Phenomenological approach to transport through three-terminal disordered wires

We study the voltage drop along three-terminal disordered wires in all transport regimes, from the ballistic to the localized regime. This is performed by measuring the voltage drop on one side of a one-dimensional disordered wire in a three-terminal setup as a function of disorder. Two models of disorder in the wire are considered: (i) the one-dimensional Anderson model with diagonal disorder and (ii) finite-width bulk-disordered waveguides. Based on the known β dependence of the voltage drop distribution of the three-terminal chaotic case, β being the Dyson symmetry index (β=1, 2, and 4 for orthogonal, unitary, and symplectic symmetries, respectively), the analysis is extended to a continuous parameter β>0 and uses the corresponding expression as a phenomenological one to reach the disordered phase. We show that our proposal encompasses all the transport regimes with β depending linearly on the disorder strength.