TY - JOUR

T1 - Frenkel-Kontorova model with pinning cusps

AU - Kao, Hsien Chung

AU - Lee, Shih Chang

AU - Tzeng, Wen Jer

N1 - Funding Information:
The authors would like to express their gratitute to Prof. R.B. Griffiths for stimulating discussions and valuable comments. This work is supported in part by grants from the National Science Council of Taiwan-Republic of China under Contract No. NSC-86-2112-M001-003.

PY - 1997

Y1 - 1997

N2 - A Frenkel-Kontorova model with a piecewise concave parabolic potential with downward cusps such that atoms could be pinned at the potential minima is exactly solved. An infinite series of first-order transitions, which may be understood as the dissociation of a large "molecule" into two smaller ones, is found as the strength of the potential increases from zero. The minimum energy configurations need not have a well-defined winding number. Given the winding number, the ground state configurations in general are highly degenerate and it is shown that one of them can be depicted by an increasing hull function. A novel type of non-recurrent minimum energy configuration, which may be viewed as defects carrying "fractional charge", exists.

AB - A Frenkel-Kontorova model with a piecewise concave parabolic potential with downward cusps such that atoms could be pinned at the potential minima is exactly solved. An infinite series of first-order transitions, which may be understood as the dissociation of a large "molecule" into two smaller ones, is found as the strength of the potential increases from zero. The minimum energy configurations need not have a well-defined winding number. Given the winding number, the ground state configurations in general are highly degenerate and it is shown that one of them can be depicted by an increasing hull function. A novel type of non-recurrent minimum energy configuration, which may be viewed as defects carrying "fractional charge", exists.

KW - Area-preserving maps

KW - Farey fraction

KW - Fractional charge

KW - Frenkel-Kontorova model

KW - Harmless staircase

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U2 - 10.1016/S0167-2789(97)00055-9

DO - 10.1016/S0167-2789(97)00055-9

M3 - Article

AN - SCOPUS:0012448947

SN - 0167-2789

VL - 107

SP - 30

EP - 42

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1

ER -