Classical and quantum chaotic synchronization in coupled dissipative time crystals
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arXiv
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| Format: | Preprint |
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2025
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| author | Postavová, Eliška Passarelli, Gianluca Lucignano, Procolo Russomanno, Angelo |
| author_facet | Postavová, Eliška Passarelli, Gianluca Lucignano, Procolo Russomanno, Angelo |
| contents | We investigate the dynamics of two coherently coupled dissipative time crystals. In the classical mean-field limit of infinite spin length, we identify a regime of chaotic synchronization, marked by a positive largest Lyapunov exponent and a Pearson correlation coefficient close to one. At the boundary of this regime, the Pearson coefficient varies abruptly, marking a crossover between staggered and uniform $z$-magnetization. To address finite-size quantum dynamics, we employ a quantum-trajectory approach and study the trajectory-resolved expectations of subsystem $z$-magnetizations. Their histograms over time and trajectory realizations exhibit maxima that undergo a staggered-to-uniform crossover analogous to the classical one. In analogy with the classical case, we interpret this behavior as quantum chaotic synchronization, with dissipative quantum chaos highlighted by the steady-state density matrix exhibiting Gaussian Unitary Ensemble statistics. The classical and quantum crossover points are different due to the noncommutativity of the infinite-time and infinite-spin-magnitude limits and the role played by entanglement in the quantum case, quantified via the two-subsystem entanglement entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classical and quantum chaotic synchronization in coupled dissipative time crystals Postavová, Eliška Passarelli, Gianluca Lucignano, Procolo Russomanno, Angelo Quantum Physics Quantum Gases Chaotic Dynamics We investigate the dynamics of two coherently coupled dissipative time crystals. In the classical mean-field limit of infinite spin length, we identify a regime of chaotic synchronization, marked by a positive largest Lyapunov exponent and a Pearson correlation coefficient close to one. At the boundary of this regime, the Pearson coefficient varies abruptly, marking a crossover between staggered and uniform $z$-magnetization. To address finite-size quantum dynamics, we employ a quantum-trajectory approach and study the trajectory-resolved expectations of subsystem $z$-magnetizations. Their histograms over time and trajectory realizations exhibit maxima that undergo a staggered-to-uniform crossover analogous to the classical one. In analogy with the classical case, we interpret this behavior as quantum chaotic synchronization, with dissipative quantum chaos highlighted by the steady-state density matrix exhibiting Gaussian Unitary Ensemble statistics. The classical and quantum crossover points are different due to the noncommutativity of the infinite-time and infinite-spin-magnitude limits and the role played by entanglement in the quantum case, quantified via the two-subsystem entanglement entropy. |
| title | Classical and quantum chaotic synchronization in coupled dissipative time crystals |
| topic | Quantum Physics Quantum Gases Chaotic Dynamics |
| url | https://arxiv.org/abs/2509.20922 |