In this work, we investigate dissipative quantum transport properties of an open system. After presenting the background of ballistic quantum transport calculations, a simple scattering mechanism, called Büttiker Probes, is introduced. Then, we assess the properties of the Büttiker Probe model and examine its application to semiconductor devices. Based on the Büttiker Probes and a basis reduction, a new method to calculate dissipative quantum transport properties is presented. With this method, the computational burden can be lowered signicantly. Finally, we present the fully self consistent non-equilibrium Green's function formalism. This is very sophisticated way of treating dissipative quantum transport. However, it implies an immense computational effort. Within this model, we investigate current conservation in detail.
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