# Invariant states of linear quantum stochastic systems under Weyl perturbations of the Hamiltonian and coupling operators. (arXiv:1711.03503v1 [math-ph])

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.