2013/08/06 by Mustafa A. Amin, Eugene A. Lim, I-Sheng Yang
Physics and Astronomy · #hep-th #astro-ph.CO #hep-ph #nlin.PS #nlin.SI
paper · pdf · doi:10.1103/physrevlett.111.224101
published as Phys. Rev. Lett. 111, 224101 (2013) · 4 pages, 4 figures, updated link to the companion paper and fixed some typos
arxiv created 2013/08/06 · arxiv updated 2013/12/04
We derive a closed-form expression for the phase shift experienced by 1+1 dimensional kinks colliding at ultra-relativistic velocities (gamma v >> 1), valid for arbitrary periodic potentials. Our closed-form expression is the leading order result of a more general scattering theory of solitary waves described in a companion paper [Amin, Lim and Yang, arXiv:1308.0606]. This theory relies on a small kinematic parameter 1/(gamma v) << 1 rather than a small parameter in the Lagrangian. Our analytic results can be directly extracted from the Lagrangian without solving the equation of motion. Based on our closed-form expression, we prove that kink-kink and kink-antikink collisions have identical phase shifts at leading order.