Quantum and thermal effects in dark soliton formation and dynamics in a 1D Bose gas

We numerically study the imprinting and dynamics of dark solitons in a bosonic atomic gas in a tightly-confined one-dimensional harmonic trap both with and without an optical lattice. Quantum and thermal fluctuations are synthesized within the truncated Wigner approximation in the quasi-condensate description. We track the soliton coordinates and calculate position and velocity uncertainties. We find that the phase fluctuations {\em lower} the classically predicted soliton speed and seed instabilities. Individual runs show interactions of solitons with sound waves, splitting and disappearing solitons.