A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization

• URL: http://arxiv.org/abs/2601.20186v1
• Date: Wed, 28 Jan 2026 02:36:56 GMT
• Title: A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization
• Authors: Song-hai Li, Najmeh Es'haqi-Sani, Xingli Li, Wenlin Li,
• Abstract summary: We show that a continuous time crystal is a nonlinear quantum self-sustaining system exhibiting quantum synchronization among its constituents.<n>Results reduce the identification of time crystals in many-body systems to the evaluation of only two-body correlations.
• Score: 1.548692649098646
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Although classical nonlinear dynamics suggests that sufficiently strong nonlinearity can sustain oscillations, quantization of such model typically yields a time-independent steady state that respects time-translation symmetry and thus precludes time-crystal behavior. We identify dephasing as the primary mechanism enforcing this symmetry, which can be suppressed by intercomponent phase correlations. Consequently, a sufficient condition for realizing a continuous time crystal is a nonlinear quantum self-sustaining system exhibiting quantum synchronization among its constituents. As a concrete example, we demonstrate spontaneous oscillations in a synchronized array of van der Pol oscillators, corroborated by both semiclassical dynamics and the quantum Liouville spectrum. These results reduce the identification of time crystals in many-body systems to the evaluation of only two-body correlations and provide a framework for classifying uncorrelated time crystals as trivial.

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