S-matrix formulation of mesoscopic systems and evanescent modes

Validity of the Landauer-Buttiker formalism for studying linear transport in mesoscopic systems is well established theoretically as well as experimentally. Akkermans et al (1991 Phys. Rev. Lett. 66 76) have shown that the formalism can be extended to study thermodynamic properties like persistent currents. This extension was verified for simple one-dimensional systems. We study the applicability of Akkermans et al's formula for quasi-one-dimensional systems with several conducting channels. In the case that all modes are propagating the formula is still valid but in the case of evanescent modes it requires reinterpretation.