Quantum spin dynamics

TL;DR

This paper derives the classical Landau-Lifshitz equation from quantum mechanics using a non-Hermitian Hamiltonian, compares classical and quantum spin dynamics, and proposes quantum analogs of classical equations including temperature effects.

Contribution

It introduces a quantum derivation of the Landau-Lifshitz-Gilbert equation and methods to incorporate temperature into quantum spin dynamics.

Findings

Quantum mechanical equations resemble classical spin dynamics.

Non-Hermitian Hamiltonian models energy dissipation.

Proposed quantum equations include temperature effects.

Abstract

The classical Landau-Lifshitz equation has been derived from quantum mechanics. Starting point is the assumption of a non-Hermitian Hamilton operator to take the energy dissipation into account. The corresponding quantum mechanical time dependent Schr\"odinger, Liouville and Heisenberg equation have been described and the similarities and differences between classical and quantum mechanical spin dynamics have been discussed. Furthermore, a time dependent Schr\"odinger equation corresponding to the classical Landau-Lifshitz-Gilbert equation and two ways to include temperature into the quantum mechanical spin dynamics have been proposed.