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An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems

Interacting one-dimensional quantum systems play a pivotal role in physics. Exact solutions can be obtained for the homogeneous case using the Bethe ansatz and bosonisation techniques. However, these approaches are not applicable when external confinement is present. Recent theoretical advances beyo...

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Autores principales: Andersen, M. E. S., Dehkharghani, A. S., Volosniev, A. G., Lindgren, E. J., Zinner, N. T.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4914841/
https://www.ncbi.nlm.nih.gov/pubmed/27324113
http://dx.doi.org/10.1038/srep28362
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author Andersen, M. E. S.
Dehkharghani, A. S.
Volosniev, A. G.
Lindgren, E. J.
Zinner, N. T.
author_facet Andersen, M. E. S.
Dehkharghani, A. S.
Volosniev, A. G.
Lindgren, E. J.
Zinner, N. T.
author_sort Andersen, M. E. S.
collection PubMed
description Interacting one-dimensional quantum systems play a pivotal role in physics. Exact solutions can be obtained for the homogeneous case using the Bethe ansatz and bosonisation techniques. However, these approaches are not applicable when external confinement is present. Recent theoretical advances beyond the Bethe ansatz and bosonisation allow us to predict the behaviour of one-dimensional confined systems with strong short-range interactions, and new experiments with cold atomic Fermi gases have already confirmed these theories. Here we demonstrate that a simple linear combination of the strongly interacting solution with the well-known solution in the limit of vanishing interactions provides a simple and accurate description of the system for all values of the interaction strength. This indicates that one can indeed capture the physics of confined one-dimensional systems by knowledge of the limits using wave functions that are much easier to handle than the output of typical numerical approaches. We demonstrate our scheme for experimentally relevant systems with up to six particles. Moreover, we show that our method works also in the case of mixed systems of particles with different masses. This is an important feature because these systems are known to be non-integrable and thus not solvable by the Bethe ansatz technique.
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spelling pubmed-49148412016-06-27 An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems Andersen, M. E. S. Dehkharghani, A. S. Volosniev, A. G. Lindgren, E. J. Zinner, N. T. Sci Rep Article Interacting one-dimensional quantum systems play a pivotal role in physics. Exact solutions can be obtained for the homogeneous case using the Bethe ansatz and bosonisation techniques. However, these approaches are not applicable when external confinement is present. Recent theoretical advances beyond the Bethe ansatz and bosonisation allow us to predict the behaviour of one-dimensional confined systems with strong short-range interactions, and new experiments with cold atomic Fermi gases have already confirmed these theories. Here we demonstrate that a simple linear combination of the strongly interacting solution with the well-known solution in the limit of vanishing interactions provides a simple and accurate description of the system for all values of the interaction strength. This indicates that one can indeed capture the physics of confined one-dimensional systems by knowledge of the limits using wave functions that are much easier to handle than the output of typical numerical approaches. We demonstrate our scheme for experimentally relevant systems with up to six particles. Moreover, we show that our method works also in the case of mixed systems of particles with different masses. This is an important feature because these systems are known to be non-integrable and thus not solvable by the Bethe ansatz technique. Nature Publishing Group 2016-06-21 /pmc/articles/PMC4914841/ /pubmed/27324113 http://dx.doi.org/10.1038/srep28362 Text en Copyright © 2016, Macmillan Publishers Limited http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Andersen, M. E. S.
Dehkharghani, A. S.
Volosniev, A. G.
Lindgren, E. J.
Zinner, N. T.
An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
title An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
title_full An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
title_fullStr An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
title_full_unstemmed An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
title_short An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
title_sort interpolatory ansatz captures the physics of one-dimensional confined fermi systems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4914841/
https://www.ncbi.nlm.nih.gov/pubmed/27324113
http://dx.doi.org/10.1038/srep28362
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