  We study the existence, stability, and dynamics of symmetric and
anti-symmetric states of quasi-one-dimensional polariton condensates in
double-well potentials, in the presence of nonresonant pumping and nonlinear
damping. Some prototypical features of the system, such as the bifurcation of
asymmetric solutions, are similar to the Hamiltonian analog of the double-well
system considered in the realm of atomic condensates. Nevertheless, there are
also some nontrivial differences including, e.g., the unstable nature of both
the parent and the daughter branch emerging in the relevant pitchfork
bifurcation for slightly larger values of atom numbers. Another interesting
feature that does not appear in the atomic condensate case is that the
bifurcation for attractive interactions is slightly sub-critical instead of
supercritical. These conclusions of the bifurcation analysis are corroborated
by direct numerical simulations examining the dynamics of the system in the
unstable regime.
