Solitons and exact velocity quantization of incommensurate sliders

TL;DR

This paper investigates the phenomenon where the velocity ratio in a classical one-dimensional chain system becomes quantized due to soliton dynamics, with implications for understanding frictional systems.

Contribution

It provides a detailed analysis of velocity quantization caused by soliton interactions in a simplified model of incommensurate sliders, revealing exact plateau values.

Findings

Velocity ratio is pinned to exact values over wide parameter ranges.

The phenomenon is driven by solitons being dragged by one slider.

Results depend solely on commensurability ratios.

Abstract

We analyze in some detail the recently discovered velocity quantization phenomena in the classical motion of an idealized one-dimensional solid lubricant, consisting of a harmonic chain interposed between two periodic sliders. The ratio w = v_cm/v_ext of the chain center-of-mass velocity to the externally imposed relative velocity of the sliders is pinned to exact ``plateau'' values for wide ranges of parameters, such as sliders corrugation amplitudes, external velocity, chain stiffness and dissipation, and is strictly determined by the commensurability ratios alone. The phenomenon is caused by one slider rigidly dragging the density solitons (kinks/antikinks) that the chain forms with the other slider. Possible consequences of these results for some real systems are discussed.