Exact steady state of perturbed open quantum systems

We present a general non-perturbative method to determine the exact perturbed steady state of open quantum systems, in terms of the eigenmodes of the unperturbed system. The perturbation may be of arbitrarily large amplitude. Using a generalized inverse and two diagonalizations, we construct an operator that generates the entire dependence of the steady state on the perturbation parameter. The approach also enables exact analytic operations—such as differentiation, integration, and ensemble averaging—with respect to the parameter, even when the steady state is computed numerically. We apply the method to three non-trivial open quantum systems, showing that it achieves exact results, with a computational speedup for calculations requiring large sampling, such as ensemble averaging, compared to sampling-based approaches.