Headway oscillations and phase transitions for diffusing particles with increased velocity

TL;DR

This paper investigates an asymmetric exclusion process with particles moving up to two sites per step, revealing oscillations in headway distribution, phase transitions around defects, and providing exact solutions and mean-field analysis.

Contribution

It introduces an exact solution for finite particles and sites, generalizes the matrix-product ansatz, and analyzes oscillations and phase transitions in a novel asymmetric exclusion model.

Findings

Oscillations in headway distribution are maximized at maximum particle velocity.

A phase transition separates different density profiles around a defect.

Exact solutions and mean-field results are compared, revealing non-product measure behavior.

Abstract

An asymmetric exclusion process with $N$ particles on $L$ sites is considered where particles can move one or two sites per infinitesimal time-step. An exact analysis for N=2 and a mean-field theory in comparison with simulations show even/odd oscillations in the headway distribution of particles. Oscillations become maximal if particles try to move as far as possible with regard to their maximum velocity and particle exclusion. A phase transition separates two density profiles around a generated perturbation that plays the role of a defect. The matrix-product ansatz is generalized to obtain the exact solution for finite $N$ and $L$. Thermodynamically, the headway distribution yields the mean-field result as $N^{-1}\to 0$ while it is not described generally by a product measure.