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The movement of a one-dimensional Wigner solid explained by a modified Frenkel-Kontorova model

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Abstract

We propose a Frenkel-Kontorova model for a 1D chain of electrons forming a Wigner solid over 4He. It is a highly idealized picture, but with the model at hand we can study the movement of the chain. We find out that the energetically most preferable movement is the successive sliding of a kink or an antikink through the chain. Then the force for a movement does not depend on the length of the chain. The force uniformly applied to all electrons must be larger than a force exciting only a kink or an antikink. We calculate two cases, one with stiff ‘springs’ between the electrons and one with weak ‘springs’. The side potential of the ‘dimples’ is additionally damped at the periphery. We study the cases with 33, 66, and 101 particles.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Leipzig, PF 100920, 04009, Leipzig, Germany

    Wolfgang Quapp

  2. Quantum Dynamics Unit, Okinawa Institute of Science and Technology (OIST) Graduate University, Tancha 1919-1, Okinawa, 904-0495, Japan

    Jui-Yin Lin

  3. Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, and Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain

    Josep Maria Bofill

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  1. Wolfgang Quapp
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  2. Jui-Yin Lin
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  3. Josep Maria Bofill
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Correspondence to Wolfgang Quapp.

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Quapp, W., Lin, JY. & Bofill, J.M. The movement of a one-dimensional Wigner solid explained by a modified Frenkel-Kontorova model. Eur. Phys. J. B 93, 227 (2020). https://doi.org/10.1140/epjb/e2020-10421-x

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