Landau-Lifshitz damping from Lindbladian dissipation in quantum magnets

TL;DR

This paper establishes a theoretical connection between classical Landau-Lifshitz damping and quantum Lindbladian dissipation, deriving LL dynamics from quantum principles in a mean-field framework for weak external fields.

Contribution

It provides a systematic derivation of Landau-Lifshitz damping from Lindbladian quantum dissipation, extending the classical model to include magnetization magnitude dynamics.

Findings

Derivation of LL dynamics from Lindbladian formalism

Extension of LL dynamics to magnetization length

Assumption of instantaneous Lindbladian adaptation to non-equilibrium fields

Abstract

As of now, the phenomenological classical Landau-Lifshitz (LL) damping of magnetic order is not conceptually linked to the quantum theory of dissipation of the Lindbladian formalism which is unsatisfactory for the booming research on magnetic dynamics. Here, it is shown that LL dynamics can be systematically derived from Lindbladian dynamics in a local mean-field theory for weak external fields. The derivation also extends the LL dynamics beyond the orientation $\vec{m}/|\vec{m}|$ to the length $|\vec{m}|$ of the magnetization. A key assumption is that the Lindbladian dissipation adapts to the non-equilibrium $H(t)$ instantaneously to lower its expectation value.