Wavepacket Dynamics in Energy Space of a Chaotic Trimeric Bose-Hubbard System

We study the energy redistribution of interacting bosons in a ring-shaped quantum trimer as the coupling strength between neighboring sites of the corresponding Bose-Hubbard Hamiltonian undergoes a sudden change $\delta k$. In the framework of (ultra-)cold atoms on optical lattices this perturbation corresponds to a modulation of the trapping potential height. Our analysis is based on a three-fold approach combining linear response theory calculations as well as semiclassical and random matrix theory considerations. The $\delta k$-borders of applicability of each of these methods are identified by direct comparison with the exact quantum mechanical results. We find that while the variance of the evolving quantum distribution shows a remarkable quantum-classical correspondence (QCC) for all $\delta k$-values, other moments exhibit this QCC only in the non-perturbative $\delta k$-regime.