Exact analytical solution of a classical problem of the Josephson tunnel junction
S.V. Kuplevakhsky and A.M. Glukhov
B.I. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Lenin Ave., 61103 Kharkov, Ukraine
Received April 30, 2010
We present the exact and complete analytical solution of the classical problem of the Josephson tunnel junction
of arbitrary length W Î (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.