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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/27841

    Title: Farey fractions and the Frenkel-Kontorova model
    Authors: Kao, Hsien-chung;Lee, Shih-Chang;Tzeng, Wen-Jer
    Contributors: 淡江大學物理學系
    Keywords: Exactly Solvable and Integrable Systems (nlin.SI);Condensed Matter (cond-mat)
    Date: 1997-03
    Issue Date: 2013-07-09 15:18:03 (UTC+8)
    Publisher: College Park: American Physical Society
    Abstract: We solved the Frenkel-Kontorova model with the potential V(u)=-λ(u-Int[u]-1/2)2/2 exactly. For given λ>0, there exists a positive integer qc such that the winding number ω of the minimum enthalpy state is locked to rational numbers in the qcth row of Farey fractions. For fixed ω=p/q, there is a critical λc when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey fractions.
    Relation: Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics) 55(3), pp.2628-2631
    DOI: 10.1103/PhysRevE.55.2628
    Appears in Collections:[Graduate Institute & Department of Physics] Journal Article

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