Transfer matrix formulation of a.c. conductance

Within the standard linear-response theory we derive an expression for the a.c. conductance of a quasi-one-dimensional mesoscopic system in terms of its pertinent transfer matrices. It is valid for any number of scattering channels, and hence, if the system is disordered, it is amenable for treatment within the theory of random (transfer) matrices, or, equivalently, through a diffusion equation. It is shown that previous expressions for the a.c. conductance are obtained as a special limiting form, while at zero frequency our expression reduces to Pichard formula for the d.c. conductance. Some simple applications of this formula are discussed.