Headway oscillations and phase transitions for diffusing particles with increased velocity. (English) Zbl 1179.82043
Summary: A totally asymmetric exclusion process with \(N\) particles on a periodic one-dimensional lattice of \(L\) sites is considered where particles can move one or two sites per infinitesimal timestep. 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. The expression ‘headway’ is understood as the number of empty sites in front of a particle. Oscillations become maximal if particles only move at their maximum possible speed. 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 \(N\to\infty \) while it is not described generally by a product measure.
MSC:
82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
82B24 | Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics |
82B26 | Phase transitions (general) in equilibrium statistical mechanics |
82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |