Title: The Tonks-Girardeau Gas: Then, Now, and in the Future (Video)
Abstract: In this presentation, I will review the 55+ years of progress passed since Marvin Girardeau found, in 1960, a full nonperturbative solution for the quantum hard-core bosons, further extended to the finite strength interactions in 1963 by Lieb and Liniger. This discovery brought the multi-(all the way to infinite-)dimensional reflection groups to many-body physics, ignited experimental and theoretical studies of confined scattering, and led to a new direction in experiments with ultracold quantum gases. Recent successes in control of effective particle masses in optical lattices allow us to bring new exotic reflection symmetries to the game. I will conclude with a description of a new solvable problem of four confined mass 6:2:1:3 particles associated with the symmetries of an octacube---a unique to four spatial dimensions Platonic solid, with no three-dimensional analogues.