Shape and wobbling wave excitations in Josephson junctions: Exact solutions of the (2+1)-dimensional sine-Gordon model

D. R. Gulevich; F. V. Kusmartsev; Sergey Savel’ev; V. A. Yampol’skii; Franco Nori

doi:10.1103/PhysRevB.80.094509

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Shape and wobbling wave excitations in Josephson junctions: Exact solutions of the (2+1)-dimensional sine-Gordon model

D. R. Gulevich, F. V. Kusmartsev, Sergey Savel’ev, V. A. Yampol’skii, Franco Nori

DOI 10.1103/PhysRevB.80.094509 · Physical Review B

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Abstract

We predict a class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line of an arbitrary profile. We derive a universal analytical expression for the energy of arbitrary-shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically-moving Josephson vortex and suggest an experiment to measure a time-dilation effect analogous to that in special relativity. The position of the shape excitation on a Josephson vortex acts like a “minute hand” showing the time in the rest frame associated with the vortex. Remarkably, at some conditions, the shape wave can carry negative energy: a vortex with the shape excitation can have less energy than the same vortex without it.