TY - JOUR
T1 - On the Geometry of Slow-Fast Phase Spaces and the Semiclassical Quantization
AU - Avendano-Camacho, M.
AU - Mamani-Alegria, N.
AU - Vorobiev, Y. M.
N1 - Publisher Copyright:
© 2021, Pleiades Publishing, Ltd.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85102731679&partnerID=8YFLogxK
U2 - 10.1134/S1061920821010039
DO - 10.1134/S1061920821010039
M3 - Artículo
AN - SCOPUS:85102731679
SN - 1061-9208
VL - 28
SP - 8
EP - 21
JO - Russian Journal of Mathematical Physics
JF - Russian Journal of Mathematical Physics
IS - 1
ER -