Spectral functions and localization landscape theory in speckle potentials

TL;DR

This paper introduces a novel method combining Wigner-Weyl and landscape theories to efficiently compute spectral functions of Bose-Einstein condensates in speckle-generated disordered potentials across different regimes.

Contribution

It presents a new approximation technique for spectral functions using landscape theory, applicable across quantum to semiclassical regimes, without adjustable parameters.

Findings

Accurate spectral function approximation across regimes

Efficient computation using landscape-based effective potential

Applicable to various disordered potential statistics

Abstract

Spectral function is a key tool for understanding the behavior of Bose-Einstein condensates of cold atoms in random potentials generated by a laser speckle. In this paper we introduce a new method for computing the spectral functions in disordered potentials. Using a combination of the Wigner-Weyl approach with the landscape theory, we build an approximation for the Wigner distributions of the eigenstates in the phase space and show its accuracy in all regimes, from the deep quantum regime to the intermediate and semiclassical. Based on this approximation, we devise a method to compute the spectral functions using only the landscape-based effective potential. The paper demonstrates the efficiency of the proposed approach for disordered potentials with various statistical properties without requiring any adjustable parameters.