Eur. Phys. J. B (2015) 88: 77
https://doi.org/10.1140/epjb/e2015-50832-0

Regular Article

Description of a dissipative quantum spin dynamics with a Landau-Lifshitz/Gilbert like damping and complete derivation of the classical Landau-Lifshitz equation^*

Institut für Nanostruktur- und Festkörperphysik, Universität Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany

^a e-mail: rwieser@physnet.uni-hamburg.de

Received: 2 December 2014
Received in final form: 13 February 2015
Published online: 25 March 2015

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 spin dynamics along with the time dependent Schrödinger, Liouville and Heisenberg equation has been described and the similarities and differences between classical and quantum mechanical spin dynamics have been discussed. Furthermore, a time dependent Schrödinger equation corresponding to the classical Landau-Lifshitz-Gilbert equation and two ways to include temperature into the quantum mechanical spin dynamics have been proposed.