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Open AccessArticle

Static Kinks in Chains of Interacting Atoms

1
Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, 91191 Gif-sur-Yvette, France
2
IFEG, CONICET and Universidad Nacional de Córdoba, X5016LAE Córdoba, Argentina
3
Department of physics, Universität des Saarlandes, D-66123 Saarbrücken, Germany
*
Author to whom correspondence should be addressed.
Condens. Matter 2020, 5(2), 35; https://doi.org/10.3390/condmat5020035
Received: 8 April 2020 / Revised: 4 May 2020 / Accepted: 6 May 2020 / Published: 13 May 2020
(This article belongs to the Special Issue Many Body Quantum Chaos)
We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent n 1 . The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation and its width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap. View Full-Text
Keywords: trapped ions; Frenkel–Kontorova; long–range interactions; sine-Gordon kink trapped ions; Frenkel–Kontorova; long–range interactions; sine-Gordon kink
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Landa, H.; Cormick, C.; Morigi, G. Static Kinks in Chains of Interacting Atoms. Condens. Matter 2020, 5, 35.

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