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 set-up 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 $\beta$-dependence of the voltage drop distribution of the three-terminal chaotic case, being $\beta$ the Dyson symmetry index ($\beta=1$, 2, and 4 for orthogonal, unitary, and symplectic symmetries, respectively), the analysis is extended to a continuous parameter $\beta>0$ and use the corresponding expression as a phenomenological one to reach the disordered phase. We show that our proposal encompasses all the transport regimes with $\beta$ depending linearly on the disorder strength.