  We investigate the coherent dynamics of a Bose-Einstein condensate in a
double well, subject to a density dependent gauge potential. Further, we derive
the nonlinear Josephson equations that allow us to understand the many-body
system in terms of a classical Hamiltonian that describes the motion of a
nonrigid pendulum with an initial angular offset. Finally we analyze the
phase-space trajectories of the system, and describe how the self-trapping is
affected by the presence of an interacting gauge potential.
