A totally asymmetric exclusion process with hierarchical long range connections

A non-equilibrium particle transport model, the totally asymmetric exclusion process, is studied on a one-dimensional lattice with a hierarchy of fixed long-range connections\footnote{Journal of Statistical Mechanics, P07010 (2009).}. This model breaks the particle-hole symmetry observed on an ordinary one-dimensional lattice and results in a surprisingly simple phase diagram, without a maximum-current phase. Numerical simulations of the model with open boundary conditions reveal a number of dynamic features and suggest possible applications.