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Inflow Boundary Conditions in Quantum Transport Theory

A linear (given potential) steady-state Wigner equation is considered in conjunction with inflow boundary conditions and relaxation-time terms. A brief review of the use of inflow conditions in the classical case is also discussed. An analytic expansion of solutions is shown and a recursion relation derived for the given problem under certain regularity assumptions on the given inflow data. The uniqueness of the physical current of the solutions is shown and a brief discussion of the lack of charge conservation associated with the relaxation-time is given.