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Matematicheskie Zametki, 2021, Volume 109, Issue 5, Pages 747–767
DOI: https://doi.org/10.4213/mzm12976 (Mi mzm12976) 		 
This article is cited in 2 scientific papers (total in 2 papers)

New Approach to the Procedure of Quantum Averaging for the Hamiltonian of a Resonance Harmonic Oscillator with Polynomial Perturbation for the Example of the Spectral Problem for the Cylindrical Penning Trap

E. M. Novikova

National Research University "Higher School of Economics", Moscow
Full-text PDF (622 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm12976
Abstract: For the perturbed Hamiltonian of a multifrequency resonance harmonic oscillator, a new approach to calculating the coefficients in the procedure of quantum averaging is proposed. The procedure of quantum averaging is transferred to the space of the graded algebra of symbols by using twisted product introduced in the paper. As a result, the averaged Hamiltonian is represented as a function of generators of the quantum symmetry algebra of the harmonic part of the Hamiltonian. The proposed method is applied to the spectral problem for the Hamiltonian of the cylindrical Penning trap.
Keywords: quantum averaging method, calculus of symbols, frequency resonance, twisted product, symmetry algebra.
Funding agency Grant number
National Research University Higher School of Economics
The study was implemented in the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE University) in 2020.
Received: 14.12.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 5, Pages 777–793
DOI: https://doi.org/10.1134/S0001434621050102
Bibliographic databases:
Document Type: Article
UDC: 517.958:530.145:512
Language: Russian
Citation: E. M. Novikova, “New Approach to the Procedure of Quantum Averaging for the Hamiltonian of a Resonance Harmonic Oscillator with Polynomial Perturbation for the Example of the Spectral Problem for the Cylindrical Penning Trap”, Mat. Zametki, 109:5 (2021), 747–767; Math. Notes, 109:5 (2021), 777–793
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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