Relativistic dynamics of domain wall in one-dimensional SQUID array

We investigate the dynamics of a domain wall in a one-dimensional array of superconducting quantum interference device (SQUID) composed of three conventional Josephson junctions and a pi-junction. The domain wall is formed between two domains with oppositely circulating current through the SQUID loop. It is shown that the SQUIDs in this array can be approximately described by a double sine-Gordon (DSG) model which obeys Einstein's special theory of relativity. We conduct numerical simulations of a discrete DSG equation, and show that the domain wall propagates solitonically through the SQUID array and exhibits quasi-relativistic behavior, such as the Lorentz contraction and the relativistic time dilation, which agrees reasonably well with the predictions from a relativistic equation of motion of a particle, whose rest mass is extremely small compared to that of a single electron.