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

TL;DR

This work tackles premature coherence loss in polaron-transformed quantum master equations by introducing a partial polaron transformation with a bath-weighting function $W_h()$. It derives a complete, 2nd-order, time-local master equation in the partial-PT space, including all inhomogeneous terms, and provides explicit expressions suitable for numerical implementation. A two-level system with an Ohmic bath demonstrates that adjusting $W_h()$ tunes system-bath entanglement and coherence, illustrating the method's control over the balance between polaronic renormalization and residual bath fluctuations. The framework broadens PQME applicability to Ohmic and sub-Ohmic environments and opens avenues for variational optimization and driven/anharmonic extensions, with potential impact on accurate modeling of charge and exciton transport in complex media.

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.

Figures (5)

• Figure 1: Real (upper panel) and imaginary (Lower panel) parts of ${\mathcal{K}}(t)$ for $\omega_h/\omega_c=1$ and for two cases of $\alpha=1$ and $2$.
• Figure 2: Real (upper panel) and imaginary (lower panel) parts of ${\mathcal{M}}(t)/(\hbar\omega_c)$ for $\omega_h/\omega_c=1$ and for two cases of $\alpha=1$ and $2$.
• Figure 3: Real (upper panel) and imaginary (lower panel) parts of ${\mathcal{C}}(t)/(\hbar^2\omega_c^2)$ fo r $\omega_h/\omega_c=1$ and for two cases of $\alpha=1$ and $2$.
• Figure 4: Populations of donor (site $1$) for different values of $\omega_h$ for $E_1=E_2$ and $\alpha=2$ in $W_h(\omega)$, Eq. (\ref{['eq:wh-alpha']}). Other parameters of the model are as follows: $\eta=1$, $\omega_c=200\ {\rm cm^{-1}}$, $T=300\ {\rm K}$, and $J=300\ {\rm cm^{-1}}$.
• Figure 5: Populations of donor (site $1$) for $E_1-E_2=200\ {\rm cm^{-1}}$ and $\alpha=2$ in $W_h(\omega)$, Eq. (\ref{['eq:wh-alpha']}). All other parameters are the same as in Fig. 4.