Lyapunov modes in three-dimensional Lennard-Jones fluids

TL;DR

This study investigates the Lyapunov modes in a three-dimensional Lennard-Jones fluid, revealing the presence of longitudinal hydrodynamic modes at high densities through spectral analysis of Lyapunov vectors.

Contribution

It provides the first systematic analysis of Lyapunov modes in 3D Lennard-Jones fluids, extending previous 1D findings and identifying density-dependent mode structures.

Findings

Longitudinal Lyapunov modes are observed, especially at higher densities.

Transverse modes are inconclusive across studied densities.

High density induces a new form of order in the tangent space.

Abstract

Recent studies on the phase-space dynamics of a one-dimensional Lennard-Jones fluid reveal the existence of regular collective perturbations associated with the smallest positive Lyapunov exponents of the system, called hydrodynamic Lyapunov modes, which previously could only be identified in hard-core fluids. In this work we present a systematic study of the Lyapunov exponents and Lyapunov vectors, i.e. perturbations along each direction of phase space, of a three-dimensional Lennard-Jones fluid. By performing the Fourier transform of the spatial density of the coordinate part of the Lyapunov vector components and then time-averaging this result we find convincing signatures of longitudinal modes, with inconclusive evidence of transverse modes for all studied densities. Furthermore, the longitudinal modes can be more clearly identified for the higher density values. Thus, according to our results, the mixing of modes induced both by the dynamics and the dimensionality induce a hitherto unknown type of order in the tangent space of the model herein studied at high density values.