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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 198, Number 1, Pages 19–31
DOI: https://doi.org/10.4213/tmf9541
(Mi tmf9541)
 

This article is cited in 2 scientific papers (total in 2 papers)

Quantum analogue of unstable limit cycles of a periodically perturbed inverted oscillator

V. V. Chistyakov

St. Petersburg National Research University of Information Technologies, Mechanics, and Optics, St. Petersburg, Russia
Full-text PDF (601 kB) Citations (2)
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Abstract: To study the quantum analogue of classical limit cycles, we consider the behavior of a particle in a negative quadratic potential perturbed by a sinusoidal field. We propose a type of wave function asymptotically satisfying the operator of initial conditions and still admitting analytic integration of the nonstationary Schrödinger equation. The solution demonstrates that for certain perturbation phases determined by the forcing frequency and the initial indeterminacy of the coordinate, the wave-packet center temporarily stabilizes near the potential maximum for approximately two "natural periods" of the oscillator and then moves to infinity with bifurcations in the drift direction. The effect is not masked by packet spreading, because the packet undergoes anomalous narrowing (collapse) to a size of the order of the characteristic length on the above time interval and its unbounded spreading begins only after this.
Keywords: inverted quantum oscillator, periodic perturbation, limit cycle, nonstationary Schrödinger equation, generalized Gaussian type, collapse, dynamical stabilization, bifurcation.
Funding agency Grant number
Russian Foundation for Basic Research 16-08-00997
This research was supported by the Russian Foundation for Basic Research (Grant No. 16-08-00997).
Received: 05.02.2018
Revised: 19.03.2018
English version:
Theoretical and Mathematical Physics, 2019, Volume 198, Issue 1, Pages 17–28
DOI: https://doi.org/10.1134/S0040577919010021
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Chistyakov, “Quantum analogue of unstable limit cycles of a periodically perturbed inverted oscillator”, TMF, 198:1 (2019), 19–31; Theoret. and Math. Phys., 198:1 (2019), 17–28
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9541
  • https://doi.org/10.4213/tmf9541
  • https://www.mathnet.ru/eng/tmf/v198/i1/p19
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:31
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