Title:	Quantum Origin of Limit Cycles, Fixed Points, and Critical Slowing Down
Authors:	Dutta, Shovan Zhang, Shu Haque, Masudul
Keywords:	Bifurcations Dissipative dynamics Open quantum systems Quantum-to-classical transition Spin dynamics Fokker–Planck equation Lindblad equation Semiclassical methods
Issue Date:	7-Feb-2025
Publisher:	Physical Review Letters
Citation:	Physical Review Letters, 2025, Vol. 134 (5), AR No. 050407
Abstract:	Among the most iconic features of classical dissipative dynamics are persistent limit-cycle oscillations and critical slowing down at the onset of such oscillations, where the system relaxes purely algebraically in time. On the other hand, quantum systems subject to generic Markovian dissipation decohere exponentially in time, approaching a unique steady state. Here we show how coherent limit-cycle oscillations and algebraic decay can emerge in a quantum system governed by a Markovian master equation as one approaches the classical limit, illustrating general mechanisms using a single-spin model and a two-site lossy Bose-Hubbard model. In particular, we demonstrate that the fingerprint of a limit cycle is a slow-decaying branch with vanishing decoherence rates in the Liouville spectrum, while a power-law decay is realized by a spectral collapse at the bifurcation point. We also show how these are distinct from the case of a classical fixed point, for which the quantum spectrum is gapped and can be generated from the linearized classical dynamics.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/8627
ISSN:	1079-7114
Alternative Location:	https://doi.org/10.1103/PhysRevLett.134.050407 https://doi.org/10.48550/arXiv.2405.08866
Copyright:	2025 Physical Review Letters
Appears in Collections:	Research Papers (TP)

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