Spiraling Solitons: a Continuum Model for Dynamical Phyllotaxis and Beyond

TL;DR

This paper introduces a continuum model for topological spiraling solitons in cylindrical systems, explaining their dynamics, energy and charge transport, and predicting new pulse phenomena, with applications in nanotubes and DNA transitions.

Contribution

The paper presents a minimal, local continuum model that captures key features of phyllotactic solitons, including their existence between non-degenerate structures and their dynamic properties.

Findings

Solitons exhibit locked speed and screw shift behaviors.

The model explains energy and charge transport in spiraling systems.

Predicted pulses include static and dynamic types.

Abstract

A novel, protean, topological soliton has recently been shown to emerge in systems of repulsive particles in cylindrical geometries, whose statics is described by the number-theoretical objects of phyllotaxis. Here we present a minimal and local continuum model that can explain many of the features of the phyllotactic soliton, such as locked speed, screw shift, energy transport and, for Wigner crystal on a nanotube, charge transport. The treatment is general and should apply to other spiraling systems. Unlike e.g. Sine-Gornon-like systems, our solitons can exist between non-degenerate structure, imply a power flow through the system, dynamics of the domains it separates; we also predict pulses, both static and dynamic. Applications include charge transport in Wigner Crystals on nanotubes or A- to B-DNA transitions.