An unorthodox analysis of the Frenkel-Kontorova model

✍ Scribed by Ralf Nasilowski

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 614 KB
• Volume: 230
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(95)00411-4

✦ Synopsis

The Frenkel-Kontorova model, defined by the Hamiltonian H = Y,.~ 1 (P2./2 -K cos x. + (x.-x.-x -2)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.