Effective ergodicity breaking in an exclusion process with varying system length
arXiv:1409.0329 · doi:10.1016/j.physa.2015.03.068
Abstract
Stochastic processes of interacting particles with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the exclusive queueing process that can be viewed as a one-dimensional exclusion process with varying length, by introducing Langmuir kinetics. This process can be interpreted as an effective model for a queue that interacts with other queues by allowing incoming and leaving of customers in the bulk. We find surprising indications for breaking of ergodicity in a certain parameter regime, where the asymptotic growth behavior depends on the initial length. We show that a random walk with site-dependent hopping probabilities exhibits qualitatively the same behavior.
5 pages, 7 figures
References in corpus (6)
- Phase Coexistence in Driven One Dimensional Transport
- Microtubule Length-Regulation by Molecular Motors
- A model of hyphal tip growth involving microtubule-based transport
- A dynamically extending exclusion process
- Exclusive Queueing Processes and their Application to Traffic Systems
- Boundary-induced nonequilibrium phase transition into an absorbing state