Quantum Effects on the Synchronization Dynamics of the Kuramoto Model

Abstract

The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this study, we extend this model to the quantum domain by coupling quantum interacting rotors to external baths following the Caldeira-Leggett approach. Studying the mean-field model in the overdamped limit using Feynman-Vernon theory, we show how quantum mechanics modifies the phase diagram. Specifically, we demonstrate that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We examine the phase transition into the synchronized phase at various temperatures, revealing that classical results are recovered at high temperatures while a quantum phase transition occurs at zero temperature. Additionally, we derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters, and examine the differences between classical and quantum behavior.

14 pages, 5 figures

References in corpus (11)

• Quantum synchronization of two Van der Pol oscillators
• Hysteretic transitions in the Kuramoto model with inertia
• Spin Correlations as a Probe of Quantum Synchronization in Trapped Ion Phonon-Lasers
• Synchronization and bistability of qubit coupled to a driven dissipative oscillator
• Quantum synchronization and entanglement of two qubits coupled to a driven dissipative resonator
• Quantum synchronization in dimer atomic lattices
• Quantum limit-cycles and the Rayleigh and van der Pol oscillators
• Quantum synchronization
• Quantum nonlinear dynamics of optomechanical systems in the strong coupling regime
• A path integral approach to the Langevin equation
• A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint

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• Macroscopic quantum synchronization effects
• Topological quantum synchronization of fractionalized spins
• Global Topological Dirac Synchronization
• Quantization of nonlinear non-Hamiltonian systems
• Synchronized Aharonov-Bohm Motifs via Engineered Dissipation
• Quantum limit cycles and synchronization from a measurement perspective