An unorthodox analysis of the Frenkel-Kontorova model

Ralf Nasilowski

Physica A: Statistical Mechanics and its Applications, 1996, vol. 230, issue 1, 266-284

Abstract: The Frenkel-Kontorova model, defined by the Hamiltonian H = Σn=1N (pn22 − K cos xn + (xn − xn−1 − λ)2/2), is a well-known simple 1D model of a many-particle system with two competing types of interaction (interacting particles in a spatially periodic substrate), with a peculiar ground-state behavior which is characterized by “devil's staircase” functions. The statistical mechanics of the FK model reduces to a relatively simple eigenvalue problem, for which we construct a somewhat unorthodox approximate analytic solution, based on an asymptotic formula for the modified Bessel functions. The predictions of our theory are compared with perturbation theoretical predictions and numerically calculated results.

Keywords: Frenkel-Kontorova model; Mode locking; Devil's staircases (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:230:y:1996:i:1:p:266-284

DOI: 10.1016/0378-4371(95)00411-4

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