Bidirectional non-Markovian exclusion processes

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.

Effect of local dissociations in bidirectional transport of driven particles

“…Owing to the existence of the oppositely moving molecular motors in different states, studies have been carried out to analyze how the collective motion of motor proteins affects the SSB processes [29,30]. Further, the understanding of symmetry breaking has also been extended to non-Markovian bidirectional transport processes [31]. However, the mechanisms of symmetry-breaking phenomena are still not fully understood [15,27,32].…”