Anderson localization of bogolyubov quasiparticles in interacting bose-einstein condensates

We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with a leading length xi) subjected to a random potential (with a finite correlation length sigma(R)). We derive analytically the Lyapunov exponent as a function of the quasiparticle momentum k, and we study the localization maximum k(max). For 1D speckle potentials, we find that k(max) proportional to 1/xi when xi >> sigma(R) while k(max) proportional to 1/sigma(R) when xi << sigma(R), and that the localization is strongest when xi similar to sigma(R). Numerical calculations support our analysis, and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in experiments with ultracold atoms.