Calculation of coherences in Förster and modified Redfield theories of excitation energy transfer

Abstract

Förster and modified Redfield theories play one of the central roles in the description of excitation energy transfer in molecular systems. However, in the present state, these theories describe only the dynamics of populations of local electronic excitations or delocalized exciton eigenstates, respectively, i.e., the diagonal elements of the density matrix in the corresponding representation. They do not give prescription for propagating the off-diagonal elements of the density matrix (coherences). This is commonly accepted as a limitation of these theories. Here we derive formulas for the dynamics of the coherences in the framework of Förster and modified Redfield theories and, thus, remove this limitation. These formulas provide excellent correspondence with numerically exact calculations according to the hierarchical equations of motion. Also we show that, even within the range of applicability of the standard Redfield theory, the formulas for coherences derived in the framework of the modified Redfield theory provide, in some cases, more precise results.

One-particle approximation as a simple playground for irreversible quantum evolution

“…From the physical point of view the main direction of future development consists in of application the results of this article to real and model physical systems in a manner contemplated in [5,6]. Namely, by coupling the methods described here and the theory for generalized Friedrichs model [48,49,50,51,52,53,54,55] one could obtain exact non-Markovian dynamics of a subsystem and analyze its properties, which is under active discussion in contemporary physical literature [56,57,58,59,5,6].…”

Integral representation of finite temperature non-Markovian evolution of some RWA systems

“…This is because the positivity of function ω k is important here due to the fact that we need a thermal state to be normalizable, which is usually neglected for zero-temperature RWA systems. Note that we do not use odd continuation of the spectral density which is widespread [35,36].…”

Non-Markovian Evolution of Multi-level System Interacting with Several Reservoirs. Exact and Approximate

“…This equation could be obtained in the second order of the perturbation theory with respect to coupling constant between a system and a reservoir [3, Subsec. 9.1.1], [57].…”