Exact analytical solution of a classical problem of the Josephson tunnel junction

• Published in: Физика низких температур
• Date: 2010
• Main Authors: Kuplevakhsky, S.V., Glukhov, A.M.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2010
• Subjects: Quantum coherent effects in superconductors and normal metals
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/117528
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Exact analytical solution of a classical problem of the Josephson tunnel junction / S.V. Kuplevakhsky, A.M. Glukhov // Физика низких температур. — 2010. — Т. 36, № 10-11. — С. 1253–1263. — Бібліогр.: 26 назв. — англ.

We present the exact and complete analytical solution of the classical problem of the Josephson tunnel junction of arbitrary length W ∈ (0, ∞) in the presence of externally applied magnetic fields and transport currents. Contrary to a wide-spread belief, the exact analytical solution unambiguously proves the absence of any qualitative difference between the so-called «small» (W << 1) and «large» junctions (W >> 1). Another unexpected physical implication of the exact analytical solution is the existence (in the current-carrying state) of unquantized Josephson vortices carrying fractional flux and located near one of the junction's edges. We also refine on the mathematical definition of critical transport current.