THEORY OF RANDOM MULTIPLICATIVE TRANSFER-MATRICES AND ITS IMPLICATIONS FOR QUANTUM TRANSPORT

The two-probe conductance, g, of a disordered quantum system with N tranverse scattering channels is determined by N real parameters ('levels') {λi} characterizing the transfer matrix M. The appropriate measure for M combined with a 'global' maximum entropy hypothesis, leads to a joint distribution for these levels of the same form as the standard random matrix ensembles, execpt for the occurence of a novel behavior of the level density ρ(λ), which is far from uniform, and depends importantly on the system parameters. We study this density and its implications for conductance fluctuations in detail, showing that the novel behavior of this ensemble stems from the multiplicative composition law for M.