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
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.
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.
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
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This publication is cited in the following 2 articles:
E. V. Vybornyi, S. V. Rumyantseva, “Semiclassical Asymptotics of Oscillating Tunneling for a Quadratic Hamiltonian on the Algebra su(1,1)su(1,1)”, Math. Notes, 112:5 (2022), 642–655
E. V. Vybornyi, “Magneto-dimensional resonance on curved surfaces”, Russ. J. Math. Phys., 29:4 (2022), 595
Citation in format AMSBIB
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