Nonequilibrium dynamics of coupled oscillators under the shear-velocity boundary condition

TL;DR

This paper investigates the complex nonequilibrium behaviors of coupled oscillators with inertia under shear-velocity boundary conditions, revealing non-uniform velocity profiles, non-Gaussian distributions, and intermittent kinetic energy dynamics.

Contribution

It introduces a numerical study of coupled oscillators with inertia under shear-velocity boundary conditions, highlighting unique nonequilibrium phenomena and their relation to various physical models.

Findings

Non-uniform velocity spatial profiles at high dissipation rates

Deviations from Gaussian velocity distributions

Intermittent kinetic energy evolution at low shear and temperature

Abstract

Deterministic and stochastic coupled oscillators with inertia are studied on the rectangular lattice under the shear-velocity boundary condition. Our coupled oscillator model exhibits various nontrivial phenomena and there are various relationships with wide research areas such as the coupled limit-cycle oscillators, the dislocation theory, a block-spring model of earthquakes, and the nonequilibrium molecular dynamics. We show numerically several unique nonequilibrium properties of the coupled oscillators. We find that the spatial profiles of the average value and variance of the velocity become non-uniform when the dissipation rate is large. The probability distribution of the velocity sometimes deviates from the Gaussian distribution. The time evolution of kinetic energy becomes intermittent when the shear rate is small and the temperature is small but not zero. The intermittent jumps of the kinetic energy cause a long tail in the velocity distribution.