Headway oscillations and phase transitions for diffusing particles with increased velocity

Details Headway oscillations and phase transitions for diffusing particles with increased velocity Headway oscillations and phase transitions for diffusing particles with increased velocity

2009-03-30

arxiv.org/abs/0903.5327v1

Physics

Condensed Matter

Statistical Mechanics

14 pages, 6 figures

Scientific paper

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.

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