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

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.PACS. 05.60.-k Transport processes -66.10.Cb Diffusion and thermal diffusion

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

“…The main claim of the authors of these works is that, at variance with the predictions of NFH and of previous theoretical approaches, normal heat conductivity should characterize all 1D lattice models with asymmetric potentials. Such a situation has been observed for the FPU-α + β model and for chains of oscillators coupled through a Lennard-Jones potential [31]. The authors provided an explanation of their results by arguing that the scattering of long-wavelength phonons could be attributed to the spontaneous formation of macroscopic mass gradients along the chain, typical of asymmetric interaction potentials acting between nonlinear oscillators [32].…”

Cluster sizes in a classical Lennard-Jones chain

“…The only exception to this is that at zero temperature and sufficiently high density the system has a genuinely crystaline structure. This ordered state is destroyed discontinuously in moving from zero temperature to any arbitrarily small non-zero temperature [37,38]. We will restrict our attention to the non-zero temperature case where no true phase transitions exist.…”

“…Some of the interest in this topic [36,39] stems from clustering in these chains being an easily studied example of a collective thermal excitation. Other work in this area [38] is connected with a desire to understand long-time behaviour of various hydrodynamic correlation functions. Ultimately, both of these are related to transport in the system and so the interest in the phase behaviour of these systems can been seen as related to the study of one-dimensional transport.…”

Energy diffusion in hard-point systems

“…Related manifestation of such anomalies are the divergence of viscosity in 1D lattice gases [8] and the anomalous scaling of Rayleigh and Brillouin peak widths in the hydrodynamic limit detected for the Lennard-Jones fluid [9,10]. For what concerns the actual values of α there are still some controversies.…”