Shape waves in 2D Josephson junctions: exact solutions and time dilation

Abstract

We predict a new 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 and have an analogy with shear waves in solid mechanics. Their shapes can have an arbitrary profile, which is retained when propagating. 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.

10 pages, 2 figures

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• Long-time soliton dynamics via a coarse-grained space-time method