Time Evolution of Spin Waves

TL;DR

This paper rigorously derives macroscopic spin-wave equations from quantum models, extending the Landau-Lifshitz equations to general ferromagnetic Hamiltonians using a mean-field limit approach.

Contribution

It introduces a rigorous derivation of macroscopic spin-wave equations from microscopic models, generalizing the Landau-Lifshitz equations to broader ferromagnetic systems.

Findings

Derived macroscopic spin-wave equations from quantum models.

Extended Landau-Lifshitz equations to general ferromagnetic Hamiltonians.

Established a mean-field limit approach for spin-wave analysis.

Abstract

A rigorous derivation of macroscopic spin-wave equations is demonstrated. We introduce a macroscopic mean-field limit and derive the so-called Landau-Lifshitz equations for spin waves. We first discuss the ferromagnetic Heisenberg model at T=0 and finally extend our analysis to general spin hamiltonians for the same class of ferromagnetic ground states.