Five is More: Comments on Symmetry, Integrability, and Solvability for a Few Particles in a One-Dimensional Trap
arXiv:1509.00286 · doi:10.1051/epjconf/201611302007
Abstract
This contributed conference proceeding reviews some results about a system of a few identical particles with spin trapped in one-dimensional potentials and experiencing two-body interactions. The focus is on how symmetry, integrability, and solvability depend on the trap shape, two-body interaction, the number of particles, and the number of spin components. A series of comments are presented that characterize the minimal symmetries possible for a composite system constructed from interacting single particles, with special focus on the contact interaction. For five and more particles with internal components like spin, a kind of universality called algebraically solvability is lost.
8 pages in preprint format, short conference proceeding, submitted to FB21; v2 references added and title changed. Comments welcome!
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