On the Geometry of Slow-Fast Phase Spaces and the Semiclassical Quantization

M. Avendano-Camacho; N. Mamani-Alegria; Y. M. Vorobiev

doi:10.1134/S1061920821010039

On the Geometry of Slow-Fast Phase Spaces and the Semiclassical Quantization

M. Avendano-Camacho, N. Mamani-Alegria, Y. M. Vorobiev

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

1 Scopus citations

Abstract

Abstract: In the context of the averaging method for Poisson and symplectic structures and the theory of Hannay–Berry connections, we discuss some aspects of the semiclassical quantization for a class of slow-fast Hamiltonian systems with two degrees of freedom. For a pseudodifferential Weyl operator with two small parameters corresponding to the semiclassical and adiabatic limits, we show how to construct some series of quasimodes associated to a family of Lagrangian 2-tori which are almost invariant with respect to the classical dynamics.

Original language	English
Pages (from-to)	8-21
Number of pages	14
Journal	Russian Journal of Mathematical Physics
Volume	28
Issue number	1
DOIs	https://doi.org/10.1134/S1061920821010039
State	Published - 1 Jan 2021

Bibliographical note

Funding Information:
This research was partially supported by the Mexican National Council of Science and Technology (CONACYT) under the grant CB2015 no. 258302 and the University of Sonora (UNISON) under the project USO no. 315006810.

Publisher Copyright:
© 2021, Pleiades Publishing, Ltd.

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On the Geometry of Slow-Fast Phase Spaces and the Semiclassical Quantization

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