Multichannel, multiprobe Landauer formula in the presence of a uniform magnetic field

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Abstract
The general multichannel, multiprobe Landauer formula derived by Büttiker for spinless noninteracting electrons, relating conductance coefficients to the elements of a unitary S matrix, is calculated from a linear-response formalism in the presence of a uniform magnetic field. The calculation proceeds by first writing the conductance coefficients in terms of a current-current correlation function. An expansion in scattering-wave states relates this correlation function to a set of transmission coefficients that constitute a unitary S matrix. The analytic properties of the S-matrix elements in the complex E plane are used to complete the calculation with a simple contour integral.