Super Fourier analysis and localization in disordered wires.

Abstract

The problem of calculating the zero-temperature mean conductance 〈c〉 of a disordered thick metallic wire coupled at both ends to ideal leads is formulated as a diffusion problem on a Riemannian symmetric superspace G/K (Efetov). The problem is solved exactly by Fourier transforming the diffusion kernel. Although the solution agrees with known results for the case of orthogonal and unitary symmetry, it has the surprising feature that 〈c〉 never falls below the minimum value of ${\mathit{e}}^{2}$/2h for long wires with symplectic symmetry, in leading order of the expansion around the metallic and thick limit.