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.