Condensation phenomena in non-equilibrium systems have often been modeled by the zero-range process (ZRP), which is a model of particles hopping between boxes with Markovian dynamics. In many cases, memory effects in the dynamics cannot be neglected. In an attempt to understand the possible impact of temporal correlations on the condensate, a process with non-Markovian zero-range dynamics is introduced and studied. Two main results are found: (1) In mean-field dynamics, the steady state corresponds to that of a Markovian ZRP, but with modified hopping rates which can affect condensation, and (2) for nearest-neighbor hopping in one dimension, the condensate occupies two adjacent sites on the lattice and drifts with a finite velocity.

Hirschberg, Mukamel, Schütz, PRL 103(9), 090602 (2009)