{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03360",
  "author_total": 6,
  "authors": [
    {
      "name": "Shu Yang"
    },
    {
      "name": "Jun Wang"
    },
    {
      "name": "Weidong Li"
    },
    {
      "name": "Cangtao Zhou"
    },
    {
      "name": "Jian-Song Pan"
    },
    {
      "name": "Jianwen Jie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0peeasq2as1kt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03360",
  "fulltext_url": null,
  "id": "0peeasq2as1kt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03360",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7208747377",
  "pdf_url": "https://arxiv.org/pdf/2609.03360",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0peeasq2as1kt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.03360",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03360"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Nonlinear Dissipation and Hopf Criticality in Driven Dissipative Collective Spins",
  "title_text": "Nonlinear Dissipation and Hopf Criticality in Driven Dissipative Collective Spins",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/0peeasq2as1kt",
  "venue": "arXiv",
  "versions": []
}