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Mass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D(6) Symmetry

We show that a system consisting of two interacting particles with mass ratio 3 or 1/3 in a hard-wall box can be exactly solved by using Bethe-type ansatz. The ansatz is based on a finite superposition of plane waves associated with a dihedral group D(6), which enforces the momentums after a series...

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Detalles Bibliográficos
Autores principales: Liu, Yanxia, Qi, Fan, Zhang, Yunbo, Chen, Shu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6911986/
https://www.ncbi.nlm.nih.gov/pubmed/31785556
http://dx.doi.org/10.1016/j.isci.2019.11.018
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author Liu, Yanxia
Qi, Fan
Zhang, Yunbo
Chen, Shu
author_facet Liu, Yanxia
Qi, Fan
Zhang, Yunbo
Chen, Shu
author_sort Liu, Yanxia
collection PubMed
description We show that a system consisting of two interacting particles with mass ratio 3 or 1/3 in a hard-wall box can be exactly solved by using Bethe-type ansatz. The ansatz is based on a finite superposition of plane waves associated with a dihedral group D(6), which enforces the momentums after a series of scattering and reflection processes to fulfill the D(6) symmetry. Starting from a two-body elastic collision model in a hard-wall box, we demonstrate how a finite momentum distribution is related to the D(2n) symmetry for permitted mass ratios. For a quantum system with mass ratio 3, we obtain exact eigenenergies and eigenstates by solving Bethe-type-ansatz equations for arbitrary interaction strength. A many-body excited state of the system is found to be independent of the interaction strength, i.e., the wave function looks exactly the same for non-interacting two particles or in the hard-core limit.
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spelling pubmed-69119862019-12-18 Mass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D(6) Symmetry Liu, Yanxia Qi, Fan Zhang, Yunbo Chen, Shu iScience Article We show that a system consisting of two interacting particles with mass ratio 3 or 1/3 in a hard-wall box can be exactly solved by using Bethe-type ansatz. The ansatz is based on a finite superposition of plane waves associated with a dihedral group D(6), which enforces the momentums after a series of scattering and reflection processes to fulfill the D(6) symmetry. Starting from a two-body elastic collision model in a hard-wall box, we demonstrate how a finite momentum distribution is related to the D(2n) symmetry for permitted mass ratios. For a quantum system with mass ratio 3, we obtain exact eigenenergies and eigenstates by solving Bethe-type-ansatz equations for arbitrary interaction strength. A many-body excited state of the system is found to be independent of the interaction strength, i.e., the wave function looks exactly the same for non-interacting two particles or in the hard-core limit. Elsevier 2019-11-15 /pmc/articles/PMC6911986/ /pubmed/31785556 http://dx.doi.org/10.1016/j.isci.2019.11.018 Text en © 2019 The Author(s) http://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Article
Liu, Yanxia
Qi, Fan
Zhang, Yunbo
Chen, Shu
Mass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D(6) Symmetry
title Mass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D(6) Symmetry
title_full Mass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D(6) Symmetry
title_fullStr Mass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D(6) Symmetry
title_full_unstemmed Mass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D(6) Symmetry
title_short Mass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D(6) Symmetry
title_sort mass-imbalanced atoms in a hard-wall trap: an exactly solvable model associated with d(6) symmetry
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6911986/
https://www.ncbi.nlm.nih.gov/pubmed/31785556
http://dx.doi.org/10.1016/j.isci.2019.11.018
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