The limiting nuclear polarization in a quantum dot under optical   electron-spin orientation and applicability of the box-model of the   electron-nuclear dynamics
  For the model Hamiltonian describing the electron-nuclear dynamics of a quantum dot, we obtained an exact expression for the limiting nuclear polarization as a function of the number of groups of equivalent nuclei. It is shown that the refinement of the model Hamiltonian by increasing the number of the groups results in a slow growth of the limiting nuclear polarization. This allowed us to put forward arguments in favor of applicability of the box-model (with all the nuclei being equivalent) for description of the electron-nuclear spin dynamics within the time intervals of around hundreds of periods of the optical orientation. 
G. G. Kozlov