A Statistical Theory of Designed Quantum Transport Across Disordered Networks

TL;DR

This paper develops a statistical framework explaining how symmetry and spectral features in disordered quantum networks enable highly efficient, coherent quantum transport, with analytical predictions for transfer times and efficiencies.

Contribution

It introduces a random matrix theory approach to predict quantum transport properties in disordered networks with specific symmetries and spectral conditions.

Findings

Centrosymmetry and a dominant doublet enhance quantum transport.

Analytical formulas for transfer time distribution and efficiency bounds.

Scaling laws for transport properties with network size.

Abstract

We explain how centrosymmetry, together with a dominant doublet in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalisation of the chaos assisted tunnelling mechanism, we formulate a random matrix theoretical framework for the analytical prediction of the transfer time distribution, of lower bounds of the transfer efficiency, and of the scaling behaviour of characteristic statistical properties with the size of the network.