Thursday, April 23rd, 2015
2:30pm - 3:30pm, in McCormack 2-417

Maxim Olchanyi

UMass Boston, Physics Department

An exactly solvable quantum four-body problem associated with the symmetries of an octacube

Abstract: 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 $\tilde{F}_4$ associated with the symmetries and tiling properties of an octacube—a Platonic solid unique to four dimensions, with no three-dimensional analogues. We identify all four integrals of motion, represented by the $F_4$ Chevalley polynomials in the momentum space. This is a joint work with Steven Jackson.