Landau-Lifshitz damping from Lindbladian dissipation in quantum magnets

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 $\vec{m}\mathrm{/}\mathrm{\mid }\vec{m}\mathrm{\mid }$ to the length $\mathrm{\mid }\vec{m}\mathrm{\mid }$ of the magnetization. A key assumption is that the Lindbladian dissipation adapts to the non-equilibrium $H(t)$ instantaneously to lower its expectation value.