Kato Yuzuru, Nakao Hiroya
Department of Complex and Intelligent Systems, Future University Hakodate, Hokkaido 041-8655, Japan.
Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan.
Chaos. 2022 Jun;32(6):063133. doi: 10.1063/5.0088559.
We propose a definition of the asymptotic phase for quantum nonlinear oscillators from the viewpoint of the Koopman operator theory. The asymptotic phase is a fundamental quantity for the analysis of classical limit-cycle oscillators, but it has not been defined explicitly for quantum nonlinear oscillators. In this study, we define the asymptotic phase for quantum oscillatory systems by using the eigenoperator of the backward Liouville operator associated with the fundamental oscillation frequency. By using the quantum van der Pol oscillator with a Kerr effect as an example, we illustrate that the proposed asymptotic phase appropriately yields isochronous phase values in both semiclassical and strong quantum regimes.
我们从柯普曼算子理论的角度提出了量子非线性振荡器渐近相位的定义。渐近相位是分析经典极限环振荡器的一个基本量，但尚未针对量子非线性振荡器明确界定。在本研究中，我们通过使用与基本振荡频率相关的反向刘维尔算子的本征算子来定义量子振荡系统的渐近相位。以具有克尔效应的量子范德波尔振荡器为例，我们说明了所提出的渐近相位在半经典和强量子区域中均能适当地产生等时相位值。
