Josephson Effect, Bäcklund Transformations, and Fine Structure Coupling

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Binder, Bernd
preprint description
It is shown, that the geometric phase evolution within M circularly and toroidally arranged virtual Josephson junctions (coupled discrete impedance system) can be described by the integrable case of Baecklund transformations. The phase gradient of a junction is induced by a pseudospherical curvature. The internal phase difference and external bias is mediated by sine-Gordon solitons that provide for internal and external coupling. The idealized soliton resonance or feedback condition corresponds to an oscillator potential (Long Josephson Junction LJJ condition) that can be mapped by projective geometry to Coulomb coupling. The effective coupling strength is a generalized fine structure constant that can be iteratively determined, for M= 137 extremely close to measured values of the Sommerfeld fine structure.