surface

Abstract

All Science Journal Classification (ASJC) codes

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