  Typical treatments of superconducting or superfluid Josephson junctions rely
on mean-field or two-mode models; we explore many-body dynamics of an isolated,
ultracold, Bose-gas long Josephson junction using time-evolving block
decimation simulations. We demonstrate that with increasing repulsive
interaction strength, localized dynamics emerge that influence macroscopic
condensate behavior and can lead to formation of solitons that directly oppose
the symmetry of the junction. Initial state population and phase yield insight
into dynamic tunneling regimes of a quasi one-dimensional double well
potential, from Josephson oscillations to macroscopic self-trapping. Population
imbalance simulations reveal substantial deviation of many-body dynamics from
mean-field Gross-Pitaevskii predictions, particularly as the barrier height and
interaction strength increase. In addition, the sudden approximation supports
localized particle-hole formation after a diabatic quench, and correlation
measures unveil a new dynamic regime: the Fock flashlight.
