Spin thermodynamics of periodically time-dependent systems: The quasistationary state and its decay

The effective, or Floquet, Hamiltonian for a periodically time-dependent many-body system plays a role analogous to the energy of a conservative system and can therefore be used to describe the equilibrium state. Restrictions on this analogy and the necessity of a series approximation of the effective Hamiltonian complicate the interpretation of the long-time evolution. Analysis of the effective Hamiltonian for the examples of a dipolar coupled spin system in a weak nonresonant field and for the pulsed spin-locking problem shows it to be characteristically the sum of two (or more) commuting observables plus small off-diagonal terms. This implies that the system evolves to a quasistationary state comprised of two or more independent thermodynamic baths. The properties of this state and its subsequent decay to equilibrium are discussed in detail and compared to the results of magnetic resonance experiments. This analysis overcomes the difficulties, noted in the past as the ‘‘Magnus paradox,’’ with the use of time-independent model Hamiltonians to describe approximately the true evolution of the system.