几何相位作为受驱耗散振荡器的诊断工具
The Geometric Phase as a Diagnostic for Driven-Dissipative Oscillators
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中文总结 AI 辅助
本文提出用几何相位作为统一诊断工具，表征受驱耗散振荡器的相位锁定、极限环变形及耗散相变等稳态行为，可实验获取且能记录不同相变的特征。
中文摘要 AI 辅助
受驱耗散量子振荡器会锁定相位、变形极限环并发生耗散相变，但这些行为均从同一稳态密度矩阵定义的无关量中读取。本文表明，单一几何量可将这些行为整合起来：驱动相位的缠绕会生成非平衡稳态的闭合回路，且由于刘维尔算符在数旋转下具有协变性，该回路的运动学混合态几何相位可精确简化为单一稳态的本征系统泛函。在弱驱动下，它由产生相位锁定的最近邻相干性支配，并继承同步的阿诺德舌；在霍普夫阈值附近，它记录稳态本征向量的非微扰重组；在受压缩驱动的克尔谐振器中，它在一阶和二阶耗散相变处呈现出不同特征。因此，几何相位为稳态重组提供了统一且可实验获取的表征方式。
英文摘要
Driven-dissipative quantum oscillators lock their phase, deform their limit cycles, and undergo dissipative phase transitions, yet these behaviors are read from unrelated quantities defined on the same steady-state density matrix. We show that a single geometric quantity organizes them. Winding the phase of the drive generates a closed loop of nonequilibrium steady states, and because the Liouvillian is covariant under number rotations, the kinematic mixed-state geometric phase of this loop reduces exactly to an eigensystem functional of a single steady state. Under weak driving, it is governed by the same nearest-neighbor coherences that produce phase locking and inherits the Arnold tongue of synchronization. Near the Hopf threshold, it registers the nonperturbative reorganization of the steady-state eigenvectors. And in the squeezing-driven Kerr resonator, it develops distinct signatures at the first and second order dissipative phase transitions. The geometric phase thus provides a unified and experimentally accessible characterization of steady-state reorganization.
