Quantum subdiffusion with two- and three-body interactions

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 ${\xi }_1$ of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, $m_2 \sim t^{\alpha}$,$\alpha<1$,onlengthscalesbeyond$\xi_1$. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield $\alpha \approx 0.5$ for two and three particles, while three-body interactions decrease it to $\alpha \approx 0.2$. 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.