We study the tail of the spectrum for noninteracting bosons in a blue-detuned random speckle potential. Using an instanton approach, we derive the asymptotic behavior of the density of states in $d$ dimensions. The leading corrections resulting from fluctuations around the saddle-point solution are obtained by means of the Gel'fand-Yaglom method generalized to functional determinants with zero modes. We find a good agreement with the results of numerical simulations in one dimension. The effect of weak repulsive interactions in the Lifshitz tail is also discussed.

• Received 7 May 2015

DOI:https://doi.org/10.1103/PhysRevA.92.023412