Memory Kernel Coupling Theory: Obtain Time Correlation Function from Higher-order Moments

TL;DR

The paper introduces the memory kernel coupling theory (MKCT), a new formalism that efficiently computes time correlation functions in complex quantum systems using higher-order moments, demonstrated on the spin-boson model.

Contribution

The MKCT extends Mori's formalism by decomposing the memory kernel into auxiliary kernels, enabling accurate TCF calculations with only higher-order moments as input.

Findings

Rapid decay of auxiliary kernels allows truncation with high accuracy.

The formalism is general and applicable to open quantum systems.

Numerical demonstration confirms effectiveness on the spin-boson model.

Abstract

Dynamical observables can often be described by time correlation functions (TCFs). However, efficiently calculating TCFs for complex quantum systems is a significant challenge, which generally requires solving the full dynamics of the systems. This Letter presents the memory kernel coupling theory (MKCT), a general formalism for evaluating TCFs. The MKCT builds upon Mori's memory kernel formalism for TCFs. Our theory further decomposes the memory kernel into auxiliary kernels. Rapid decay of auxiliary kernels allows us to truncate the coupled equations of motion with high accuracy. Notably, only higher-order moments are sufficient as the input for obtaining TCFs. While this formalism is general, we carry out the numerical demonstration for a typical open quantum system--the spin-boson model.