How to describe the dynamics of quantum systems interacting with environments is a central issue across broad fields of physics, chemistry, and most recently biology. Quantum Master Equation (QME) and Quantum Fokker-Planck equation (QFPE), which can be viewed as the phase space representation of a QME, have long served as important theoretical and computational tools for studying such open system quantum dynamics.    This talk will first provide a brief overview and known issues of well-known QMEs such as Redfield and Lindblad equations, and QFPE derived by Caldeira and Leggett (CL) based on Feynman-Vernon influence functional formalism. Then, I will explain two particular approaches I have developed over the years.  The first is polaron-transformed QME (PQME), which offers reasonable transition from weak to strong coupling limits and is appropriate for the dynamics of charge carriers and excitons in intermediate coupling regime, and its recent generalizations and applications.  The second is a new QFPE, which generalizes the derivation of CL to photo-induced nonequilibrium situation and has clear positive definiteness condition.    The steady state limit of this QFPE also provides corrections of CL-QFPE for the quantum and non-Markovian effects of the bath.

Quantum master equation and quantum Fokker-Planck equation for open system quantum dynamics

ACS Spring 2022

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