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Over the past few years striking experimental achievements in trapping and cooling atoms in one-dimensional optical waveguides have provided remarkable realisations of exactly solved models in the lab. More generally the study of cold atomic matter provides a unique environment to explore novel quantum many-body effects like quantum liquids, correlations, criticality and high spin phenomena.
In this talk I will describe the prototypical exactly solvable model of interacting fermions in one dimension (the Yang-Gaudin model) and their relevance to recent and future experiments. These include few-body physics to many-body phenomena such as quantum criticality, collective polaron, and Wilson ratio of the Yang-Gaudin model with spin imbalance as well as the pairing nature in spin-3/2 Fermi gases of cold atoms.
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