Exactly quantized dynamics of classical incommensurate sliders

TL;DR

This paper reveals that in a classical 1D solid lubricant system, the ratio of the chain's center-of-mass velocity to the external slider velocity exhibits exact quantized plateaus, determined solely by the system's commensurability ratios.

Contribution

It demonstrates a novel velocity quantization phenomenon in classical incommensurate sliders, explained by kink dynamics and robust across various parameters.

Findings

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

Quantization is governed solely by commensurability ratios.

Kink dragging explains the velocity plateaus.

Abstract

We report peculiar velocity quantization phenomena in the classical motion of an idealized 1D solid lubricant, consisting of a harmonic chain interposed between two periodic sliders. The ratio v_cm/v_ext of the chain center-of-mass velocity to the externally imposed relative velocity of the sliders stays 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 explained by one slider rigidly dragging the kinks that the chain forms with the other slider. Possible consequences of these results for some real systems are discussed.