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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
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.
Received: 05.02.2018 Revised: 19.03.2018
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
Linking options:
https://www.mathnet.ru/eng/tmf9541https://doi.org/10.4213/tmf9541 https://www.mathnet.ru/eng/tmf/v198/i1/p19
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Abstract page: | 321 | Full-text PDF : | 67 | References: | 31 | First page: | 10 |
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