Dynamics of narrow bright solitons in an array of attractive atoms in a Bose-Einstein condensate

We study the dynamics of a narrow bright soliton in a one-dimensional lattice of condensed attractive atoms when the soliton width is comparable to the lattice spacing. If a momentum is imprinted to a stationary state, the soliton can have oscillations around a site or it can undergo a random motion along the array. The motion is very sensitive to the atomic background distribution, and a thermal cloud or quantum field fluctuations can induce a random motion of the soliton.