Spiraling Solitons: a Continuum Model for Dynamical Phyllotaxis and Beyond

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.