Broken space-time symmetries and mechanisms of rectification of ac   fields by nonlinear (non)adiabatic response
  We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is employed to explain the effect. We consider a case of a particle in a periodic potential as an example and discuss the relevant symmetry breakings and the mechanisms of rectification of the current in such a system. 
S. Denisov, S. Flach, A. A. Ovchinnikov, O. Yevtushenko and Y.   Zolotaryuk