Defect-induced tunnelling and the conductivity of strongly disordered systems

For a model describing the motion of a zero-temperature electron gas in an environment causing a fluctuating potential and a fluctuating effective mass, a theory is developed which allows for an approximate calculation of the particle density propagation self-consistently with momentum relaxation and defect-induced tunnelling processes. All correlation functions of the system are expressed in terms of two causal kernels for which non-linear equations are derived and solved. A detailed discussion of the influence of the defect-induced tunnelling on the mobility, in particular on mobility edges, and on the Fermi glass stiffness is given and an anomalous high-frequency tail of the dynamical conductivity is predicted.