Phase Transitions and Conductivties of Floquet Fluids

We investigate the phase structure and conductivity of a relativistic fluid in a circulating electric field with a transverse magnetic field. This system exhibits behavior similar to other driven systems such as strongly coupled driven CFTs [Rangamani2015] or a simple anharmonic oscillator. We identify distinct regions of fluid behavior as a function of driving frequency, and argue that a "phase" transition will occur. Such a transition could be measurable in graphene, and may be characterized by sudden discontinuous increase in the Hall conductivity. The presence of the discontinuity depends on how the boundary is approached as the frequency or amplitude is dialed. In the region where two solution exists the measured conductivity will depend on how the system is prepared.