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Volume 9 (1999), Issue 4, Pages 385-396

Inflow Boundary Conditions in Quantum Transport Theory

1Fachbereich Mathematik, Universität Köln Weyertal, Köln 86-90 D-50931, Germany
2physics Department, Virginia Polytechnic Institute, State University, Blacksburg, VA 24061-0435, USA

Received 13 August 1997; Revised 1 December 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.