  Most of the work done in the field of Bose-Einstein condensates with balanced
gain and loss has been performed in the mean-field approximation using the
PT-symmetric Gross-Pitaevskii equation. In this work we study the many-particle
dynamics of a two-mode condensate with balanced gain and loss described by a
master equation in Lindblad form whose purity periodically drops to small
values but then is nearly completely restored. This effect cannot be covered by
the mean-field approximation, in which a completely pure condensate is assumed.
We present analytic solutions for the dynamics in the non-interacting limit and
use the Bogoliubov backreaction method to discuss the influence of the on-site
interaction. Our main result is that the strength of the purity revivals is
almost exclusively determined by the strength of the gain and loss and is
independent of the amount of particles in the system and the interaction
strength. For larger particle numbers, however, strong revivals are shifted
towards longer times, but by increasing the interaction strength these strong
revivals again occur earlier.
