Diffusion in a one-dimensional bosonic lattice gas

A one-dimensional lattice-gas model with order preservation is considered where the occupation probabilities of sites correspond to Bose statistics as a consequence of the prescribed dynamics. The master equation for the particle-cluster dynamics at the sites is formulated. The corresponding continuum nonlinear diffusion equation is derived for the space- and time-dependent concentration fluctuations. The equation can be regarded, in the presence of a drift force, as the Burgers equation when terms irrelevant in the sense of renormalization-group ideas are neglected. Collective centre-of-mass and tagged-particle diffusion are investigated by numerical simulations and the results agree with the analytical derivations. Subdiffusive behaviour of the mean-square displacement of tagged particles and normal collective and centre-of-mass diffusion are observed when no bias is present. The dispersion of the centre-of-mass displacement exhibits superdiffusive behaviour in the case of mean drift of the particles. Discrepancies of about 20% between the numerically determined superdiffusion coefficients and the predictions of the mode-coupling theory are found and discussed.