Abstract

Electrical conduction is studied along parabolically confined quasi-one dimensional channels in the framework of linear-response theory. In the absence of a magnetic field an expression for the conductance is obtained, that agrees with those in the previous, literature on this subject, as well as with the limit of the conductance in the Born approximation. A similar but new expression is obtained in the presence of a magnetic field perpendicular to the channel. This expression is more general than those contained in previous literature as it accounts explicitly for the Hall field. Some particular cases are also discussed.