Charge Hopping Dynamics along a Disordered Chain in Quantum Environments: Comparative Study of Different Rate Kernels

TL;DR

This study compares various rate kernels to understand charge hopping dynamics in disordered quantum environments, revealing the importance of quantum effects and guiding the choice of models for large-scale simulations.

Contribution

It provides a comprehensive computational comparison of five rate kernels for charge transport in disordered quantum systems, highlighting their accuracy and limitations.

Findings

FGR rate predicts higher sensitivity to disorder than classical models.

SPI approximation reasonably captures quantum effects.

SC approximation can be unreliable, sometimes worse than classical models.

Abstract

This work presents a computational study of charge hopping dynamics along a one dimensional chain with Gaussian site energy disorder and linearly coupled quantum bath. Time dependent square displacements are calculated directly from numerical solutions of Pauli master equations, for five different rate kernels: exact Fermi golden rule (FGR) rate expression, stationary phase interpolation (SPI) approximation, semiclassical (SC) approximation, classical Marcus rate expression, and Miller-Abrahams expression. All results demonstrate diffusive behavior in the steady state limit. The results based on the FGR rate expression show that the charge transport in quantum bath can be much more sensitive to the disorder than the prediction from the classical Marcus expression. While the SPI approximation captures this general trend reasonably well, the SC approximation tends to be unreliable at both quantitative and qualitative levels, and becomes even worse than the classical Marcus expression under certain conditions. These results offer useful guidance in the choice of approximate rate kernels for larger scale simulations, and also demonstrate significant but fragile positive effects of quantum environments on the charge hopping dynamics.