The field of thermodynamics is one of the crown jewels of classical
physics. However, only comparatively recently, due to the advent of
experiments in cold atomic systems with long coherence times, has our
detailed understanding of its connection to quantum statistical
mechanics seen remarkable progress.

Extending these ideas and concepts to the non-equilibrium setting is a
challenging topic, in itself 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 concept of temperature.

We find that it is nonetheless possible to identify several
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.

References: Phys. Rev. Lett. 112, 150401 (2014); Phys. Rev. E 90, 012110
(2014); Phys. Rev. Lett. 115, 030402 (2015); Phys. Rev. Lett. 116,
250401 (2016)

About the speaker:
Prof. Roderich Moessner is a condensed matter physicist with seminal
contributions in frustrated magnets, topological phases and glass
physics. After working in Princeton, the Ecole Normale Supérieure de
Paris and Oxford University, he is now serving as the director of the
Max Planck Institute for the Physics of Complex Systems in Dresden,
Germany. For the co-discovery of emergent magnetic monopoles in spin ice
materials, he has been awarded the Condensed Matter Division Prize of
the European Physical Society in 2012. And in 2013 he received the
Gottfried Wilhelm Leibniz Prize (Germany's most prestigious research
funding prize) jointly with Achim Rosch for their contributions to the
physics of strongly interacting quantum systems.