Revisiting the quantum open system dynamics of central spin model

TL;DR

This paper provides an exact analysis of the dynamics of a central spin interacting with a fermionic spin bath, deriving Kraus operators and a Lindblad master equation, and discusses non-Markovian effects.

Contribution

It offers a novel exact solution for the open quantum system dynamics of a central spin with a fermionic bath, including Kraus operators and a Lindblad equation.

Findings

Exact reduced dynamics of the central spin obtained

Kraus operators constructed for the system

Lindblad master equation derived

Abstract

In this article we revisit the theory of open quantum systems from the perspective of fermionic baths. Specifically, we concentrate on the dynamics of a central spin half particle interacting with a spin bath. We have calculated the exact reduced dynamics of the central spin and constructed the Kraus operators in relation to that. Further, the exact Lindblad type cannonical master equation corresponding to the reduced dynamics is constructed. We have also briefly touch upon the aspect of non-Markovianity from the backdrop of the reduced dynamics of the central spin.