Abstract
A lattice of repelling particles is a good model for studying certain properties that take place at atomic scale in Solid State Physics. In this chapter we study theoretically and experimentally the generation and propagation of kinks in such kind of systems. We propose a simple experimental setup consisting in an array of pendulums, having magnets at the extreme, i.e., that form a set of coupled magnetic dipoles. We excite pulses at one boundary of the system and demonstrate the existence of transient-kinks, whose dynamics are in very good agreement with the theoretical predictions given by the \(\alpha \)-FPU equation. The peculiarities of the experimental system allows to study a broad range of phenomena. On one hand, by the effect of the finite size of the magnets, the model captures the dynamics of different inverse power law inter-particle interactions, ranging from the monopole limit to the dipole interaction. On the other hand, we propose the use of an external substrate potential at the bottom of the lattice that mimics the substrate potential of a crystal. Thus, the results obtained in the experimental setup can be extrapolated to other systems described by this equation.
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Acknowledgements
All authors acknowledge grant FIS2015-65998-C2-2-P from Ministerio de Economía y Competitividad (MINECO), Spain, which funded this research. AM gratefully acknowledge to Generalitat Valenciana (Santiago Grisolia program). LJSC gratefully acknowledge the support of PAID-01-14 at Universitat Politècnica de València. JFRA also aknowledges the (2017/FQM-280) grant from Junta de Andalucía.
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Mehrem, A. et al. (2018). Kinks in a Lattice of Repelling Particles. In: Archilla, J., Palmero, F., Lemos, M., Sánchez-Rey, B., Casado-Pascual, J. (eds) Nonlinear Systems, Vol. 2. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-72218-4_11
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DOI: https://doi.org/10.1007/978-3-319-72218-4_11
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