  Condensation transition in a non-Markovian zero-range process is studied in
one and higher dimensions. In the mean-field approximation, corresponding to
infinite range hopping, the model exhibits condensation with a stationary
condensate, as in the Markovian case, but with a modified phase diagram. In the
case of nearest-neighbor hopping, the condensate is found to drift by a
"slinky" motion from one site to the next. The mechanism of the drift is
explored numerically in detail. A modified model with nearest-neighbor hopping
which allows exact calculation of the steady state is introduced. The steady
state of this model is found to be a product measure, and the condensate is
stationary.
