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 tight-binding model Hamiltonian is expressed in terms of the pertinent transfer matrices, Consequently, one can study dynamic response functions of disordered systems within the powerful framework of random (transfer) matrices, which proved to be extremely useful in the analysis of DC conductance. We employ this formalism to investigate the low-frequency behaviour of In G(E, omega ). As expected, the linear term vanishes, whereas the quadratic term can be expressed in terms of the eigenvalues of the DC transfer matrix. In a strictly one-dimensional case it can be written in terms of the DC conductance and its energy derivatives. The thermodynamic limit L to infinity cannot be taken term by term. It is conjectured that, in general, (lnG(E, omega )) is not self-averaging, in agreement with previous numerical results.