Spatiotemporally ordered patterns in a chain of coupled dissipative kicked rotors

Abstract

In this work we consider the dynamics of a chain of many coupled kicked rotors with dissipation. We map a rich phase diagram with many dynamical regimes. We focus mainly on a regime where the system shows period doubling, and forms patterns that are persistent and depend on the stroboscopic time with period double than that of the driving: The system shows a form of spatiotemporal ordering analogous to quantum Floquet time crystals. Spatiotemporally ordered patterns can be understood by means of a linear-stability analysis that predicts an instability region that contains the spatiotemporally ordered regime. The boundary of the instability region coincides with the lower boundary of the spatiotemporally ordered regime, and the most unstable mode has length scale double than the lattice spacing, a feature that we observe in the spatiotemporally ordered patterns: Period doubling occurs both in time and space. We propose an implementation of this model in an array of SQUID Josephson junctions with a pulsed time-periodic flux.

15 pages, 13 figures, linear stability analysis added

References in corpus (1)

• Colloquium: Quantum and Classical Discrete Time Crystals

Cited by in corpus (8)

• Exploring nonlinear dynamics in periodically driven time crystal: from synchronized to chaotic motion
• Theory for dissipative time crystals in coupled parametric oscillators
• Bifurcations and Intermittency in Coupled Dissipative Kicked Rotors
• Stable time rondeau crystals in dissipative many-body systems
• Chaos in Time: A Dissipative Continuous Quasi Time Crystals
• Intrinsic space-time crystalline order in a hybrid Josephson junction
• Coherence and Transients in Nonlocally Coupled Dissipative Kicked Rotors
• Dynamics of wavepackets and entanglement in many-body kicked rotors under quantum resonance