Effect of conformations on charge transport in a thin elastic tube

TL;DR

This paper explores how the conformations of a thin elastic tube influence charge transport, deriving exact solutions for the tube's shape and analyzing their impact on electron delocalization along the tube.

Contribution

It introduces a class of exact conformational solutions called conformon lattices and links these to periodic potentials affecting charge transport.

Findings

Exact periodic solutions for tube conformations using Jacobi elliptic functions

Conformations induce periodic quantum potentials for electrons

Electron wave functions show delocalization along the tube's axis

Abstract

We study the effect of conformations on charge transport in a thin elastic tube. Using the Kirchhoff model for a tube with any given Poisson ratio, cross-sectional shape and intrinsic twist, we obtain a class of exact solutions for its conformation. The tube's torsion is found in terms of its intrinsic twist and its Poisson ratio, while its curvature satisfies a nonlinear differential equation which supports exact {\it periodic} solutions in the form of Jacobi elliptic functions, which we call {\it conformon lattice} solutions. These solutions typically describe conformations with loops. Each solution induces a corresponding quantum effective {\it periodic} potential in the Schr\"{o}dinger equation for an electron in the tube. The wave function describes the delocalization of the electron along the central axis of the tube. We discuss some possible applications of this novel mechanism of charge transport.