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Revival of oscillation and symmetry breaking in coupled quantum oscillators. (English) Zbl 1465.81015

Summary: Restoration of oscillations from an oscillation suppressed state in coupled oscillators is an important topic of research and has been studied widely in recent years. However, the same in the quantum regime has not been explored yet. Recent works established that under certain coupling conditions, coupled quantum oscillators are susceptible to suppression of oscillations, such as amplitude death and oscillation death. In this paper, for the first time, we demonstrate that quantum oscillation suppression states can be revoked and rhythmogenesis can be established in coupled quantum oscillators by controlling a feedback parameter in the coupling path. However, in sharp contrast to the classical system, we show that in the deep quantum regime, the feedback parameter fails to revive oscillations, and rather results in a transition from a quantum amplitude death state to the recently discovered quantum oscillation death state. We use the formalism of an open quantum system and a phase space representation of quantum mechanics to establish our results. Therefore, our study establishes that the revival scheme proposed for classical systems does not always result in restoration of oscillations in quantum systems, but in the deep quantum regime, it may give counterintuitive behaviors that are of a pure quantum mechanical origin.
©2021 American Institute of Physics

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81R40 Symmetry breaking in quantum theory
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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