AC CONDUCTANCE, TRANSFER-MATRIX AND SMALL-FREQUENCY EXPANSION IN QUASI-ONE-DIMENSIONAL SYSTEMS

The Ac conductance G(E, omega) (at Fermi energy E and frequency omega) of a quasi-one-dimensional system of finite length L governed by a ti ght-binding model Hamiltonian is expressed in terms of the pertinent t ransfer matrices. Consequently, one can study dynamic response functio ns of disordered systems within the powerful framework of random (tran sfer) matrices, which proved to be extremely useful in the analysis of oc conductance. We employ this formalism to investigate the low-frequ ency behaviour of In G(E, omega). As expected, the linear term vanishe s, whereas the quadratic term can be expressed in terms of the eigenva lues of the Dc transfer matrix. In a strictly one-dimensional case it can be written in terms of the Dc conductance and its energy derivativ es. The thermodynamic limit L --> infinity cannot be taken term by ter m. It is conjectured that, in general, (In G(E, omega)) is not self-av eraging, in agreement with previous numerical results.