  We derive Heisenberg equations for arbitrary high order moments of creation
and annihilation operators in the case of the quantum master equation with a
multimode generator which is quadratic in creation and annihilation operators
and obtain their solutions. Based on them we also derive similar equations for
the case of the quantum master equation, which occur after averaging the
dynamics with a quadratic generator with respect to the classical Poisson
process. This allows us to show that dynamics of arbitrary finite-order moments
of creation and annihilation operators is fully defined by finite number of
linear differential equations in this case.
