Quantum conductance problems and the Jacobi ensemble

Abstract

In one-dimensional transport problems, the scattering matrix S is decomposed into a block structure corresponding to reflection and transmission matrices at the two ends. For S a random unitary matrix, the singular value probability distribution function of these blocks is calculated. The same is done when S is constrained to be symmetric, or to be self-dual quaternion real, as is relevant in the presence of particular time reversal symmetries. The latter results are shown to be very similar to those obtained under the (unphysical) assumption that S has real elements, or has real quaternion elements, respectively. Three methods are used: metric forms, a variant of the Ingham-Seigel matrix in..