On the driven Frenkel-Kontorova model: II. Chaotic sliding and nonequilibrium melting and freezing

TL;DR

This paper investigates the chaotic sliding, nonequilibrium melting, and freezing transitions in the driven Frenkel-Kontorova model, revealing phase transition-like behavior and non-equilibrium states with effective temperature.

Contribution

It introduces the concept of fluid-sliding states with chaos and effective temperature, and analyzes the transition mechanisms between frozen and molten states, including hysteresis and bifurcations.

Findings

Identification of a spatio-temporally chaotic fluid-sliding state.

Observation of hysteresis in the freezing-melting transition.

Transition mechanisms involve saddle-node bifurcations and nucleation processes.

Abstract

The dynamical behavior of a weakly damped harmonic chain in a spatially periodic potential (Frenkel-Kontorova model) under the subject of an external force is investigated. We show that the chain can be in a spatio-temporally chaotic state called fluid-sliding state. This is proven by calculating correlation functions and Lyapunov spectra. An effective temperature is attributed to the fluid-sliding state. Even though the velocity fluctuations are Gaussian distributed, the fluid-sliding state is clearly not in equilibrium because the equipartition theorem is violated. We also study the transition between frozen states (stationary solutions) and=7F molten states (fluid-sliding states). The transition is similar to a first-order phase transition, and it shows hysteresis. The depinning-pinning transition (freezing) is a nucleation process. The frozen state contains usually two domains of different particle densities. The pinning-depinning transition (melting) is caused by saddle-node bifurcations of the stationary states. It depends on the history. Melting is accompanied by precursors, called micro-slips, which reconfigurate the chain locally. Even though we investigate the dynamics at zero temperature, the behavior of the Frenkel-Kontorova model is qualitatively similar to the behavior of similar models at nonzero temperature.