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

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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 languageEnglish
Pages (from-to)8-21
Number of pages14
JournalRussian Journal of Mathematical Physics
Issue number1
StatePublished - 1 Jan 2021

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