Many-body synchronisation in a classical Hamiltonian system

Abstract

We study synchronisation between periodically driven, interacting classical spins undergoing a Hamiltonian dynamics. In the thermodynamic limit there is a transition between a regime where all the spins oscillate synchronously for an infinite time with a period twice as the driving period (synchronized regime) and a regime where the oscillations die after a finite transient (chaotic regime). We emphasize the peculiarity of our result, having been synchronisation observed so far only in driven-dissipative systems. We discuss how our findings can be interpreted as a period-doubling time crystal and we show that synchronisation can appear both for an overall regular and an overall chaotic dynamics.

arXiv comment5 pages, 4 figures + Supplementary (2 pages, 2 figures). Version published in PRL

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Cited by in corpus (22)

• Classical Prethermal Phases of Matter
• Dissipative time crystal in a strongly interacting Rydberg gas
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• Boundary time crystals in collective $d$-level systems
• Measurement Induced Continuous Time Crystals
• Classical approaches to prethermal discrete time crystals in one, two, and three dimensions
• Dissipative time crystals with long-range Lindbladians
• Emergent parametric resonances and time-crystal phases in driven BCS systems
• An instanton-like excitation of a discrete time crystal
• Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
• Genuine Multipartite Correlations in a Boundary Time Crystal
• Stochastic discrete time crystals: Entropy production and subharmonic synchronization
• Bistability and time crystals in long-ranged directed percolation
• Exotic synchronization in continuous time crystals outside the symmetric subspace
• Dynamics of fluctuation correlation in periodically driven classical system
• Prethermal time-crystalline spin ice and monopole confinement in a driven magnet
• Thermal melting of discrete time crystals: a dynamical phase transition induced by thermal fluctuations
• Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
• Space-time symmetry breaking in nonequilibrium frustrated magnetism
• Theory for dissipative time crystals in coupled parametric oscillators
• Fragility to quantum fluctuations of classical Hamiltonian period doubling
• Seeding crystallization in time