2009/12/23 by Róbert Juhász
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Asymmetric simple exclusion process #Boundary (topology) #Cellular Automata and Applications #Chemistry #Cluster (spacecraft) #Computer science #Constraint (computer-aided design) #Current (fluid) #Delocalized electron #Embedding #Geometry #Jump #Logarithm #Mathematical analysis #Mathematics #Mechanics #Physics #Quantum mechanics #Shock (circulatory) #Statistical physics #Steady state (chemistry) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #Type (biology) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2010/03/p03010
published as J. Stat. Mech. (2010) P03010 · 24 pages, 13 figures
arxiv created 2009/12/23 · openalex publication_date 2010/03/11 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A two-lane exclusion process is studied where particles move in the two lanes in opposite directions and are able to change lanes. The focus is on the steady state behavior in situations where a positive current is constrained to an extended subsystem (either by appropriate boundary conditions or by the embedding environment) where, in the absence of the constraint, the current would be negative. We have found two qualitatively different kinds of steady states and formulated the conditions for them in terms of the transition rates. In the first type of steady state, a localized cluster of particles forms with an anti-shock located in the subsystem and the current vanishes exponentially with the extension of the subsystem. This behavior is analogous to that of the one-lane partially asymmetric simple exclusion process, and can be realized e.g. when the local drive is induced by making the jump rates in two lanes unequal. In the second type of steady state, which is realized e.g. if the local drive is induced purely by the bias in the lane change rates, and which thus has no counterpart in the one-lane model, a delocalized cluster of particles forms which performs a diffusive motion as a whole and, as a consequence, the current vanishes inversely proportionally to the extension of the subsystem. The model is also studied in the presence of quenched disorder, where, in the case of delocalization, phenomenological considerations predict anomalously slow, logarithmic decay of the current with the system size in contrast with the usual power law.