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.
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Acknowledgments
The authors thank Carlos Villegas Blas for fruitful discussions and comments.
Funding
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.
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Avendano-Camacho, M., Mamani-Alegria, N. & Vorobiev, Y.M. On the Geometry of Slow-Fast Phase Spaces and the Semiclassical Quantization. Russ. J. Math. Phys. 28, 8–21 (2021). https://doi.org/10.1134/S1061920821010039
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DOI: https://doi.org/10.1134/S1061920821010039