Diffusion of excitation and power-law localization in long-range-coupled strongly disordered systems

TL;DR

This paper studies how excitation spreads in disordered systems with long-range interactions, revealing three diffusion regimes and a power-law distribution at long times, with an analytical model explaining these phenomena.

Contribution

It introduces an analytical solution for excitation diffusion in strongly disordered long-range coupled systems, linking dynamics to system parameters.

Findings

Identified ballistic, diffusive, and saturation regimes in excitation diffusion.

Derived formulas relating diffusion characteristics to system size and disorder.

Discovered power-law distribution of occupations at long times.

Abstract

We investigate diffusion of excitation in one- and two-dimensional lattices with random on-site energies and deterministic long-range couplings (hopping) inversely proportional to the distance. Three regimes of diffusion are observed in strongly disordered systems: ballistic motion at short time, standard diffusion for intermediate times, and a stationary phase (saturation) at long times. We propose an analytical solution valid in the strong-coupling regime which explains the observed dynamics and relates the ballistic velocity, diffusion coefficient, and asymptotic diffusion range to the system size and disorder strength via simple formulas. We show also that in the long-time asymptotic limit of diffusion from a single site the occupations form a heavy-tailed power-law distribution.