  Brownian motion is ballistic on short time scales and diffusive on long time
scales. Our theoretical investigations indicate that one can observe the exact
opposite - an "anomaleous diffusion process" where initially diffusive motion
becomes ballistic on longer time scales - in an ultracold atom system with a
size comparable to macromolecules. This system is a quantum matter-wave bright
soliton subject to decoherence via three-particle losses for which we
investigate the center-of-mass motion. Our simulations show that such unusual
center-of-mass dynamics should be observable on experimentally accessible time
scales.
