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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.

Interplays between Mesoscopic Josephson Junctions and the Harper Equation