  We present a theoretical framework for equilibrium and nonequilibrium
dynamical simulation of quantum states with spin-density-wave (SDW) order.
Within a semiclassical adiabatic approximation that retains electron degrees of
freedom, we demonstrate that the SDW order parameter obeys a generalized
Landau-Lifshitz equation. With the aid of an enhanced kernel polynomial method,
our linear-scaling quantum Landau-Lifshitz dynamics (QLLD) method enables
dynamical SDW simulations with $N \simeq 10^5$ lattice sites. Our real-space
formulation can be used to compute dynamical responses, such as dynamical
structure factor, of complex and even inhomogeneous SDW configurations at zero
or finite temperatures. Applying the QLLD to study the relaxation of a
noncoplanar topological SDW under the excitation of a short pulse, we further
demonstrate the crucial role of spatial correlations and fluctuations in the
SDW dynamics.
