Spectral correlations in Anderson insulating wires

TL;DR

This paper derives the spectral level correlations in Anderson insulators across all symmetry classes, linking theoretical results with experimental feasibility in cold atom systems.

Contribution

It provides a comprehensive calculation of spectral correlations for Anderson insulators in all Wigner-Dyson classes, introducing a local generating function approach.

Findings

Good agreement with numerical simulations

Spectral form factor accessible in cold atom experiments

Unified treatment across symmetry classes

Abstract

We calculate the spectral level-level correlation function of Anderson insulating wires for all three Wigner-Dyson classes. A measurement of its Fourier transform, the spectral form factor, is within reach of state-of-the-art cold atom quantum quench experiments, and we find good agreement with recent numerical simulations of the latter. Our derivation builds on a representation of the level-level correlation function in terms of a local generating function which may prove useful in other contexts.