Random-matrix modeling of semi-linear response, the generalized variable range hopping picture, and the conductance of mesoscopic rings

Semi-linear response theory determines the absorption coefficient of a driven system using a resistor network calculation: Each unperturbed energy level of a particle in a vibrating trap, or of an electron in a mesoscopic ring, is regarded as a node ($n$) of the network; The transition rates ($w_{mn}$) between the nodes are regarded as the elements of a random matrix that describes the network. If the size-distribution of the connecting elements is wide (e.g. log-normal-like rather than Gaussian-like) the result for the absorption coefficient differs enormously from the conventional Kubo prediction of linear response theory. We use a generalized variable range hopping scheme for the analysis. In particular we apply this approach to obtain practical approximations for the conductance of mesoscopic rings. In this context Mott's picture of diffusion and localization is revisited.