This talk is a review of the current status of the experimental and theoretical studies of one-dimensional quantum-degenerate gases. I will particularly emphasize the high predictive power in such settings of several well-known integrable models, including Girardeau’s hard-core Bose and Fermi gases, Lieb-Liniger-McGuire’s delta-interacting bosons, and Yang-Gaudin’s delta-interacting spin-1/2 fermions.
I will further discuss the experimentally observable consequences of the integrability itself. The most prominent of those are the suppression of thermalization–already observed in the laboratory–and the prohibition of chemical reactions.
I will also describe several integrable-model-related theoretical results recently obtained within the atomic community. Among them are the large-momentum asymptotics of the momentum distribution in short-range-interacting models; the n-body correlation function of the Lieb-Liniger-McGuire system near the hard-core regime; the three-body correlation function for the same system in all regimes. I will also describe the interesting model of p-wave-interacting hard-core fermions, where all correlation functions require no more than two lines of calculation.
The talk will conclude with a list of open problems that may be of interest for experts in the filed of integrable models. The most prominent problem is the mystery of the universal trap-independent long-range behavior of the correlation function of hard-core bosons.

University of Southern California