Interplays between Mesoscopic Josephson Junctions and the Harper Equation

Proofs are given that by resorting to the discretization of the superconducting phase variable leads to the conversion of the eigenvalue equation of a mesoscopic Josephson junction under a dc voltage into a generalized version of the Harper equation with anisotropy parameter. A full conversion proceeds, however, in terms of selected parameters. Classical limits and further generalizations are also shortly discussed.