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

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 spontaneous 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 q² 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.