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

Spectral functions and localization landscape theory in speckle potentials