Effect of conformations on charge transport in a thin elastic tube

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 periodic solutions in the form of Jacobi elliptic functions, which we call conformon lattice solutions. These solutions typically describe conformations with loops. Each solution induces a corresponding quantum effective periodic potential in the Schrödinger 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.