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Brownian motion is ballistic on short time scales and diffusive on long timescales. Our theoretical investigations indicate that one can observe the exactopposite - an "anomaleous diffusion process" where initially diffusive motionbecomes ballistic on longer time scales - in an ultracold atom system with asize comparable to macromolecules. This system is a quantum matter-wave brightsoliton subject to decoherence via three-particle losses for which weinvestigate the center-of-mass motion. Our simulations show that such unusualcenter-of-mass dynamics should be observable on experimentally accessible timescales.

From short-time diffusive to long-time ballistic dynamics: the unusual center-of-mass motion of quantum bright solitons