On the definition of a diffusion constant in a nonequilibrium system

A diffusion constant for electrons in a current-carrying semiconductor can be unambiguously defined in nearly uniform systems. For frequency-dependent density gradients it is {Mathematical expression} where {Mathematical expression} is the velocity correlation function with respect to the steady state in a bias field. This result has been elucidated in the relaxation approximation by different approaches to the diffusion problem. Essential for its derivation is a statistical independence assumption of space and velocities, and in order to get a classical diffusion law of Fick's type certain velocities have to be distributed according to the steady state in a bias field. Diffusion constant and noise temperature are discussed for a few band structures in the relaxation approximation. © 1971 Springer-Verlag.