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Topological Quantum Computing Quantum Simulation Quantum State Preparation Representation

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

arXiv
Authors: Maxim Olshanii, Steven G. Jackson

Year

2015

Paper ID

27644

Status

Preprint

Abstract Read

~2 min

Abstract Words

104

Citations

N/A

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 {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 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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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1508.05954 [2] arXiv https://arxiv.org/abs/1508.05954 [3] Publisher https://arxiv.org/abs/1508.05954

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