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.