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 -