A Novel Construction of Complex-valued Gaussian Processes with Arbitrary Spectral Densities and its Application to Excitation Energy Transfer

TL;DR

This paper introduces a new method to construct complex-valued Gaussian processes for modeling quantum phonon baths, enabling efficient simulation of non-Markovian excitation energy transfer in light harvesting systems with arbitrary spectral densities.

Contribution

The paper presents a novel construction of Gaussian processes and a computational scheme for simulating quantum phonon baths, advancing the understanding of non-Markovian effects in excitation energy transfer.

Findings

The new method accurately models thermal quantum phonon baths.

It enables simulation of non-Markovian dynamics under various spectral densities.

The approach scales linearly, suitable for large systems.

Abstract

The recent experimental discoveries about excitation energy transfer (EET) in light harvesting antenna (LHA) attract a lot of interest. As an open non-equilibrium quantum system, the EET demands more rigorous theoretical framework to understand the interaction between system and environment and therein the evolution of reduced density matrix. A phonon is often used to model the fluctuating environment and convolutes the reduced quantum system temporarily. In this paper, we propose a novel way to construct complex-valued Gaussian processes to describe thermal quantum phonon bath exactly by converting the convolution of influence functional into the time correlation of complex Gaussian random field. Based on the construction, we propose a rigorous and efficient computational method, the covariance decomposition (CD) and conditional propagation scheme, to simulate the temporarily entangled reduced system. The new method allows us to study the non-Markovian effect without perturbation under the influence of different spectral densities of the linear system-phonon coupling coefficients. Its application in the study of EET in the Fenna-Matthews-Olson (FMO) model Hamiltonian under four different spectral densities is discussed. Since the scaling of our algorithm is linear due to its Monte Carlo nature, the future application of the method for large LHA systems is attractive. In addition, this method can be used to study the effect of correlated initial condition on the reduced dynamics in the future.