Multiple-time-scale analysis for pinned breathers in Bose-Hubbard chains

Localized and pinned discrete breathers in Bose-Einstein condensates in optical lattices or in arrays of optical waveguides oscillate with frequencies which are much higher than those present in the spectrum of the background. Hence, the interaction between localized breathers and their surroundings is extremely weak leading to a multiple-time-scale perturbation expansion. We identify the leading order in the asymptotic expansion of the breather amplitude which does not average to zero after one full oscillation. The reduced model predicts a lower bound of the breather drift times and explains the topological differences between breathers in dimers, trimers, and in spatially extended one-dimensional lattices even in the presence of transport from boundary heat-baths. These analytical boundaries hold true for lattices of any length, due to the highly localized nature of breathers.