Nonlinear Excitations in Magnetic Lattices with Long-Range Interactions

Abstract

We study - experimentally, theoretically, and numerically - nonlinear excitations in lattices of magnets with long-range interactions. We examine breather solutions, which are spatially localized and periodic in time, in a chain with algebraically-decaying interactions. It was established two decades ago [S. Flach, Phys. Rev. E 58, R4116 (1998)] that lattices with long-range interactions can have breather solutions in which the spatial decay of the tails has a crossover from exponential to algebraic decay. In this Letter, we revisit this problem in the setting of a chain of repelling magnets with a mass defect and verify, both numerically and experimentally, the existence of breathers with such a crossover.

References in corpus (9)

• Synchronization in complex networks
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals
• Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics
• Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs
• Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos
• Instabilities and relaxation to equilibrium in long-range oscillator chains
• Dimension dependent energy thresholds for discrete breathers
• Low-frequency discrete breathers in long-range systems without on-site potential

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