ABSTRACT:

The theory of open quantum systems studies the dynamics of a system of interest under the influence of 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 commonly employed weak-coupling approximation. I’ll focus on three methods: i) a brute force approach that takes into account higher-order terms in the perturbation series [1], ii) an analytic continuation based approach that allows us to obtain the correct asymptotic state [2,3], and iii) a canonically consistent master equation that utilizes the information about the asymptotic state to correctly steer the quantum dynamics [4]. The underlying common theme to all these approaches is their ability to go beyond weak coupling and we corroborate these methods with the exactly solvable quantum dissipative harmonic oscillator. The approaches have varying levels of difficulty but could be used in a wide range of applications where quantum noise does not weakly influence the system of interest.

[1] J. Thingna, H. Zhou, and J.-S. Wang, J. Chem. Phys. 141, 194101 (2014).

[2] J. Thingna, J.-S. Wang, and P. Hänggi, J. Chem. Phys. 136, 194110 (2012).

[3] J. Thingna, J.-S. Wang, and P. Hänggi, Phys. Rev. E 88, 052127 (2013).

[4] T. Becker, A. Schnell, and J. Thingna [in preparation] (2022).