Description of Shapiro steps on the potential energy surface of a Frenkel–Kontorova model Part I: The chain in a variable box

Abstract

We explain the vibrations of a Frenkel–Kontorova (FK) model under Shapiro steps by the action of an external alternating force. We demonstrate Shapiro steps for a case with soft ‘springs’ between an 8-particles FK chain. Shapiro steps start with a single jump over the highest $$\hbox {SP}_4$$ SP 4 in the global valley through the PES. They finish with doubled, and again doubled oscillations. We study in this part I a traditional FK model with periodic boundary conditions.

An Analysis of Some Properties and the Use of the Twist Map for the Finite Frenkel–Kontorova Model

“…If one pulls the ends, all of the bellows relax. Newton trajectories with force f can be used to calculate many kinds of solitones of the FK chain and, thus, intermediate minima of the potential energy surface and saddle points with an increasing index [3,6,19,[46][47][48].…”