Electrical conduction is studied along parabolically confined quasi-one dimensional channels, in the framework of a revised linear-response theory, for elastic scattering. For zero magnetic field an explicit multichannel expression for the conductance is obtained that agrees with those of the literature. A similar but new multichannel expression is obtained in the presence of a magnetic field B||z perpendicular to the channel along the x axis. An explicit connection is made between the characteristic time for the tunnel-scattering process and the transmission and reflection coefficients that appear in either expression. As expected, for uncoupled channels the finite field expression gives the complete (Landauer-type) conductance of N parallel channels, a result that has not yet been reported in the literature. In addition, it accounts explicitly for the Hall field and the confining potential and is valid, with slight modifications, for tilted magnetic fields in the (x,z) plane.
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