Long Josephson Junctions in Magnetic Field

We develop a model to account for the recently observed phase jump of electrons in Josephson Junction, in a magnetic field, as the electrons cross the junction. We suggest that electrons are trapped in the potential formed by a kink anti-kink pair. When the electron escapes from this potential well it suffers a potential jump as it crosses the junction. Electrons at lower depths suffer greater potential jumps. The potential jumps were evaluated by using the Lax pair for the Sine Gordon equation and then using Gelfand-Levitan equation on the bound states formed by the kink-anti kink pair.