A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917227020681216 |
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| author | Li, Song-hai Es'haqi-Sani, Najmeh Li, Xingli Li, Wenlin |
| author_facet | Li, Song-hai Es'haqi-Sani, Najmeh Li, Xingli Li, Wenlin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization Li, Song-hai Es'haqi-Sani, Najmeh Li, Xingli Li, Wenlin Quantum Physics 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. |
| title | A general interpretation of nonlinear connected time crystals: quantum self-sustaining combined with quantum synchronization |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.20186 |