Classical limit of a quantal nano-magnet in an anisotropic environment

The time evolution of a model quantal magnetic moment proportional to an angular momentum, S, is studied and compared to that of a classical magnetic moment. The presence of an anisotropy quadratic term in the Hamiltonian makes classical and quantal behaviours qualitatively different for small values of the angular momentum, S. When S is increased, the classical behaviour is retrieved for a finite amount of time, even in the presence of magnetic anisotropy terms; however, in general, this limit is only reached for very large S values. The classical vs quantal behaviour is discussed in terms of three characteristic times of the system: the classical precession time, the quantal revival time and the spreading time. This allows showing that the closer to equilibrium the initial conditions are, the easier the classical limit is reached.