  We investigate the mean-field dynamics of a Bose-Einstein condensate (BEC)
described by the Gross-Pitaevskii equation (GPE) in a double-well potential
with particle gain and loss, rendering the system PT-symmetric. The stationary
solutions of the system show a change from elliptically stable behavior to
hyperbolically unstable behavior caused by the appearance of PT-broken
solutions of the GPE and influenced by the nonlinear interaction. The dynamical
behavior is visualized using the Bloch sphere formalism. However, the dynamics
is not restricted to the surface of the sphere due to the nonlinear and
non-Hermitian nature of the system.
