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We investigate multimode electronic transport in a quantum wire in the presence of a uniform magnetic field. Using a finite-difference scheme for the evaluation of the free-electron Schrodinger equation, we obtain Harper s equation, which is transformed into an eigenvalue problem. The resulting scattering states of the wire are used to describe the magnetoconductance for free electrons as well as for a periodic lattice potential. In the latter case we obtain a conductance pattern that is related to the Hofstadter butterBy. The calculated current distribution in a disordered quantum Hall device confirms the edge-state picture of the transport in the quantum Hall regime.

We study numerically the influence of momentum-conserving dephasing on the transport in a disordered chain of scatterers. Loss of phase memory is caused by coupling the transport channels to dephasing reservoirs. In contrast to previously used models, the dephasing reservoirs are linked to the transport channels between the scatterers, and momentum conserving dephasing can be investigated. Our setup provides a model for nanosystems exhibiting conductance quantization at higher temperatures in spite of the presence of phononic interaction. We are able to confirm numerically some theoretical predictions.

The influence of dissipative scattering on the integer quantum Hall effect is investigated numerically. Dissipation is implemented by connecting the sample to auxiliary phase-destroying electron reservoirs. Our calculations reveal a surprising stability of the Hall plateaus against dissipation, even in the regime of strong backscattering.