On the relation between electrical noise spectra and AC conductivity in disordered systems

We show that the low frequency, f spectra of current fluctuations, S(f), and complex AC conductivity sigma(f)=sigma'(f)+i sigma ''(f), are linked by the relationship following from the fluctuationdissipation, FD, theorem, sigma'(f)/S(f)proportional to f(2). We measured sigma(f) and S(f) in impurity conduction in lightly doped semiconductors, where at sufficiently low temperatures, sigma'(f) and sigma ''(f), follow a power function of f. At higher temperatures, in a mixed, hopping and extended state transport regime, noise becomes very strong and S(f) proportional to 1/f(2); with a flat sigma(f), implied by the FD theorem.