Particle creation and annihilation in an exclusion process on networks

TL;DR

This paper models a complex network of particles with creation and annihilation, analyzing phase transitions and steady states using mean-field theory and simulations, revealing how non-conserving rates influence system behavior.

Contribution

It introduces a comprehensive analysis of an exclusion process on networks with particle attachment and detachment, highlighting the effects on phase diagrams and steady states.

Findings

Number of steady-state phases depends on network segments.

Non-conserving rates non-monotonically affect phase diagram topology.

Critical non-conserving rates identified for phase transitions.

Abstract

To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary system properties such as particle density, phase transitions and phase diagrams are derived theoretically utilising the mean-field approach. The steady-state phases have been categorized into various sub-classes based upon the phase transitions occurring across the junction. It is found that the number of steady-state phases depends on the number of incoming and outgoing segments at the junction. Further, an increase in the particle non-conserving rates significantly affects the topology of the phase diagram and the number of stationary phases changes in a non-monotonic way. For both the case of equal and unequal incoming and outgoing segments, the critical values of non-conserving rates at which the topology of the phase diagram changes are identified. The theoretical results are validated using extensive Monte Carlo simulations.