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The Ginzburg-Landau model below its critical temperature in a temporally oscillating external field is studied both theoretically and numerically. As the frequency or the amplitude of the external field is changed, a nonequilibrium phase transition is observed. This transition separates spatially uniform, symmetry-restoring oscillations from symmetry-breaking oscillations. Near the transition a perturbation theory is developed, and a switching phenomenon is found in the symmetry-broken phase. Our results confirm the equivalence of the present transition to that found in Monte Carlo simulations of kinetic Ising systems in oscillating fields, demonstrating that the nonequilibrium phase transition in both cases belongs to the universality class of the equilibrium Ising model in zero field. This conclusion is in agreement with symmetry arguments [G. Grinstein, C. Jayaprakash, and Y. He, Phys. Rev. Lett. 55, 2527 (1985)] and recent numerical results [G. Korniss, C. J. White, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E 63, 016120 (2001)]. Furthermore, a theoretical result for the structure function of the local magnetization with thermal noise, based on the Ornstein-Zernike approximation, agrees well with numerical results in one dimension.

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Within the context of the Brownian ratchet model, a molecular rotary system was studied that can perform unidirectional rotations induced by linearly polarized ac fields, and produce positive work under loads. The model is based on the Langevin equation for a particle in a two-dimensional (2D) three-tooth ratchet potential of threefold symmetry.The performance of the system is characterized by the coercive torque, i.e., the strength of the load competing with the torque induced by the ac driving field, and the energy efficiency in force conversion from the driving field to torque. We propose a master equation for coarse-grained states, which takes into account boundary motion between states, and develop a kinetic description to estimate mean angular momentum (MAM) and powers relevant to the energy balance equation. The framework of analysis incorporates several 2D characteristics, and is applicable to a wide class of models of smooth 2D ratchet potential. We confirm that the obtained expressions for MAM, power, and efficiency of the model can predict qualitative behaviors. We also discuss the usefulness of the torque/power relationship for experimental analyses, and propose a characteristic for 2D ratchet systems.