  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.
