Static kinks in chains of interacting atoms

Autores
Landa, Haggai; Cormick, Maria Cecilia; Morigi, Giovanna
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent n ≥ 1. The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation and its width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap.
Fil: Landa, Haggai. Université Paris-Saclay; Francia
Fil: Cormick, Maria Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Morigi, Giovanna. Universitat Saarland; Alemania
Materia
FRENKEL
KONTOROVA
LONG
RANGE INTERACTIONS
SINE-GORDON KINK
TRAPPED IONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/137359
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/137359
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Static kinks in chains of interacting atomsLanda, HaggaiCormick, Maria CeciliaMorigi, GiovannaFRENKELKONTOROVALONGRANGE INTERACTIONSSINE-GORDON KINKTRAPPED IONShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent n ≥ 1. The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation and its width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap.Fil: Landa, Haggai. Université Paris-Saclay; FranciaFil: Cormick, Maria Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Morigi, Giovanna. Universitat Saarland; AlemaniaMolecular Diversity Preservation International2020-05-13info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/137359Landa, Haggai; Cormick, Maria Cecilia; Morigi, Giovanna; Static kinks in chains of interacting atoms; Molecular Diversity Preservation International; Condensed Matter; 5; 2; 13-5-2020; 1-82410-3896CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2004.03823info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2410-3896/5/2/35info:eu-repo/semantics/altIdentifier/doi/10.3390/condmat5020035info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:01:15Zoai:ri.conicet.gov.ar:11336/137359instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:01:15.377CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Static kinks in chains of interacting atoms
title Static kinks in chains of interacting atoms
spellingShingle Static kinks in chains of interacting atoms
Landa, Haggai
FRENKEL
KONTOROVA
LONG
RANGE INTERACTIONS
SINE-GORDON KINK
TRAPPED IONS
title_short Static kinks in chains of interacting atoms
title_full Static kinks in chains of interacting atoms
title_fullStr Static kinks in chains of interacting atoms
title_full_unstemmed Static kinks in chains of interacting atoms
title_sort Static kinks in chains of interacting atoms
dc.creator.none.fl_str_mv Landa, Haggai
Cormick, Maria Cecilia
Morigi, Giovanna
author Landa, Haggai
author_facet Landa, Haggai
Cormick, Maria Cecilia
Morigi, Giovanna
author_role author
author2 Cormick, Maria Cecilia
Morigi, Giovanna
author2_role author
author
dc.subject.none.fl_str_mv FRENKEL
KONTOROVA
LONG
RANGE INTERACTIONS
SINE-GORDON KINK
TRAPPED IONS
topic FRENKEL
KONTOROVA
LONG
RANGE INTERACTIONS
SINE-GORDON KINK
TRAPPED IONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent n ≥ 1. The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation and its width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap.
Fil: Landa, Haggai. Université Paris-Saclay; Francia
Fil: Cormick, Maria Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Morigi, Giovanna. Universitat Saarland; Alemania
description We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent n ≥ 1. The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation and its width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap.
publishDate 2020
dc.date.none.fl_str_mv 2020-05-13
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/137359
Landa, Haggai; Cormick, Maria Cecilia; Morigi, Giovanna; Static kinks in chains of interacting atoms; Molecular Diversity Preservation International; Condensed Matter; 5; 2; 13-5-2020; 1-8
2410-3896
CONICET Digital
CONICET
url http://hdl.handle.net/11336/137359
identifier_str_mv Landa, Haggai; Cormick, Maria Cecilia; Morigi, Giovanna; Static kinks in chains of interacting atoms; Molecular Diversity Preservation International; Condensed Matter; 5; 2; 13-5-2020; 1-8
2410-3896
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2004.03823
info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2410-3896/5/2/35
info:eu-repo/semantics/altIdentifier/doi/10.3390/condmat5020035
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Molecular Diversity Preservation International
publisher.none.fl_str_mv Molecular Diversity Preservation International
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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