Colloquium: Dr. Marcos Rigol, Penn State University

Integrable quantum many-body systems, paradigms of exact solvability 

and mathematical beauty, are now routinely realized in ultracold gases 

experiments. Control of the effective dimensionality and the degree of 

isolation in those experiments have given access to the quasi-1D regime and 

long coherence times necessary to observe (near) integrability and study its 

effects in quantum dynamics far from equilibrium. During the latter, the 

constraints imposed by the non-trivial set of conserved quantities that make a 

system integrable generally preclude observables from equilibrating to thermal values [1]. In integrable systems, it is natural to describe observables after 

relaxation by means of an updated (generalized) statistical mechanical 

ensemble: the generalized Gibbs ensemble (GGE), constructed by maximizing the entropy subject to the constraints imposed by integrability [1,2]. We review 

experimental and theoretical results on this topic, and discuss a justification 

of the GGE based on the generalization of the eigenstate thermalization 

hypothesis.