N-Z equation from assignment maps

TL;DR

This paper extends the Nakajima-Zwanzig equation using assignment maps to better analyze non-Markovian dynamics in open quantum systems with initial or evolving discord, demonstrated through quantum lattice models.

Contribution

It introduces a modified N-Z equation incorporating assignment maps to handle initial and dynamic discord in system-environment states.

Findings

Bounded the influence of inhomogeneous terms on non-Markovian behavior.

Showed how environment dimension affects non-Markovian dynamics.

Extended applicability of N-Z equation to more general quantum states.

Abstract

The Nakajima-Zwanzig(N-Z) equation is a powerful tool to analyze the open quantum system and non-Markovian behavior. In this paper, we modify the N-Z equation with assignment maps. This approach extends the application to those situations in which the bipartite state of the system and environment contains non-negligible discord initial and/or during the dynamics. We applied the equation in quantum lattice model and bound the influence of inhomogeneous terms, which figure out how the dimension of the environment impact the non-Markovian behavior.