Generalized quantum master equation from memory kernel coupling theory

Abstract

The generalized quantum master equation provides a powerful framework for non-Markovian dynamics of open quantum systems. However, the accurate and efficient evaluation of the memory kernel remains a challenge. In this work, we introduce a comprehensive tensorial extension to the Memory Kernel Coupling Theory (MKCT) to overcome this bottleneck. By elevating the original scalar formalism to a tensorial framework, the extended MKCT enables the calculation of general expectation values and cross-correlation functions. We demonstrate the numerical accuracy and efficiency of this method across multiple benchmark systems: capturing transient populations and coherences in the spin-boson model, resolving the excitonic absorption spectrum of the Fenna-Matthews-Olson complex, and simulating charge mobility in one-dimensional lattice models. These successful applications establish the tensorial MKCT as a highly efficient tool for investigating complex dynamics in open quantum systems.

Figures (7)

• Figure 1: Time evolution of the reduced density matrix for the spin-boson model. Panel (a) depicts the population dynamics, while panel (b) demonstrates the coherence. The simulation parameters are $\omega_s=2$, $\Omega=1$, $\beta=2$, $\lambda=0.2$, and $\omega_\text{C}=5$. A Padé approximant of order [9/16] was employed to obtain the memory kernel $\bm{\mathcal{K}}_1(t)$.
• Figure 2: Time evolution of the cross-correlation function $\expval{\sigma_x(t)\sigma_y(0)}$ for a spin-boson model. Panels (a) and (b) depict the real and imaginary parts of the correlation function, respectively. Panels (c) and (d) show the real and imaginary parts of the spectrum $S(\omega)$. The simulation parameters are identical to that of FIG. \ref{['fig:pop_tls']}
• Figure 3: Comparison of the absorption spectrum of the FMO complex computed using MKCT and DEOM. Panel (a) shows the spectra obtained from MKCT (red solid line) and DEOM (black dashed line), alongside the experimental spectrum from Ref. cho2005exp_spectra (black open circles). Panel (b) compares the CPU time required by MKCT and DEOM on an AMD EPYC 7502 processor. The parameter used are $T=77 \, \text{K}$, $\lambda=35 \, \text{cm}^{-1}$, and $\omega_C=50\,\text{fs}^{-1}$. A Padé approximant of order [7/13] was used.
• Figure 4: MSD and mobility simulated by MKCT and DEOM at various friction strengths. Panels (a) and (b) show the time evolution of the MSD at different $\gamma$ values computed from MKCT and DEOM, respectively. Panel (c) presents the mobility $\mu$ as a function of the friction coefficient $\gamma$. The simulation parameters are $J = 0.1$, $\lambda = 1$, $\Omega = 1$, and $\beta = 1$.
• Figure 5: Time evolution of populations for tight-binding model with a global bath. Panel (a) and (b) depicts the results for low temperature ($\beta=2$) and high temeprature ($\beta=0.02$), respectively. The simulation parameters are: $\epsilon_0=1$, $V=0.3$, $\lambda=0.24$, and $\omega_C=4$. A Padé approximant of order [7/13] was used.