Nonequilibrium Green function techniques applied to hot-electron quantum transport

During the last few years considerable effort has been devoted to deriving quantum transport equations for semiconductors under extreme conditions (high electric fields, spatial quantization in one or two directions). Here we review the results obtained with nonequilibrium Green function techniques as formulated by Baym and Kadanoff, or by Keldysh. In particular, the following topics will be discussed: (i) Systematic approaches to reduce the transport equation governing the correlation function to a transport equation for the Wigner function; (ii) Approximations reducing the nonmarkovian quantum transport equation to a numerically tractable form, and results for model semiconductors; (iii) Recent progress is extending the formalism to inhomogeneous systems. In all sections we try to direct the reader's attention to points where the present understanding is (at best) incomplete, and indicate possible lines for future work. (orig.)