Unusual Diffusivity in Strongly Disordered Quantum Lattices: Random Dimer Model

TL;DR

This paper investigates the transport properties of highly disordered quantum lattices, revealing a transition between disorder regimes, oscillating diffusivity behavior, and the impact of noise, with implications for quantum technology applications.

Contribution

It introduces a detailed analysis of diffusivity oscillations in the random dimer model and explores how noise affects localization and transport in strongly disordered quantum systems.

Findings

Identifies a transition between weak and strong disorder regimes.

Predicts oscillating diffusivity with specific decay and frequency characteristics.

Shows noise suppresses oscillations and promotes constant diffusion.

Abstract

Recent advances in transport properties measurements of disordered materials and lattice simulations, using superconducting qubits, have rekindled interest in Anderson localization, motivating our study of highly disordered quantum lattices. Initially, our statistical analysis of localized eigenstates reveals a distinct transition between weak and strong disorder regimes, suggesting a random distribution of dimers in highly disordered systems. Subsequently, the random dimer model predicts an oscillating diffusivity that decays as $t^{-1/2}$, is inversely proportional to the disorder strength, and maintains a constant frequency with an initial phase shift of $\pi/4$. The first peak exhibits a universal scaling of $\sigma^{-1}$ both in peak time and amplitude. Finally, we find that stochastic noise suppresses these oscillations and induces hopping between localized eigenstates, resulting in constant diffusion over long times. Our predictions challenge the conventional understanding of incoherent hopping under strong disorder. This offers new insights to optimize disordered systems for optoelectrical and quantum information technologies.