Semiclassical spectral function and density of states in speckle potentials

TL;DR

This paper introduces a new semiclassical analytical method using stationary phase approximations to accurately compute the spectral function and density of states in speckle potentials across the entire energy spectrum, aligning well with numerical data.

Contribution

The authors develop a novel semiclassical approach that captures quantum corrections at low energies in speckle potentials, extending the analytical understanding across all energy regimes.

Findings

Accurate analytical expressions for spectral function and density of states in speckle potentials.

Good agreement between analytical results and numerical simulations.

Unified description of energy spectrum from low to high energies.

Abstract

We present a novel analytical method for calculating the spectral function and the density of states in speckle potentials, valid in the semiclassical regime. Our approach relies on stationary phase approximations, allowing us to describe the singular quantum corrections at low energies. We apply it to the calculation of the spectral function and the density of states in one and two-dimensional speckle potentials. By connecting our results with those of previous work valid in the high energy sector, we end up with a consistent description of the whole energy spectrum, in good agreement with numerical simulations.