  We discuss the semiclassical and classical character of the dynamics of a
single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the
semiclassical level, we extend our previous approach presented in D. Stanek, C.
Raas, and G. S. Uhrig, Phys. Rev. B 88, 155305 (2013) by the explicit
consideration of the conservation of the total spin. On the classical level, we
compare the results of the classical equations of motions in absence and
presence of an external field to the full quantum result obtained by
density-matrix renormalization (DMRG). We show that for large bath sizes and
not too low magnetic field the classical dynamics, averaged over Gaussian
distributed initial spin vectors, agrees quantitatively with the
quantum-mechanical one. This observation paves the way for an efficient
approach for certain parameter regimes.
