Equivalence of the transmission-eigenvalue density in supersymmetric and scaling theories of disordered wires without time-reversal symmetry

The transmission-eigenvalue density in a disordered wire without time-reversal symmetry is calculated exactly by means of the supersymmetric theory. The calculation is based on the introduction of a fictitious vector potential that couples the retarded and advanced components of the supervector field. The result is shown to be identical to that of the scaling theory in the thick-wire limit.