Non-equilibrium and non-linear projection methods for open quantum systems

I will discuss several directions of recent development of projection methods in open quantum systems' theory. Specifically, I will present the derivation of quantum master equations for non-equilibrium projectors of the Argyres-Kelly type with a coherent state of an environment. These projectors are important for obtaining systematic perturbative corrections for quantum optical Hamiltonians, for which pumping can be approximated by a c-number in the leading order. I will also consider nonlinear Kawasaki-Gunton projectors for general ansatzes. I will show that these projectors can be used to obtain systematic perturbative corrections for quantum Gaussian dynamics. Additionally, I will demonstrate that they can be used to obtain dynamics in the stroboscopic limit of quantum temperature measurements.