  For a Bose-Hubbard dimer, we study quenches of the site energy imbalance,
taking a highly asymmetric Hamiltonian to a fully symmetric one. The ramp is
carried out over a finite time that interpolates between the instantaneous and
adiabatic limits. We provide results for the excess energy of the final state
compared to the ground state energy of the final Hamiltonian, as a function of
the quench rate. This excess energy serves as the analog of the defect density
that is considered in the Kibble-Zurek picture of ramps across phase
transitions. We also examine the fate of quantum `self-trapping' when the ramp
is not instantaneous.
