MAGNUS PARADOX AND AVERAGING METHOD

The paper investigates the long-time evolution of a dipole-coupled spin-system subject to a small external rf irradiation on the basis of the Krylov-Bogoliubov-Mitropolsky averaging method. It is shown that this method gives the correct results in contrast to the average Hamiltonian theory based on the Magnus expansion, which gives rise to the so-called "Magnus paradox" in this case. In the averaging method along with the Hamiltonian the density matrix is also expanded and nonreversibility is led into the Liouville equation. The additional slowly varying part of the density matrix causes experimentally observed slow changes of inverse spin temperature and average value of dipole energy. In the Krylov-Bogoliubov-Mitropolsky averaging method the correct description of nonconservative and nonreversible effects is possible.