Nonadiabaticity and large fluctuations in a many-particle Landau-Zener problem

We consider the behavior of an interacting many-particle system under slow external driving---a many-body generalization of the Landau-Zener paradigm. We find that a conspiracy of interactions and driving leads to physics profoundly different from that of the single-particle limit: for practically all values of the driving rate the particle distributions in Hilbert space are very broad, a phenomenon caused by a strong amplification of quantum fluctuations in the driving process. These fluctuations are ``nonadiabatic'' in that even at very slow driving it is exceedingly difficult to push the center of the distribution toward the limit of full ground-state occupancy. We obtain these results by a number of complementary theoretical approaches, including diagrammatic perturbation theory, semiclassical analysis, and exact diagonalization.