Abstract

The field of thermodynamics is one of the crown jewels of classical physics. Extending its ideas and concepts to the non-equilibrium setting is a challenging topic of perennial interest. Here, we study perhaps the simplest non-equilibrium class of quantum problems, namely Floquet systems, i.e. systems whose Hamiltonians depend on time periodically, H(t + T) = H(t). For these, there is no energy conservation, and hence not even a natural definition of temperature. We find that it is nonetheless possible to identify three fundamentally distinct thermodynamic ensembles. We also ask if there exists a sharp notion of a phase in such driven, interacting quantum systems. Disorder turns out to play a crucial role, enabling the existence of states which are straightforward analogues of equilibrium states with broken symmetries and topological order, while others—genuinely new to the Floquet problem—are characterized by a combination of order and non-trivial periodic dynamics.

This work was done in collaboration with Arnab Das, Vedika Khemani, Achilleas Lazarides and Shivaji Sondhi: Phys. Rev. Lett. 112, 150401 (2014); Phys. Rev. E 90 , 012110 (2014); Phys. Rev. Lett. 115, 030402 (2015); arXiv:1508.03344.