Abstract
In this article, we show that eigenenergies and eigenstates of a system consisting of four one-dimensional hard-core particles with masses 6m, 2m, m, and 3m in a hard-wall box can be found exactly using Bethe Ansatz. The Ansatz is based on the exceptional affine reflection group associated with the symmetries and tiling properties of an octacube—a Platonic solid unique to four-dimensions, with no three-dimensional analogues. We also uncover the Liouville integrability structure of our problem: the four integrals of motion in involution are identified as invariant polynomials of the finite reflection group F4, taken as functions of the components of momenta.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
