Bidirectional Non-Markovian Exclusion Processes

TL;DR

This paper investigates how non-Markovian site exchange times influence bidirectional particle transport modeled by ASEP, revealing that most exchange rules lead to behavior similar to unidirectional transport, with notable differences under the minimum rule.

Contribution

It introduces non-Markovian exchange times into bidirectional ASEP and analyzes their effects, highlighting the impact of different exchange rules on system behavior.

Findings

Most exchange processes recover unidirectional asymptotic behavior.

The minimum rule enhances efficiency for fast decaying exchange times.

Differences arise primarily under the minimum rule with specific exchange time distributions.

Abstract

Bidirectional transport in (quasi) one-dimensional systems generically leads to cluster-formation and small particle currents. This kind of transport can be described by the asymmetric simple exclusion process (ASEP) with two species of particles. In this work, we consider the effect of non-Markovian site exchange times between particles. Different realizations of the exchange process can be considered: The exchange times can be assigned to the lattice bonds or each particle. In the latter case we specify additionally which of the two exchange times is executed, the earlier one (minimum rule) or the later one (maximum rule). In a combined numerical and analytical approach we find evidence that we recover the same asymptotic behavior as for unidirectional transport for most realizations of the exchange process. Differences in the asymptotic behavior of the system have been found for the minimum rule which is more efficient for fast decaying exchange time distributions.