title
Sliding Paths for Series of Frenkel-Kontorova Models -- 
A contribution to the concept of 1D-superlubricity

by

W.Quapp   and  J.M.Bofill

submitted to Eur. Phys. J. B 2019 

abstract
Newton trajectories are used to calculate low energy pathways for a
series of Frenkel-Kontorova models with 6 and up to 69 particles   
 thus up to a medium chain, and an expedition to 101 particles.    
The model is a finite chain with free-end boundary conditions.     
It has two competing potentials and an additional, external force. 
We optimize stationary structures and calculate the low energy paths between
global minimums for a movement of the chain over its on-site potential,
if an external tilting by a push- and/or pull direction is applied.
We propose to understand a low energy path for a possibility of a
superlubricity of the chain.
We compare different misfit parameters. The result is that the minimums 
differ only little, however, the critical length of the chain,
N_{cr}, depends on the misfit parameter. N_{cr} describes the end of a
'good' calculability of the Newton trajectory which follows the low energy
pathway of the chain through the potential energy surface, for a movement
of the chain along the axis. We discuss reasons for the boundary of an 
N_{cr}. However, we assume that the low energy paths exist beyond their
calculability by NTs.

keywords 
Frenkel-Kontorova model, misfit parameter, critical length, tilting and
sliding, Newton trajectory,  superlubricity