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We show that the spreading of the center-of-mass density of ultracoldattractively interacting bosons can become superballistic in the presence ofdecoherence, via single-, two- and/or three-body losses. In the limit of weakdecoherence, we analytically solve the numerical model introduced in [Phys.Rev. A 91, 063616 (2015)]. The analytical predictions allow us to identifyexperimentally accessible parameter regimes for which we predict superballisticspreading of the center-of-mass density. Ultracold attractive Bose gases formweakly bound molecules; quantum matter-wave bright solitons. Ourcomputer-simulations combine ideas from classical field methods ("truncatedWigner") and piecewise deterministic stochastic processes. While the truncatedWigner approach to use an average over classical paths as a substitute for aquantum superposition is often an uncontrolled approximation, here it predictsthe exact root-mean-square width when modeling an expanding Gaussian wavepacket. In the superballistic regime, the leading-order of the spreading of thecenter-of-mass density can thus be modeled as a quantum superposition ofclassical Gaussian random walks in velocity space.

Superballistic center-of-mass motion in one-dimensional attractive Bose gases: Decoherence-induced Gaussian random walks in velocity space