Comparison of Quantum and Classical Relaxation in Spin Dynamics

The classical Landau-Lifshitz equation with a 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 ($\mathbf{S}$) has been compared with the expectation value of the spin operator ($\stackrel{^}{\mathbf{S}}$). A good agreement between classical and quantum mechanical trajectories can be found for Hamiltonians linear in $\stackrel{^}{\mathbf{S}}$ or $S$, respectively. Quadratic or higher order terms in the Hamiltonian result in a disagreement.