  The Landauer-Butikker formalism is an important formalism to study mesoscopic
systems. Its validity for linear transport is well established theoretically as
well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)]
had shown that the formalism can be extended to study thermodynamic properties
like persistent currents. It was earlier verified for simple one dimensional
systems. We study this formula very carefully and conclude that it requires
reinterpretation in quasi one dimension. This is essentially because of the
presence of evanescent modes in quasi one dimension.
