Combining quantum master equations with linearized semiclassical methods

Prof Eitan Geva, University of Michigan, USA

Thursday, June 12,  2025, 11:00 AM, Los Angeles Seminar Room

Abstract: A variety of important dynamical processes that take place in biologically and
technologically important complex molecular systems involve an intricate network of
interrelated photo-induced electronic energy and charge transfer pathways. The
simulation of the inherently quantum-mechanical electronic dynamics underlying
these pathways poses multiple formidable challenges associated with simulating the
intrinsically quantum dynamics of a system that consists of many coupled electronic
and nuclear degrees of freedom (DOF). One strategy for tackling this challenge is to
treat the electronic DOF of interest as an open quantum system and restrict the input
regarding the remaining electronic and nuclear DOF (the so-called “bath”) to the
minimum necessary to account for their effect on the electronic DOF of interest.
Quantum master equations (QMEs) provide a flexible and general-purpose
framework for formulating the effect of the bath DOF on the dynamics of the
electronic DOF of interest in terms of temporally and dimensionally compact reduced
quantities known as memory kernels, whose matrix elements are associated with
electronic energy/charge transfer and decoherence rates.

A wide variety of different types of QMEs is available, ranging from formally exact
non-Markovian Nakajima–Zwanzig generalized quantum master equations (GQMEs)
to a wide variety of perturbative QMEs. Those QMEs differ with respect to the choice
of the quantity of interest (the subset of electronic populations and coherences one
wishes to focus on), which terms in the overall Hamiltonian are treated as a small
perturbation (in the case of perturbative QMEs), and whether or not additional
approximations based on assuming separation of time scales are employed. In this
talk, I will overview computational approaches that were developed and explored by
my group which combine QMEs with linearized semiclassical methods to simulate
photo-induced electronic energy and charge transfer dynamics in complex molecular
systems as well fundamental aspects quantum open system dynamics.