Dynamical Study of a System of Interacting Spins

This paper considers the relaxation towards thermal equilibrium of a system of two unlike spins $I$ and $S$, using a general decoupling method, which takes the interaction with the heat bath into account. One obtains a system of two integral equations which describe the time dependence of the average values of the spin operators. One finds from these relaxation times of interacting spins. In the case where the two spins are identical, it is shown that if the Zeeman energy of the spins, when placed in a magnetic field, is less than the interaction energy, the interaction is a pseudoperiodic function of the time, which corresponds to an exchange of energy between the lattice and the temperature reservoir furnished by the dipole-dipole interaction between the spins $I$ and $S$.