Quantum chaotic subdiffusion in random potentials

Abstract

Two interacting particles (TIP) in a disordered chain propagate beyond the single-particle localization length ${\ensuremath{\xi}}_{1}$ up to a scale ${\ensuremath{\xi}}_{2}>{\ensuremath{\xi}}_{1}$. An initially strongly localized TIP state expands almost ballistically up to ${\ensuremath{\xi}}_{1}$. The expansion of the TIP wave function beyond the distance ${\ensuremath{\xi}}_{1}\ensuremath{\gg}1$ is governed by highly connected Fock states in the space of noninteracting eigenfunctions. The resulting dynamics is subdiffusive, and the second moment grows as ${m}_{2}\ensuremath{\sim}{t}^{1/2}$, precisely as in the strong chaos regime for corresponding nonlinear wave equations. This surprising outcome stems from the huge Fock connectivity and resulting quantum chaos. The TIP expansion finally slows down towards a complete halt---in contrast to the nonlinear case.