Correlated projection operator approach to non-Markovian dynamics in spin baths

TL;DR

This paper introduces a correlated projection operator method to better model non-Markovian dynamics in open quantum systems, specifically for a central spin interacting with a spin bath, surpassing traditional weak-coupling approaches.

Contribution

The authors apply a correlated projection superoperator technique to derive analytical solutions for non-Markovian spin dynamics, improving upon standard methods for strongly coupled systems.

Findings

The correlated projection approach yields results closer to the exact solution.

It significantly outperforms traditional weak-coupling methods.

Applicable to complex physical systems like quantum dots.

Abstract

The dynamics of an open quantum system is usually studied by performing a weak-coupling and weak-correlation expansion in the system-bath interaction. For systems exhibiting strong couplings and highly non-Markovian behavior this approach is not justified. We apply a recently proposed correlated projection superoperator technique to the model of a central spin coupled to a spin bath via full Heisenberg interaction. Analytical solutions to both the Nakajima-Zwanzig and the time-convolutionless master equation are determined and compared with the results of the exact solution. The correlated projection operator technique significantly improves the standard methods and can be applied to many physical problems such as the hyperfine interaction in a quantum dot.