Semiclassical spectral function for matter waves in random potentials
  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. 
Martin-Isbj\"orn Trappe, Dominique Delande, and Cord A. M\"uller
cond-mat.quant-gas