Beyond weak-coupling quantum master equations

The theory of open quantum systems studies the dynamics of a system of interest under the influence of an uncontrolled random noise. The main goal is to obtain the reduced system dynamics in presence of an infinitely large environment that randomly influences the quantum system. This objective is typically achieved using a wide variety of perturbative quantum master equations with applications ranging from quantum optics, chemical physics, statistical physics, and more recently quantum information and thermodynamics. In this talk, I'll introduce some of the most common quantum master equations such as the Redfield and Lindblad and elucidate on the common misconceptions and pitfalls. I'll focus on the accuracy of such equations and discuss some recent ideas on correcting these approaches that help going beyond the weak coupling approximation. I'll introduce a Canonically Consistent Quantum Master Equation (CCQME) that utilizes the information about the strong-coupling equilibrium state, i.e., a mean-force Gibbs state [1], to correctly steer the quantum dynamics [2]. The approach goes beyond weak coupling methods and we corroborate the CCQME with the exactly solvable (Hu-Paz-Zhang) quantum dissipative harmonic oscillator and the numerically exact Hierarchy Equation Of Motion (HEOM) approach for the spin-boson model. The approach could be used in a wide range of applications where quantum noise does not weakly influence the system of interest. [1] J. Thingna, J.-S. Wang, and P. Hänggi, J. Chem. Phys. 136, 194110 (2012). [2] T. Becker, A. Schnell, and J. Thingna arXiv:2205.12848 (2022).