The Geometric Phase as a Diagnostic for Driven-Dissipative Oscillators

• URL: http://arxiv.org/abs/2608.25742v1
• Date: Wed, 26 Aug 2026 12:52:36 GMT
• Title: The Geometric Phase as a Diagnostic for Driven-Dissipative Oscillators
• Abstract summary: We show that driven-dissipative quantum oscillators lock their phase, deform their limit cycles, and undergo dissipative phase transitions.<n>This behavior is read from unrelated quantities defined on the same steady-state density matrix.<n>We show that a single geometric quantity organizes them.
• Score: 13.38226745175549
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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