Balance Equations

Abstract

In this chapter a set of quantum mechanical balance equations will be derived, which can be further used as a starting point in order to establishing a workable scheme for concrete transport calculations. Contrary to earlier balance equation approaches [48, 49, 50, 51], no preliminary assumptions will be made regarding the nature of the external electromagnetic field supplying the driving force that is able to maintain the current flow. In particular, it is not necessary to restrict the derivation to uniform fields or fields that are slowly varying in space, which makes the formalism capable of studying — at least in principle — also charge transport and energy dissipation in mesoscopic structures and other layered structured where electric potentials may considerably fluctuate on a small distance scale. For the sake of clarity, all operators that are associated to physical variables (Hamiltonian, momentum, current, etc.) will be denoted by a hat, on top of the defining symbols throughout this chapter.