Quantum asymptotic amplitude for quantum oscillatory systems from the Koopman operator viewpoint
arxiv(2024)
摘要
We have recently proposed a fully quantum-mechanical definition of the
asymptotic phase for quantum nonlinear oscillators, which is also applicable in
the strong quantum regime [Kato and Nakao 2022 Chaos 32 063133]. In this study,
we propose a definition of the quantum asymptotic amplitude for quantum
oscillatory systems, which extends naturally the definition of the asymptotic
amplitude for classical nonlinear oscillators on the basis of the Koopman
operator theory. We introduce the asymptotic amplitude for quantum oscillatory
systems by using the eigenoperator of the backward Liouville operator
associated with the largest non-zero real eigenvalue. Using examples of the
quantum van der Pol oscillator with the quantum Kerr effect, exhibiting quantum
limit-cycle oscillations, and the quantum van der Pol model with the quantum
squeezing and degenerate parametric oscillator with nonlinear damping,
exhibiting quantum noise-induced oscillations, we illustrate that the proposed
quantum asymptotic amplitude appropriately yields isostable amplitude values
that decay exponentially with a constant rate.
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