Soliton pinning by long-range order in aperiodic systems

TL;DR

This paper explores how solitons behave in inhomogeneous chains with aperiodic order, revealing unique pinning and propagation phenomena that differ from periodic and random systems, with potential implications for molecular chains.

Contribution

It demonstrates that aperiodic systems exhibit distinctive soliton pinning and propagation behaviors, extending understanding beyond periodic and random models, and introduces simple collective coordinate explanations for these phenomena.

Findings

Aperiodic chains show soliton pinning similar to random chains but with lower depinning forces.

Soliton propagation in aperiodic chains differs from periodic chains with large unit cells.

Most phenomena can be explained by collective coordinate models, except for long-range order effects.

Abstract

We investigate propagation of a kink soliton along inhomogeneous chains with two different constituents, arranged either periodically, aperiodically, or randomly. For the discrete sine-Gordon equation and the Fibonacci and Thue-Morse chains taken as examples, we have found that the phenomenology of aperiodic systems is very peculiar: On the one hand, they exhibit soliton pinning as in the random chain, although the depinning forces are clearly smaller. In addition, solitons are seen to propagate differently in the aperiodic chains than on periodic chains with large unit cells, given by approximations to the full aperiodic sequence. We show that most of these phenomena can be understood by means of simple collective coordinate arguments, with the exception of long range order effects. In the conclusion we comment on the interesting implications that our work could bring about in the field of solitons in molecular (e.g., DNA) chains.