Landauer and Thouless Conductance: a Band Random Matrix Approach

We numerically analyze the transmission through a thin disordered wire offinite length attached to perfect leads, by making use of banded random Hamiltonian matrices. We compare the Landauer and the Thouless conductances. and find that they are proportional to each other in the diffusive regime, while in the localized regime the Landauer conductance is approximately proportional to the square ofthe Thouless one. Fluctuations ofthe Landauer conductance were also numerically computed; they are shown to slowly approach the theoretically