Exact ground state of the Frenkel-Kontorova model with repeated parabolic potential .1. Basic results

[摘要] 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.

[关键词] DEVILS STAIRCASE;PERIODIC-ORBITS;SYMPLECTIC MAPS;STANDARD MAP;TWIST MAP;CANTORI;TRAJECTORIES;DYNAMICS