Thermodynamics for many-body systems evolving under a periodic time-dependent Hamiltonian: Application to pulsed magnetic resonance

A discussion is presented on the use of statistical thermodynamics to describe the long-time behavior of a many-body Hamiltonian that also depends periodically on time. Floquet’s theorem is applied to the dynamics of the system in order to exploit the time symmetry. This approach produces an effective Hamiltonian that propagates the system over one time cycle. This is taken as the fundamental constant of the motion for the system and forms the basis for the thermodynamic description. Under suitable conditions, the resulting formulas for the equilibrium values of observables have a strong analogy to the usual thermodynamic expressions for time independent systems. These ideas are applied to describe the equilibrium magnetization for multiply pulsed spin systems, in particular to the Ostroff-Waugh and Waugh-Huber-Haeberlen pulse sequences. For these systems a quasistationary state develops after a few times $T_2$. This is followed by a slow decay to an equilibrium state. The dynamics of the decay is discussed in terms of an application of the Provotorov theory of saturation to the effective Hamiltonian.