Generalized quantum master equations in and out of equilibrium: When can one win?
Seminar | April 28 | 2-4 p.m. | 775B Tan Hall
Dr. Andres Montoya-Castillo, Stanford University
Generalized quantum and classical master equations provide a formal framework to describe the time evolution of observables and correlation functions of complex many-body systems based on the projection operator method. This broadly applicable formalism has made possible efficient and accurate calculations of, for example, diffusion constants of liquids, density fluctuations in glasses, and energy and charge transfer processes in the condensed phase. Generalized quantum master equations (GQMEs), specifically, have provided invaluable intuition about chemical and physical processes where the quantum treatment of particles is necessary, although they are often applied in perturbative limits. Here I show how one can create a framework that explicitly unifies and clarifies the connections between the Nakajima-Zwanzig treatment of reduced density matrix dynamics and the more general Mori approach to GQMEs. I will then demonstrate that this approach can be used to dramatically improve the accuracy of the quantum dynamics of even crude quantum-classical trajectory-based approaches, such as mean field theories. In particular, I will show how one may understand the origin of these improvements and how to utilize this knowledge to extend the GQME formalism to a wide variety of problems, including electron transfer and proton-coupled electron transfer at an interface.