期刊
NEW JOURNAL OF PHYSICS
卷 17, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/17/10/105005
关键词
Bethe Ansatz; hard-core particles; kaleidoscope; reflection group; gas mixture; optical lattice
资金
- National Science Foundation [PHY-1402249]
- Office of Naval Research [N00014-12-1-0400]
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 3min a hard-wall box can be found exactly using Bethe Ansatz. The Ansatz is based on the exceptional affine reflection group (F) over tilde (4) 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 F-4, taken as functions of the components of momenta.
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