  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.
