The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results

Abstract

The problem of finding the exact energies and configurations for the Frenkel-Kontorova model consisting of particles in one dimension connected to their nearest-neighbors by springs and placed in a periodic potential consisting of segments from parabolas of identical (positive) curvature but arbitrary height and spacing, is reduced to that of minimizing a certain convex function defined on a finite simplex.

arXiv comment12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6 Postscript figures, accepted by Phys. Rev. B

References in corpus (2)

• Farey Tree and the Frenkel-Kontorova Model
• The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment

Cited by in corpus (2)

• Frenkel-Kontorova Models, Pinned Particle Configurations and Burgers Shocks
• The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment