Computer study of the collective modes of a one dimensional disordered chain

It is found, on the basis of molecular dynamics experiments, that the density fluctuation of wavenumber k, in a one dimensional disordered chain of Lennard-Jones rods, decays like a damped cosine with frequency ωk and lifetime τk such that the dispersion relation ω = ωk is very similar to that of an harmonic chain and that τk goes as k−1/3 at small k. This latter observation is shown to be consistent with the conjecture that the single particle velocity autocorrelation function behaves asymptotically as t−3. It is concluded that the Lennard-Jones chain does not display a hydrodynamic decay.