Dynamics of the infinitely-thin kink

TL;DR

This paper investigates the dynamics of an infinitely-thin domain-wall kink, revealing that its zero mode is largely suppressed and proposing a revised method for mode expansion.

Contribution

It demonstrates that the zero mode of the infinitely-thin kink is nearly frozen and introduces a generalized Fourier analysis as a more accurate approach for mode expansion.

Findings

Zero mode is almost completely frozen in the thin kink limit.

A single arbitrary frequency mode remains dynamically constrained.

Traditional collective coordinate expansion is not fully general.

Abstract

We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes -- implicit collective coordinates -- is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.