Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition

TL;DR

This paper investigates quantum diffusion on molecular tubes, revealing a universal scaling law for the transition from 1D to 2D transport, with implications for biological and synthetic systems.

Contribution

It introduces a universal scaling relation for quantum diffusion on tubular surfaces, independent of disorder and noise, based on the ratio of localization length to tube circumference.

Findings

Universal scaling relation for diffusion coefficient

Application to biological chlorosomes and synthetic aggregates

Prediction of transport regimes based on system parameters

Abstract

The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the disorder and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality.