Quantum Landau-Lifshitz and Landau-Lifshitz-Gilbert equations: another type of quantum master equation or not?

The classical Landau-Lifshitz (LL) and Landau-Lifshitz-Gilbert (LLG) equations are foundational in describing magnetization dynamics. Extending these equations to the quantum realm presents significant challenges. While a quantum LL equation was proposed in [Phys. Rev. Lett. 110, 147201 (2013)], a corresponding quantum version of the LLG equation has remained elusive until now. In our recent work [arXiv:2403.09255], we introduce a quantum LLG equation that inherently conserves the purity of the quantum state, addressing a critical gap in the theoretical framework.

This presentation explores whether the quantum LL and LLG equations constitute merely another form of quantum master equations or represent a fundamentally different approach to quantum dynamics. We examine the quantum LLG dynamics of a dimer consisting of two interacting spin-1/2 particles. For ferromagnetic coupling, the evolution of initially uncorrelated spins mirrors classical LLG dynamics, indicating a correspondence between our quantum model and classical behavior in certain limits. However, in the antiferromagnetic scenario, we observe pronounced deviations from classical expectations, leading to a spinless state characterized by non-local quantum correlations.

When the spins are initially in a mixed entangled state, we uncover an unusual revival-type behavior in quantum correlations, distinctly different from the typical decoherence and relaxation processes described by standard Lindblad-type quantum master equations. These findings suggest that the quantum LL and LLG equations are different from the conventional framework of quantum master equations.

We will discuss the unique properties of the quantum LL and LLG equations, compare them with Lindblad-type master equations, and explore the implications for understanding qubit dynamics innon-equilibrium quantum systems. With this presentation, we want to open a discussion on whether these equations represent another type of quantum master equation or if they offer a novel perspective on quantum dynamics beyond existing paradigms.