2 research outputs found
Analytical Approach to the One-Dimensional Disordered Exclusion Process with Open Boundaries and Random Sequential Dynamics
A one dimensional disordered particle hopping rate asymmetric exclusion
process (ASEP) with open boundaries and a random sequential dynamics is studied
analytically. Combining the exact results of the steady states in the pure case
with a perturbative mean field-like approach the broken particle-hole symmetry
is highlighted and the phase diagram is studied in the parameter space
, where and represent respectively the
injection rate and the extraction rate of particles. The model displays, as in
the pure case, high-density, low-density and maximum-current phases. All
critical lines are determined analytically showing that the high-density
low-density first order phase transition occurs at . We show
that the maximum-current phase extends its stability region as the disorder is
increased and the usual -decay of the density profile in this
phase is universal. Assuming that some exact results for the disordered model
on a ring hold for a system with open boundaries, we derive some analytical
results for platoon phase transition within the low-density phase and we give
an analytical expression of its corresponding critical injection rate
. As it was observed numerically, we show that the quenched
disorder induces a cusp in the current-density relation at maximum flow in a
certain region of parameter space and determine the analytical expression of
its slope. The results of numerical simulations we develop agree with the
analytical ones.Comment: 23 pages, 7 figures. to appear in J. Stat. Phy