| In this thesis, we study mixtures of one-dimensional Tonks-Girardeau (i.e. hard-core), with an emphasis on mass ratios for which some mass triplets constitute an integrable system. The work extends the links between crystallographic root systems and integrable dynamical systems explored by Girardeau, Lieb & Liniger, McGuire, and Gaudin in the 1960's to the non-crystallographic root systems. While genuine integrability exists exclusively on an infinite line, for particular mass triplets in a particular spatial order, we nevertheless find some traces of it---such as a slowdown of thermalization---in both three-body systems on a ring and in many-body mass mixtures. |
