Few particle diffusion in localizing potentials: Chaos and regularity

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.