Motion of condensates in non-Markovian zero-range dynamics

TL;DR

This paper investigates how condensates form and move in a non-Markovian zero-range process, revealing a drifting condensate in certain conditions and providing exact solutions for a modified model.

Contribution

It introduces a non-Markovian zero-range model with a detailed analysis of condensate dynamics and provides an exactly solvable variant with a stationary condensate.

Findings

Condensation occurs with a modified phase diagram in mean-field approximation.

In nearest-neighbor hopping, the condensate drifts via a 'slinky' motion.

An exactly solvable model shows a stationary condensate with a product measure.

Abstract

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.