Nonlinear Dissipation and Hopf Criticality in Driven Dissipative Collective Spins
Abstract
Self-sustained oscillations combine finite-amplitude stabilization with a neutral phase degree of freedom. We develop this bifurcation-based framework for driven-dissipative collective spins and show that the microscopic structure of the U(1)-covariant dissipation selects the background attractor, while the explicit U(1)-breaking channel governs its local bifurcation response. In the thermodynamic-limit mean-field dynamics, a single linear U(1)-covariant jump produces only polar fixed-point backgrounds, whereas nonlinear covariant dissipation provides amplitude-dependent saturation and stabilizes a finite-latitude self-sustained-oscillator manifold through a supercritical Hopf bifurcation. Under coherent U(1) breaking, exact resonance leads to a reversible double-zero degeneracy with vanishing critical frequency rather than a standard Hopf onset. Finite detuning unfolds this singularity into a genuine finite-frequency Hopf boundary, which exists only on the self-sustained-oscillator side and can be either supercritical or subcritical. By contrast, a single linear dissipative U(1)-breaking jump cannot generate a standard Hopf instability: when its phase-pinning invariant vanishes the azimuthal direction remains neutral, whereas otherwise the phase-locked fixed points have a purely real Jacobian spectrum. These results establish a general design principle: nonlinear covariant dissipation selects the selfsustained background, while the structure of the symmetry-breaking channel determines whether the resulting local response is double-zero, genuinely Hopf, or non-Hopf.
Related
- From Effective Temperature to Non-Boltzmann State Selection in Driven-Dissipative Quantum Criticality
- Monolithically integrated photonic neural network at driven-dissipative criticality
- Collective excitations of driven-dissipative quantum fluids of light
- When irrelevance governs: dissipation-regression scaling in open quantum criticality
- Dissipation-Sensitivity Trade-Off in Dissipative Bosonic Systems
BibTeX
@misc{yang2026nonlinear,
title = {{Nonlinear Dissipation and Hopf Criticality in Driven Dissipative Collective Spins}},
author = {Shu Yang and Jun Wang and Weidong Li and Cangtao Zhou and Jian-Song Pan and Jianwen Jie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03360},
eprint = {2609.03360},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03360},
}
RIS
TY - UNPB
TI - Nonlinear Dissipation and Hopf Criticality in Driven Dissipative Collective Spins
AU - Shu Yang
AU - Jun Wang
AU - Weidong Li
AU - Cangtao Zhou
AU - Jian-Song Pan
AU - Jianwen Jie
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.03360
UR - https://arxiv.org/abs/2609.03360
AB - Self-sustained oscillations combine finite-amplitude stabilization with a neutral phase degree of freedom. We develop this bifurcation-based framework for driven-dissipative collective spins and show that the microscopic structure of the U(1)-covariant dissipation selects the background attractor, while the explicit U(1)-breaking channel governs its local bifurcation response. In the thermodynamic-limit mean-field dynamics, a single linear U(1)-covariant jump produces only polar fixed-point backgrounds, whereas nonlinear covariant dissipation provides amplitude-dependent saturation and stabilizes a finite-latitude self-sustained-oscillator manifold through a supercritical Hopf bifurcation. Under coherent U(1) breaking, exact resonance leads to a reversible double-zero degeneracy with vanishing critical frequency rather than a standard Hopf onset. Finite detuning unfolds this singularity into a genuine finite-frequency Hopf boundary, which exists only on the self-sustained-oscillator side and can be either supercritical or subcritical. By contrast, a single linear dissipative U(1)-breaking jump cannot generate a standard Hopf instability: when its phase-pinning invariant vanishes the azimuthal direction remains neutral, whereas otherwise the phase-locked fixed points have a purely real Jacobian spectrum. These results establish a general design principle: nonlinear covariant dissipation selects the selfsustained background, while the structure of the symmetry-breaking channel determines whether the resulting local response is double-zero, genuinely Hopf, or non-Hopf.
ER -