Local fields in non–linear quantum transport

In order to describe frequency-dependent quantum transport properties, it is necessary to take into account local fields. However, since the microscopic charge and current distributions are rapidly varying functions of space and time the solution of Maxwell’s equations is a complex task. Especially in the presence of non–linear effects, a selfconsistent theory of frequency and time dependent transport is very challenging [1]. Here, we address this question for a simple but nonetheless non-trivial system, namely a single-channel quantum wire of interacting electrons with one potential barrier embedded in three dimensions (3D). The interaction is taken into account using the Luttinger model [2, 3]. The system has a non–linear dc-current-voltage characteristic due to the simultaneous presence of both, the electron-electron interaction and the tunnel barrier [4, 5]. We demonstrate explicitly the essential features of self– consistency for an infinite barrier. The connection between local and external field is worked out and generalized to the situation of a finite barrier. The results of the present considerations are the starting point for the more general case, namely the nonlinear, frequency dependent transport effects in (1D) disordered systems containing many impurities.