Wigner measures and quantum Aubry–Mather theory

Article type: Research Article

Authors: Gomes, Diogo A. | Valls, Claudia

Affiliations: Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Note: [] Supported in part by FCT/POCTI/FEDER and FCT/POCI/MAT/55745/2004.

Note: [] Supported in part by the Center for Mathematical Analysis, Geometry, and Dynamical Systems, through FCT/POCTI/FEDER and grant SFRH/BPD/14404/2003.

Abstract: In this paper we investigate the quantum action problem using Wigner measures on the torus. We prove existence, study its main properties, and prove convergence to Mather measures in the semiclassical limit. We also indicate how to extend these techniques to the study of stochastic Mather measures.

Journal: Asymptotic Analysis, vol. 51, no. 1, pp. 47-61, 2007