Dynamics of condensation in zero-range processes

The dynamics of a class of zero-range processes exhibiting a condensation transition in the stationary state is studied. The system evolves in time starting from a random disordered initial condition. The analytical study of the large-time behaviour of the system in its mean-field geometry provides a guide for the numerical study of the one-dimensional version of the model. Most qualitative features of the mean-field case are still present in the one-dimensional system, both in the condensed phase and at criticality. In particular the scaling analysis, valid for the mean-field system at large time and for large values of the site occupancy, still holds in one dimension. For the latter the dynamical exponent z characteristic of the growth of the condensate is changed from its mean-field value 2 to 3. At criticality, the dynamical exponent zc characteristic of the growth of critical fluctuations is changed from 2 to 4. In presence of a bias, z = zc = 2, as in the mean-field case. PACS numbers: 02.50.Ey, 05.40.-a, 64.60.-i, 64.75.+g Submitted to: J. Phys. A: Math. Gen.