The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
R. B. Griffiths, H. J. Schellnhuber, H. Urbschat
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.
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