Numerical Feynman integrals for density operator dynamics using master equation interpolants: faster convergence and significant reduction of computational cost

TL;DR

This paper introduces a physics-informed interpolation method for Feynman integrals that significantly reduces computational costs and improves accuracy in density operator dynamics calculations for open quantum systems.

Contribution

It presents a novel interpolation approach using physical information to enhance Feynman integral calculations, enabling accurate results with fewer time steps.

Findings

Achieves accurate density operator dynamics with as few as 2 time steps.

Reduces memory and CPU time significantly compared to traditional methods.

Maintains original Feynman integral calculations while improving intermediate estimates.

Abstract

The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an approximation of the density operator at a sparse grid of points in time. Instead of relying only on \textit{ad hoc} interpolation methods such as splines to estimate the system density operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the density operator dynamics to be captured with as little as 2 time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating density operator dynamics within a desired accuracy. Since this method does not change the way the Feynman integral itself is calculated, the value of the density operator approximation at the points in time used to discretize the Feynamn integral will be the same whether or not this method is used, but its approximation in between these points in time is considerably improved by this method.