  We study the connection between the semiclassical phase space of the
Bose--Hubbard dimer and inherently quantum phenomena in this model, such as
entanglement and dissipation-induced coherence. Near the semiclassical
self-trapping fixed points, the dynamics of EPR entanglement and condensate
fraction consists of beats among just three eigenstates. Since persistent EPR
entangled states arise only in the neighborhood of these fixed points, our
analysis explains essentially all of the entanglement dynamics in the system.
We derive accurate analytical approximations by expanding about the
strong-coupling limit; surprisingly, their realm of validity is nearly the
entire parameter space for which the self-trapping fixed points exist. Finally,
we show significant enhancement of entanglement can be produced by applying
localized dissipation.
