Note: On the memory kernel and the reduced system propagator

TL;DR

This paper establishes a formal connection between the memory kernel in the Nakajima-Zwanzig-Mori approach and the reduced system propagator, enabling easier computation of memory kernels in complex system-bath models.

Contribution

It introduces a simple formalism linking two prominent approaches, simplifying the calculation of memory kernels without high-order observable computations.

Findings

The formalism is applicable to models with electron-electron and electron-phonon couplings.

It effectively handles systems driven out of equilibrium.

The method simplifies the computation of memory kernels in generalized models.

Abstract

We relate the memory kernel in the Nakajima-Zwanzig-Mori time-convolution approach to the reduced system propagator which is often used to obtain the kernel in the Tokuyama-Mori time-convolutionless approach. The connection provides a robust and simple formalism to compute the memory kernel for a generalized system-bath model circumventing the need to compute high order system-bath observables. We illustrate this for a model system with electron-electron and electron-phonon couplings, driven away from equilibrium.