  The existence and degeneracies of quantum exceptional, diabolical, and hybrid
(i.e., diabolically degenerated exceptional) singularities of simple bosonic
systems composed of up to five modes with damping and/or amplification are
analyzed. Their dynamics governed by quadratic non-Hermitian Hamiltonians is
followed using the Heisenberg-Langevin equations. Conditions for the
observation of inherited quantum hybrid points, observed directly in the
dynamics of field operators, having up to third-order exceptional and
second-order diabolical degeneracies are revealed. Exceptional and diabolical
genuine points and their degeneracies observed in the dynamics of second-order
field-operator moments are analyzed. Surprisingly, exceptional degeneracies of
only second and third orders are revealed. Nevertheless the analyzed bosonic
systems exhibit rich dynamics, also owing to their common second-order
diabolical degeneracies.
