Dimerized ground states of the Frenkel-Kontorova model with a transversal degree of freedom

We consider the ground states of a generalized Frenkel-Kontorova model with a transversal degree of freedom. The substrate potential is taken to be sinusoidal in the longitudinal direction and parabolic in the transversal one. We assume that the atoms in the chain repel each other with a Coulomb law...

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Bibliographic Details
Published inPhysics letters. A Vol. 191; no. 3; pp. 257 - 260
Main Authors Braun, Oleg M., Chubykalo, Oksana A., Vázquez, Luis
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.08.1994
Elsevier Science
Subjects
Classical and quantum physics: mechanics and fields
Classical mechanics of discrete systems: general mathematical aspects
Exact sciences and technology
Physics
Quantum mechanics
Solutions of wave equations: bound states
Degrees of freedom
Ground states
Linear stability
Interaction potentials
Frenkel Kontorova model
Equations of motion
Dimerization
Phase transitions
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Summary:We consider the ground states of a generalized Frenkel-Kontorova model with a transversal degree of freedom. The substrate potential is taken to be sinusoidal in the longitudinal direction and parabolic in the transversal one. We assume that the atoms in the chain repel each other with a Coulomb law and that the interaction has a long-range scale. The trivial ground state in this system undergoes a phase transition to a dimerized (zigzag) ground state when the repulsion exceeds some critical value. We show that for much larger values of the interaction parameters there exists the next (zigzag-2) dimerized ground state which cannot be obtained from the previous one in a bifurcational way.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(94)90136-8