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

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...

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Bibliographic Details
Published inNew journal of physics Vol. 17; no. 10; pp. 105005 - 105012
Main Authors Olshanii, Maxim, Jackson, Steven G
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 19.10.2015
Subjects
Bethe Ansatz
Eigenvectors
Four body problem
Functions (mathematics)
gas mixture
hard-core particles
Invariants
kaleidoscope
Mathematical analysis
optical lattice
Particles (of physics)
Physics
Polynomials
Reflection
reflection group
Symmetry
Three dimensional
Tiling
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Summary: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.
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ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/17/10/105005