Shape waves are excitations propagating along Josephson vortices or

fluxons In physics, a fluxon is a quantum of electromagnetic flux. The term may have any of several related meanings. Superconductivity In the context of superconductivity, in type II superconductors fluxons (also known as Abrikosov vortices) can for ...

. In the case of two-dimensional

Josephson junctions In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mec ...

(thick long Josephson junctions with an extra dimension) described by the 2D sine-Gordon equation, shape waves are distortions of a

Josephson vortex In superconductivity, a Josephson vortex (after Brian Josephson from Cambridge University) is a quantum vortex of supercurrents in a Josephson junction (see Josephson effect). The supercurrents circulate around the vortex center which is situated i ...

line of an arbitrary profile. Shape waves have remarkable properties exhibiting Lorentz contraction and

time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...

similar to that in

special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...

. Position of the shape wave excitation on a

acts like a “minute-hand” showing the time in the rest-frame associated with the vortex. At some conditions, a moving vortex with the shape excitation can have less energy than the same vortex without it.

References

* Waves {{physics-stub