Perturbation Methods for Non-Markovian Quantum State Diffusion Equation

TL;DR

This paper explores two perturbation techniques for solving the non-Markovian quantum state diffusion equation, comparing their effectiveness and providing analytical solutions for specific initial states to analyze entanglement dynamics.

Contribution

It introduces and compares two novel perturbation methods for the NMQSD equation, enhancing understanding of their accuracy and applicability.

Findings

Both perturbation methods are effective for bipartite systems.

Analytical solutions enable detailed entanglement dynamics analysis.

The methods' accuracy is validated against exact solutions.

Abstract

Two perturbation methods for the non-Markovian quantum state diffusion (NMQSD) equation are investigated. The first perturbation method under investigation is based on a functional expansion of the NMQSD equation, while the second one expands the NMQSD equation in terms of the coupling strength. We have compared the advantages of the two methods based on bipartite systems where the accuracy of both perturbation methods can be examined by comparing the approximations with the exact solutions. Additionally, we provide an analytical solution for a special family of system's initial states, and the entanglement dynamics is discussed based on this solution.