发表机构
Shenzhen Technology University; Renmin University of China; Sichuan University（深圳理工大学; 中国人民大学; 四川大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对受驱耗散集体自旋，揭示非线性协变耗散选择自持振荡背景，对称性破缺通道结构决定局域响应类型，为相关系统的动力学设计提供了通用原则。
AI 中文摘要
开放多体系统中的自持振荡可由两种不同动力学要素构建：有限振幅背景吸引子的选择及其后续中性相位的控制。我们为受驱耗散集体自旋发展这种基于分岔的图像，展示微观耗散结构如何决定可用背景及其对显式U(1)对称性破缺的响应。在热力学极限平均场动力学中，单一线性U(1)协变跃迁仅产生极化定点背景；而非线性协变耗散提供振幅依赖的饱和，通过超临界霍普夫分岔稳定有限纬度的自持振子流形。在相干U(1)对称性破缺下，精确共振导致可逆双零简并，临界频率消失，而非标准霍普夫 onset。有限失谐将此奇点展开为真正的有限频率霍普夫边界，该边界仅存在于自持振荡侧，可呈超临界或亚临界。相比之下，单一线性耗散U(1)破缺跃迁无法产生标准霍普夫不稳定性：当其相位钉扎不变量消失时，方位角方向保持中性；否则相位锁定定点具有纯实雅可比谱。这些结果确立了通用设计原则：非线性协变耗散选择自持背景，而对称性破缺通道的结构决定所得局域响应是双零、真正霍普夫还是非霍普夫型。
英文摘要
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.
Comments20 pages, 7 figures
