Stationary Nonequilibrium Particle-Number Distribution Density Formed by Particle Sources and Sinks

We analyze an inhomogeneous diffusion equation with the given potential profile and the particle source and sink. The possibility of forming a nonequilibrium but stationary state of the system is discussed. For a time-constant point source, we obtain general formulas determining the nonequilibrium stationary density distributions of the particle number as a function of potential-profile shape. The influence of sources and sinks on the flow structure in a diffusion system is determined. Some examples are considered.