Kinetic theory of resonance and relaxation in spin systems

The possibility of existence of nonequilibrium phase transitions, bistability phenomena and other critical properties of the two-level spin systems considered in the two previous papers is investigated. Under suitable assumptions, an evolution equation for the mean value of the Zeeman operator is obtained from kinetic equations derived in part I. Qualitative methods of analysis of autonomous differential equations are used to study properties of the evolution equation. Vector fields generated by this equation are analyzed. Stationary solutions and their stability are discussed. It is shown that under suitable conditions, the steady state solutions exhibit a hysteresis cycle. Time-dependent solutions of the evolution equation are presented and discussed.