Semiclassical spectral function for matter waves in random potentials

TL;DR

This paper develops a semiclassical expansion for the spectral function of matter waves in random potentials, providing quantum corrections to classical behavior and validating results with numerical data.

Contribution

It introduces an $ ext{hbar}$-expansion for the spectral function, offering new analytical quantum corrections in the high-energy regime for disordered systems.

Findings

Quantum corrections improve classical spectral function predictions.

Analytical results match numerical simulations for Gaussian and speckle potentials.

Method applicable to two-dimensional disordered matter wave systems.

Abstract

An $\hbar$-expansion is presented for the ensemble-averaged spectral function of noninteracting matter waves in random potentials. We obtain the leading quantum corrections to the deep classical limit at high energies by the Wigner-Weyl formalism. The analytical results are checked with success against numerical data for Gaussian and laser speckle potentials with Gaussian spatial correlation in two dimensions.