  This paper is concerned with the sensitivity of invariant states in linear
quantum stochastic systems with respect to nonlinear perturbations. The system
variables are governed by a Markovian Hudson-Parthasarathy quantum stochastic
differential equation (QSDE) driven by quantum Wiener processes of external
bosonic fields in the vacuum state. The quadratic system Hamiltonian and the
linear system-field coupling operators, corresponding to a nominal open quantum
harmonic oscillator, are subject to perturbations represented in a Weyl
quantization form. Assuming that the nominal linear QSDE has a Hurwitz dynamics
matrix and using the Wigner-Moyal phase-space framework, we carry out an
infinitesimal perturbation analysis of the quasi-characteristic function for
the invariant quantum state of the nonlinear perturbed system. The resulting
correction of the invariant states in the spatial frequency domain may find
applications to their approximate computation, analysis of relaxation dynamics
and non-Gaussian state generation in nonlinear quantum stochastic systems.
