Comparison of quantum and classical relaxation in spin dynamics

TL;DR

This paper compares quantum and classical spin relaxation dynamics, showing good agreement for linear Hamiltonians but discrepancies for quadratic or higher order terms, highlighting the limits of classical approximations.

Contribution

It derives the classical Landau-Lifshitz equation from quantum mechanics and compares classical and quantum spin trajectories under various Hamiltonians.

Findings

Classical and quantum trajectories agree for linear Hamiltonians.

Disagreement arises with quadratic or higher order Hamiltonians.

The classical Landau-Lifshitz equation can be derived from quantum dynamics.

Abstract

The classical Landau-Lifshitz equation with damping term has been derived from the time evolution of a quantum mechanical wave function under the assumption of a non-hermitian Hamilton operator. Further, the trajectory of a classical spin $\mathrm{S}$ has been compared with the expectation value of the spin operator $\mathrm{\hat{S}}$. A good agreement between classical and quantum mechanical trajectories can be found for Hamiltonians linear in $\mathrm{\hat{S}}$ respectively $\mathrm{S}$. Quadratic or higher order terms in the Hamiltonian result in a disagreement.