  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.
