Spectral correlations in Anderson insulating wires

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.

4 pages, 2 figures, supplementary material

References in corpus (11)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Topological Anderson Insulator
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• Coherent Backscattering of Ultracold Atoms
• Topology vs. Anderson localization: non-perturbative solutions in one dimension
• Coherent Forward Scattering Peak Induced by Anderson Localization
• Coherent forward scattering in 2D disordered systems
• Dynamics of localized waves in 1D random potentials: statistical theory of the coherent forward scattering peak
• Local correlations of different eigenfunctions in a disordered wire
• Dynamics of Anderson localization in disordered wires
• Spectral correlations in finite-size Anderson insulators