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Nonlinear Dissipation and Hopf Criticality in Driven Dissipative Collective Spins — arXiv:2609.03360

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.03360
License (as archived): CC0-1.0
Archived: 2026-10-17T03:03:22.408Z
SHA-256 of the archived text: 90a685d6299e071ce603e4dedf7829060b5fdaf552753c1c8dabd76138da8d19
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Nonlinear Dissipation and Hopf Criticality in Driven Dissipative Collective Spins — arXiv:2609.03360 — arXiv (en), https://arxiv.org/abs/2609.03360 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ce5784fa2467 (Metraipolis archive dc_ce5784fa2467, sha256 90a685d6299e071ce603e4dedf7829060b5fdaf552753c1c8dabd76138da8d19)

BibTeX

@misc{dcce5784fa2467,
  title = {Nonlinear Dissipation and Hopf Criticality in Driven Dissipative Collective Spins — arXiv:2609.03360},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.03360},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ce5784fa2467; sha256 90a685d6299e071ce603e4dedf7829060b5fdaf552753c1c8dabd76138da8d19},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.03360. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-04 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.03360 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T02:49:19.489Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-04?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).