Spectral Densities, Structured Noise and Ensemble Averaging within Open Quantum Dynamics

TL;DR

This paper advances the Numerical Integration of Schrödinger Equation (NISE) method for open quantum systems by improving long-time behavior, handling structured spectral densities, and demonstrating applications in absorption spectra and population dynamics.

Contribution

It introduces a modified ensemble-averaging procedure for Thermalized NISE and a noise generating algorithm for structured spectral densities, enhancing simulation accuracy and applicability.

Findings

Improved long-time thermalization behavior of NISE.

Effective handling of structured spectral densities.

Successful application to absorption spectra and population dynamics.

Abstract

Although recent advances in simulating open quantum systems have lead to significant progress, the applicability of numerically exact methods is still restricted to rather small systems. Hence, more approximate methods remain relevant due to their computational efficiency, enabling simulations of larger systems over extended timescales. In this study, we present advances for one such method, namely the Numerical Integration of Schr\"odinger Equation (NISE). Firstly, we introduce a modified ensemble-averaging procedure that improves the long-time behavior of the thermalized variant of the NISE scheme, termed Thermalized NISE. Secondly, we demonstrate how to use the NISE in conjunction with (highly) structured spectral densities by utilizing a noise generating algorithm for arbitrary structured noise. This algorithm also serves as a tool for establishing best practices in determining spectral densities from excited state calculations along molecular dynamics or quantum mechanics/molecular mechanics trajectories. Finally, we assess the ability of the NISE approach to calculate absorption spectra and demonstrate the utility of the proposed modifications by determining population dynamics.