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Simple extension of the Frenkel-Kontorova model: a different world

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Zeitschrift für Physik B Condensed Matter

Abstract

Incommensurate configurations of Torus and Cantorus type, respectively, in a 3-harmonics variant of the Frenkel-Kontorova model are investigated. Novel phenomena that further relativize and generalize the conventional scenario based on the “standard map” are observed. In particular various competing types of Cantorus configurations can be detected. Besides cascades of secondorder Torus-Cantorus transitions the groundstate phase diagram contains an extremely complicated pattern of second-order and quasi-first order Cantorus-Cantorus transition lines. The system also supports metastable Cantorus configurations, especially unsymmetrical ones coming in degenerate pairs. The annihilation of hysteretic configurations is shown to be driven by exponentially localized soft modes.

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Authors and Affiliations

  1. Fachbereich Physik, Universität Oldenburg, D-2900, Oldenburg, Federal Republic of Germany

    H. J. Schellnhuber & H. Urbschat

  2. Institute of Nonlinear Science, University of California at Santa Cruz, 95064, CA, USA

    H. J. Schellnhuber & J. Wilbrink

Authors
  1. H. J. Schellnhuber
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  2. H. Urbschat
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  3. J. Wilbrink
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Schellnhuber, H.J., Urbschat, H. & Wilbrink, J. Simple extension of the Frenkel-Kontorova model: a different world. Z. Physik B - Condensed Matter 80, 305–312 (1990). https://doi.org/10.1007/BF01357519

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  • DOI: https://doi.org/10.1007/BF01357519

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