Partially polaron-transformed quantum master equation for exciton and charge transport dynamics

TL;DR

This paper introduces a partial polaron transformation within the quantum master equation framework to better capture coherence effects in exciton and charge transport, especially in complex environments.

Contribution

It develops a formal framework for a partial polaron transformation in the quantum master equation, improving accuracy over the full transformation in certain regimes.

Findings

Derived a closed-form 2nd order time-local PQME with partial PT

Demonstrated the approach's feasibility through model calculations

Provided detailed expressions for numerical implementation

Abstract

Polaron-transformed quantum master equation (PQME) offers a unified framework to describe the dynamics of quantum systems in both limits of weak and strong couplings to environmental degrees of freedom. Thus, PQME serves as an efficient method to describe charge and exciton transfer/transport dynamics for a broad range of parameters in condensed or complex environments. However, in some cases, the polaron transformation (PT) being employed in the formulation invokes an over-relaxation of slow modes and results in premature suppression of important coherence terms. A formal framework to address this issue is developed in the present work by employing a partial PT that has smaller weights for low frequency bath modes. It is shown here that a closed form expression of a 2nd order time-local PQME including all the inhomogeneous terms can be derived for a general form of partial PT, although more complicated than that for the full PT. All the expressions needed for numerical calculation are derived in detail. Applications to a model of two-level system coupled to a bath of harmonic oscillators, with test calculations focused on those due to homogeneous relaxation terms, demonstrate the feasibility and the utility of the present approach.