Finite-temperature dynamics of matter-wave dark solitons in linear and periodic potentials: an example of an anti-damped Josephson junction

摘要

We study matter-wave dark solitons in atomic Bose-Einstein condensates atfinite temperatures, under the effect of linear and periodic potentials. Ourmodel, namely a dissipative Gross-Pitaevskii equation, is treated analyticallyby means of dark soliton perturbation theory, which results in a Newtonianequation of motion for the dark soliton center. This reduced model, whichincorporates an effective washboard potential and an anti-damping term,constitutes an example of an anti-damped Josephson junction. We present aqualitative (local and global) analysis of the equation of motion. Forsufficiently small wavenumbers of the periodic potential and weak linearpotentials, the results are found to be in good agreement with pertinent onesobtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.