The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics

TL;DR

This study uses molecular dynamics to analyze how one-dimensional Lennard-Jones particles exhibit a transition from phonon-like to diffusive spectral behavior, revealing a breakdown of hydrodynamics due to correlations in low dimensions.

Contribution

It demonstrates the qualitative change in spectral shape and the breakdown of hydrodynamics in a 1D Lennard-Jones system caused by density reduction and clustering.

Findings

Spectral shape changes from phonon-like to diffusive with density decrease

Spectral linewidths do not follow q^2 behavior at small wavenumbers

Hydrodynamics breaks down due to correlations in one-dimensional systems

Abstract

The dynamical correlations of a model consisting of particles constrained on the line and interacting with a nearest--neighbour Lennard--Jones potential are computed by molecular--dynamics simulations. A drastic qualitative change of the spectral shape, from a phonon--like to a diffusive form, is observed upon reducing the particle density even ad moderate temperatures. The latter scenario is due to the spontaneus fragmentation of the crystal--like structure into an ensemble of "clusters" colliding among themselves. In both cases, the spectral linewidths do not follow the usual q^2 behaviour for small wavenumbers q, thus signalling a breakdown of linearized hydrodynamics. This anomaly is traced back by the presence of correlations due to the reduced dimensionality.