Instanton theory for bosons in disordered speckle potential

TL;DR

This paper applies instanton theory to analyze the spectral tail of non-interacting bosons in a disordered speckle potential, deriving asymptotic density of states and considering interaction effects.

Contribution

It introduces an instanton-based analytical framework for the Lifshitz tail in bosonic speckle potentials, including fluctuation corrections and interaction effects.

Findings

Analytical asymptotics match numerical results in 1D.

Fluctuation corrections are computed using generalized Gel'fand-Yaglom method.

Weak interactions influence the Lifshitz tail behavior.

Abstract

We study the tail of the spectrum for non-interacting 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.