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.
arXiv comment5 pages, 7 figures
References in corpus (17)
- Statistical Physics of Vehicular Traffic and Some Related Systems
- Phase Coexistence in Driven One Dimensional Transport
- Shock formation in an exclusion process with creation and annihilation
- Localization of shocks in driven diffusive systems without particle number conservation
- Microtubule Length-Regulation by Molecular Motors
- A model of hyphal tip growth involving microtubule-based transport
- A dynamically extending exclusion process
- Hysteresis in one-dimensional reaction-diffusion systems
- Modelling bacterial flagellar growth
- Broken Ergodicity in a Stochastic Model with Condensation
- Exclusive Queueing Processes and their Application to Traffic Systems
- Dynamical phase transition of a 1D transport process including death
- Exact dynamical state of the exclusive queueing process with deterministic hopping
- Boundary-induced nonequilibrium phase transition into an absorbing state
- Exclusion in a priority queue
- Density profiles of the exclusive queueing process
- Critical behavior of the exclusive queueing process