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 (Flach 1998 Phys. Rev. E 58 R4116) 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 article, 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.
Highlights
There has been considerable progress in understanding localization in nonlinear lattices over the past three decades [1]
We focus on breathers in a magnetic chain and demonstrate that there is a crossover from exponential decay to algebraic decay in the spatial profile of these breathers
The dashed red curve in figure 3 represents the power spectral density (PSD) of particles −4 to 0, and the solid blue curve represents the PSD of the defect particle
Summary
There has been considerable progress in understanding localization in nonlinear lattices over the past three decades [1]. The span of systems in which breathers have been studied is broad and diverse They include optical waveguide arrays and photorefractive crystals [3], micromechanical cantilever arrays [4], Josephsonjunction ladders [5, 6], layered antiferromagnetic crystals [7, 8], halide-bridged transition-metal complexes [9], dynamical models of the DNA double strand [10], Bose–Einstein condensates (BECs) in optical lattices [11], and many others. Many of these studies concern models with coupling between elements only in the form of nearestneighbor interactions. Until recently, they were often assumed to be a fundamental ingredient for the formation of so-called ‘chimera states’ [27,28,29]
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