Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/handle/123456789/30470 |
Resumo: | The scaling of the largest eigenvalue λ0 of the one-body density matrix of a system with respect to its particle number N defines an exponent C and a coefficient B via the asymptotic relation λ0 ∼ B NC. The case C = 1 corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a wellknown result also confirmed by bosonization gives instead C = 1/2. Here we investigate the inhomogeneous case, initially addressing the behavior of C in the presence of a general external trapping potential V . We argue that the value C = 1/2 characterizes the hard-core system independently of the nature of the potential V . We then define the exponents γ and β, which describe the scaling of the peak of the momentum distribution with N and the natural orbital corresponding to λ0, respectively, and we derive the scaling relation γ + 2β = C. Taking as a specific case the power-law potential V (x) ∝ x2n, we give analytical formulas for γ and β as functions of n. Analytical predictions for the coefficient B are also obtained. These formulas are derived by exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent |
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Colcelli, A.Vitti, JacopoMussardo, G.Trombettoni, A.2020-10-20T23:56:19Z2020-10-20T23:56:19Z2018-12-26COLCELLI, A.; VITI, J.; MUSSARDO, G.; TROMBETTONI, A.. Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas. Physical Review A, [S.L.], v. 98, n. 6, p. 063633-063633, 26 dez. 2018. Disponível em: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.063633. Acesso em: 18 ago. 2020. http://dx.doi.org/10.1103/physreva.98.0636332469-9934https://repositorio.ufrn.br/handle/123456789/3047010.1103/physreva.98.063633American Physical SocietyTonks-Girardeau gasUniversal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleThe scaling of the largest eigenvalue λ0 of the one-body density matrix of a system with respect to its particle number N defines an exponent C and a coefficient B via the asymptotic relation λ0 ∼ B NC. The case C = 1 corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a wellknown result also confirmed by bosonization gives instead C = 1/2. Here we investigate the inhomogeneous case, initially addressing the behavior of C in the presence of a general external trapping potential V . We argue that the value C = 1/2 characterizes the hard-core system independently of the nature of the potential V . We then define the exponents γ and β, which describe the scaling of the peak of the momentum distribution with N and the natural orbital corresponding to λ0, respectively, and we derive the scaling relation γ + 2β = C. Taking as a specific case the power-law potential V (x) ∝ x2n, we give analytical formulas for γ and β as functions of n. Analytical predictions for the coefficient B are also obtained. These formulas are derived by exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellentengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNinfo:eu-repo/semantics/openAccessORIGINALUniversalOff-diagonal_VITI_2018.pdfUniversalOff-diagonal_VITI_2018.pdfapplication/pdf724242https://repositorio.ufrn.br/bitstream/123456789/30470/1/UniversalOff-diagonal_VITI_2018.pdf33c02f75fb9a169e1056bd4c6c65c155MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/30470/2/license.txte9597aa2854d128fd968be5edc8a28d9MD52TEXTUniversalOff-diagonal_VITI_2018.pdf.txtUniversalOff-diagonal_VITI_2018.pdf.txtExtracted texttext/plain59514https://repositorio.ufrn.br/bitstream/123456789/30470/3/UniversalOff-diagonal_VITI_2018.pdf.txt7bfea9e22a7741a849a9fb5f3ab39b76MD53THUMBNAILUniversalOff-diagonal_VITI_2018.pdf.jpgUniversalOff-diagonal_VITI_2018.pdf.jpgGenerated Thumbnailimage/jpeg1744https://repositorio.ufrn.br/bitstream/123456789/30470/4/UniversalOff-diagonal_VITI_2018.pdf.jpg4d9f02d928c05e4de2b567ac86e1aac4MD54123456789/304702020-10-25 04:56:09.089oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2020-10-25T07:56:09Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas |
title |
Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas |
spellingShingle |
Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas Colcelli, A. Tonks-Girardeau gas |
title_short |
Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas |
title_full |
Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas |
title_fullStr |
Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas |
title_full_unstemmed |
Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas |
title_sort |
Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas |
author |
Colcelli, A. |
author_facet |
Colcelli, A. Vitti, Jacopo Mussardo, G. Trombettoni, A. |
author_role |
author |
author2 |
Vitti, Jacopo Mussardo, G. Trombettoni, A. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Colcelli, A. Vitti, Jacopo Mussardo, G. Trombettoni, A. |
dc.subject.por.fl_str_mv |
Tonks-Girardeau gas |
topic |
Tonks-Girardeau gas |
description |
The scaling of the largest eigenvalue λ0 of the one-body density matrix of a system with respect to its particle number N defines an exponent C and a coefficient B via the asymptotic relation λ0 ∼ B NC. The case C = 1 corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a wellknown result also confirmed by bosonization gives instead C = 1/2. Here we investigate the inhomogeneous case, initially addressing the behavior of C in the presence of a general external trapping potential V . We argue that the value C = 1/2 characterizes the hard-core system independently of the nature of the potential V . We then define the exponents γ and β, which describe the scaling of the peak of the momentum distribution with N and the natural orbital corresponding to λ0, respectively, and we derive the scaling relation γ + 2β = C. Taking as a specific case the power-law potential V (x) ∝ x2n, we give analytical formulas for γ and β as functions of n. Analytical predictions for the coefficient B are also obtained. These formulas are derived by exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018-12-26 |
dc.date.accessioned.fl_str_mv |
2020-10-20T23:56:19Z |
dc.date.available.fl_str_mv |
2020-10-20T23:56:19Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
COLCELLI, A.; VITI, J.; MUSSARDO, G.; TROMBETTONI, A.. Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas. Physical Review A, [S.L.], v. 98, n. 6, p. 063633-063633, 26 dez. 2018. Disponível em: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.063633. Acesso em: 18 ago. 2020. http://dx.doi.org/10.1103/physreva.98.063633 |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/handle/123456789/30470 |
dc.identifier.issn.none.fl_str_mv |
2469-9934 |
dc.identifier.doi.none.fl_str_mv |
10.1103/physreva.98.063633 |
identifier_str_mv |
COLCELLI, A.; VITI, J.; MUSSARDO, G.; TROMBETTONI, A.. Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas. Physical Review A, [S.L.], v. 98, n. 6, p. 063633-063633, 26 dez. 2018. Disponível em: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.063633. Acesso em: 18 ago. 2020. http://dx.doi.org/10.1103/physreva.98.063633 2469-9934 10.1103/physreva.98.063633 |
url |
https://repositorio.ufrn.br/handle/123456789/30470 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
American Physical Society |
publisher.none.fl_str_mv |
American Physical Society |
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