We study the dynamics of a few-quantum-particle cloud in the presence of two-and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ1 of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m2 ∼ t α , α < 1, on length scales beyond ξ1. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices.

In this work we study the dynamics of wave packets propagation of a few interacting quantum particles with different types of spatial inhomogeneity. Single particle or, equivalently, many noninteracting particles are localized in the case of spatial disorder, and experience localization-delocalization transition in the case of quasi-periodic inhomogeneity. In the other limiting case of many interacting particles, the problem is solved in the mean-field approximation, which leads to discrete nonlinear Schrodinger equation. There localization is destroyed due to dynamical chaos inherent to nonlinearity. It results in wave packets subdiffusion, their self-similarity in the asymptotic limit, the dependence of the subdiffusion rate from the nonlinearity order. We demonstrate that analogous features emerge in disordered lattice even for two quantum particles due to quantum chaos, much away from the validity of the mean-field approximation. The subdiffusion exponent decreases with the increasing order of interaction, as found in nonlinear equations. On the contrary, in the case of a quasi-periodic potential we find regular quantum dynamics and almost ballistic wave packets propagation. Wherein a small additive of disorder destroys the regular quantum dynamics.