M. V. Karasev, “New global asymptotics and anomalies for the problem of quantization of the adiabatic invariant”, Funktsional. Anal. i Prilozhen., 24:2 (1990), 24–36; Funct. Anal. Appl., 24:2 (1990), 104

Citation in format AMSBIB

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\by M.~V.~Karasev

\paper New global asymptotics and anomalies for the problem of quantization of the adiabatic invariant

\jour Funktsional. Anal. i Prilozhen.

\yr 1990

\vol 24

\issue 2

\pages 24--36

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\zmath{https://zbmath.org/?q=an:0715.58036}

\transl

\jour Funct. Anal. Appl.

\yr 1990

\vol 24

\issue 2

\pages 104--114

\crossref{https://doi.org/10.1007/BF01077703}

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This publication is cited in the following 30 articles:

M. Avendano-Camacho, N. Mamani-Alegria, Y. M. Vorobiev, “On the Geometry of Slow-Fast Phase Spaces and the Semiclassical Quantization”, Russ. J. Math. Phys., 28:1 (2021), 8
K.J.A. Reijnders, D.S. Minenkov, M.I. Katsnelson, S.Yu. Dobrokhotov, “Electronic optics in graphene in the semiclassical approximation”, Annals of Physics, 397 (2018), 65
M. V. Karasev, “Magneto-dimensional resonance. Pseudospin phase and hidden quantum number”, Russ. J. Math. Phys., 24:3 (2017), 326
M. V. Karasev, “Contribution to the symplectic structure in the quantization rule due to noncommutativity of adiabatic parameters”, Russ. J. Math. Phys., 23:2 (2016), 207
M. V. Karasev, “Adiabatic approximation via hodograph translation and zero-curvature equations”, Russ. J. Math. Phys., 21:2 (2014), 197
S. B. Kuksin, A. I. Neishtadt, “On quantum averaging, quantum KAM, and quantum diffusion”, Russian Math. Surveys, 68:2 (2013), 335–348
M. Avendaño Camacho, Yu. Vorobiev, “On the global structure of normal forms for slow-fast Hamiltonian systems”, Russ. J. Math. Phys., 20:2 (2013), 138
M. Avendaño-Camacho, J. A. Vallejo, Yu. Vorobiev, “Higher order corrections to adiabatic invariants of generalized slow-fast Hamiltonian systems”, Journal of Mathematical Physics, 54:8 (2013)
Bruning, J, “Quantum dynamics in a thin film, I. Propagation of localized perturbations”, Russian Journal of Mathematical Physics, 15:1 (2008), 1
J. Brüning, S. Yu. Dobrokhotov, R. V. Nekrasov, T. Ya. Tudorovskiy, “Quantum dynamics in a thin film, I. Propagation of localized perturbations”, Russ. J. Math. Phys., 15:1 (2008), 1
M. V. Karasev, “Magneto-metric Hamiltonians on quantum surfaces in the configuration space”, Russ. J. Math. Phys., 14:1 (2007), 57
M. V. Karasev, “Geometric dynamics on quantum Nano-surfaces and low-energy spectrum in a homogeneous magnetic field”, Russ. J. Math. Phys., 14:4 (2007), 440
J. Brüning, S. Dobrokhotov, S. Sekerzh-Zenkovich, T. Tudorovskiy, “Spectral series of the Schrödinger operator in thin waveguides with periodic structure, I adiabatic approximation and semiclassical asymptotics in the 2D case”, Russ. J. Math. Phys., 13:4 (2006), 380
M. Karasev, “Noncommutative algebras, nano-structures, and quantum dynamics generated by resonances. III”, Russ. J. Math. Phys., 13:2 (2006), 131
V. V. Belov, S. Yu. Dobrokhotov, V. P. Maslov, T. Ya. Tudorovskii, “A generalized adiabatic principle for electron dynamics in curved nanostructures”, Phys. Usp., 48:9 (2005), 962–968
S. Yu. Dobrokhotov, M. A. Poteryakhin, “Normal Forms near Two-Dimensional Resonance Tori for the Multidimensional Anharmonic Oscillator”, Math. Notes, 76:5 (2004), 653–664
Alberto PARMEGGIANI, “ON THE SPECTRUM AND THE LOWEST EIGENVALUE OF CERTAIN NON-COMMUTATIVE HARMONIC OSCILLATORS”, Kyushu J. Math., 58:2 (2004), 277
V. V. Belov, O. S. Dobrokhotov, S. Yu. Dobrokhotov, “Isotropic Tori, Complex Germ and Maslov Index, Normal Forms and Quasimodes of Multidimensional Spectral Problems”, Math. Notes, 69:4 (2001), 437–466
C. Emmrich, H. Römer, “Multicomponent Wentzel–Kramers–Brillouin approximation on arbitrary symplectic manifolds: A star product approach”, Journal of Mathematical Physics, 39:7 (1998), 3530
Mikhail Karasev, Yuri Vorobjev, “Integral Representations over Isotropic Submanifolds and Equations of Zero Curvature”, Advances in Mathematics, 135:2 (1998), 220