A Model for a Driven Frenkel-Kontorova Chain

W. Quapp and J. M. Bofill

Mathematisches Institut, Universität Leipzig, PF 100920,
D-04009 Leipzig,  Germany
and
Departament de Qu'imica Inorg`anica i  Org`anica, Secci'o de Qu'imica Org`anica, and
  Institut de Qu'imica Te`orica i Computacional, (IQTCUB),
Universitat de Barcelona, Mart'i i Franqu`es 1, 08028 Barcelona, Spain

Abstract:
We study a Frenkel-Kontorova model of a finite chain with free-end boundary
conditions.  The model has two competing potentials.
Newton trajectories are an ideal tool to understand the circumstances under
a driving of a Frenkel-Kontorova chain by external forces. To  reach the
insights we calculate some stationary structures for a chain with 23 particles.
We search the lowest energy saddle points for a complete minimum energy path
of the chain for a movement over the full period of the on-site potential, a
sliding. If an additional tilting is set, then one is interested in barrier 
breakdown points on the potential energy surface for a critical tilting force
named the static frictional force. In symmetric cases, such barrier breakdown 
points are often valley-ridge inflection points of the potential energy surface.
We explain the theory and demonstrate it with an example. 
We propose a model for a DC drive, as well as an AC drive, of the chain
using special directional vectors of the external force.