Asymmetric simple exclusion process with position-dependent hopping rates: Phase diagram from boundary-layer analysis.

In this paper, we study a one-dimensional totally asymmetric simple exclusion process with position-dependent
hopping rates. Under open boundary conditions, this system exhibits boundary-induced phase transitions in the
steady state. Similarly to totally asymmetric simple exclusion processes with uniform hopping, the phase diagram
consists of low-density, high-density, and maximal-current phases. In various phases, the shape of the average
particle density profile across the lattice including its boundary-layer parts changes significantly. Using the tools
of boundary-layer analysis, we obtain explicit solutions for the density profile in different phases. A detailed
analysis of these solutions under different boundary conditions helps us obtain the equations for various phase
boundaries.Next, we showhowthe shape of the entire density profile including the location of the boundary layers
can be predicted from the fixed points of the differential equation describing the boundary layers.We discuss this
in detail through several examples of density profiles in various phases. The maximal-current phase appears to be
an especially interesting phase where the boundary layer flows to a bifurcation point on the fixed-point diagram.