Effects of disorder on the dynamics of the XY chain.
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFOP |
Texto Completo: | http://www.repositorio.ufop.br/handle/123456789/4482 https://doi.org/10.1103/PhysRevB.68.014406 |
Resumo: | We investigate the effects of disorder on the dynamics of the s51/2 XY model in one dimension. The energy couplings are randomly drawn independently from a bimodal distribution. We use an extension of the method of recurrence relations, in which an averaging over realizations of disorder is incorporated into the definition of the scalar product of the dynamical Hilbert space of sj z (t), to determine analytically the first six basis vectors as well as the corresponding recurrants. We then use an ansatz for the higher-order recurrants, based on the behavior of the first ones exactly determined, to obtain the time-dependent correlation functions and spectral densities for several degrees of disorder. We find that the dynamics at long times is governed by the stronger couplings present in the system even if only a very small amount of disorder is present. In the long-time limit, the correlation functions oscillate at the cutoff frequency of the disorderless stronger-coupling case, with the spectral densities displaying tails that end at the stronger-coupling cutoff frequency. |
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Nunes, Maria Eugenia SilvaFlorencio Junior, João2015-02-24T18:36:36Z2015-02-24T18:36:36Z2003NUNES, M. E. S.; FLORENCIO JUNIOR, J. Effects of disorder on the dynamics of the XY chain. Physical Review B - Solid State, v. 68, p. 14406-14411, 2003. Disponível em: <http://journals.aps.org/prb/pdf/10.1103/PhysRevB.68.014406>. Acesso em: 23 fev. 2015.1550-235Xhttp://www.repositorio.ufop.br/handle/123456789/4482https://doi.org/10.1103/PhysRevB.68.014406We investigate the effects of disorder on the dynamics of the s51/2 XY model in one dimension. The energy couplings are randomly drawn independently from a bimodal distribution. We use an extension of the method of recurrence relations, in which an averaging over realizations of disorder is incorporated into the definition of the scalar product of the dynamical Hilbert space of sj z (t), to determine analytically the first six basis vectors as well as the corresponding recurrants. We then use an ansatz for the higher-order recurrants, based on the behavior of the first ones exactly determined, to obtain the time-dependent correlation functions and spectral densities for several degrees of disorder. We find that the dynamics at long times is governed by the stronger couplings present in the system even if only a very small amount of disorder is present. In the long-time limit, the correlation functions oscillate at the cutoff frequency of the disorderless stronger-coupling case, with the spectral densities displaying tails that end at the stronger-coupling cutoff frequency.Effects of disorder on the dynamics of the XY chain.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleO periódico Physical Review B permite o arquivamento da versão/PDF do editor no Repositório Institucional. Fonte: Sherpa/Romeo <http://www.sherpa.ac.uk/romeo/search.php?issn=0163-1829>. Acesso em: 03 jan. 2017.info:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOPLICENSElicense.txtlicense.txttext/plain; charset=utf-82636http://www.repositorio.ufop.br/bitstream/123456789/4482/2/license.txtc2ffdd99e58acf69202dff00d361f23aMD52ORIGINALARTIGO_EffectsDisorderDynamics.pdfARTIGO_EffectsDisorderDynamics.pdfapplication/pdf72798http://www.repositorio.ufop.br/bitstream/123456789/4482/1/ARTIGO_EffectsDisorderDynamics.pdf759f162eb2eaa3e32f0cc5e613945aabMD51123456789/44822019-06-18 14:23:29.182oai:localhost: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Repositório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332019-06-18T18:23:29Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false |
dc.title.pt_BR.fl_str_mv |
Effects of disorder on the dynamics of the XY chain. |
title |
Effects of disorder on the dynamics of the XY chain. |
spellingShingle |
Effects of disorder on the dynamics of the XY chain. Nunes, Maria Eugenia Silva |
title_short |
Effects of disorder on the dynamics of the XY chain. |
title_full |
Effects of disorder on the dynamics of the XY chain. |
title_fullStr |
Effects of disorder on the dynamics of the XY chain. |
title_full_unstemmed |
Effects of disorder on the dynamics of the XY chain. |
title_sort |
Effects of disorder on the dynamics of the XY chain. |
author |
Nunes, Maria Eugenia Silva |
author_facet |
Nunes, Maria Eugenia Silva Florencio Junior, João |
author_role |
author |
author2 |
Florencio Junior, João |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Nunes, Maria Eugenia Silva Florencio Junior, João |
description |
We investigate the effects of disorder on the dynamics of the s51/2 XY model in one dimension. The energy couplings are randomly drawn independently from a bimodal distribution. We use an extension of the method of recurrence relations, in which an averaging over realizations of disorder is incorporated into the definition of the scalar product of the dynamical Hilbert space of sj z (t), to determine analytically the first six basis vectors as well as the corresponding recurrants. We then use an ansatz for the higher-order recurrants, based on the behavior of the first ones exactly determined, to obtain the time-dependent correlation functions and spectral densities for several degrees of disorder. We find that the dynamics at long times is governed by the stronger couplings present in the system even if only a very small amount of disorder is present. In the long-time limit, the correlation functions oscillate at the cutoff frequency of the disorderless stronger-coupling case, with the spectral densities displaying tails that end at the stronger-coupling cutoff frequency. |
publishDate |
2003 |
dc.date.issued.fl_str_mv |
2003 |
dc.date.accessioned.fl_str_mv |
2015-02-24T18:36:36Z |
dc.date.available.fl_str_mv |
2015-02-24T18:36:36Z |
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 |
NUNES, M. E. S.; FLORENCIO JUNIOR, J. Effects of disorder on the dynamics of the XY chain. Physical Review B - Solid State, v. 68, p. 14406-14411, 2003. Disponível em: <http://journals.aps.org/prb/pdf/10.1103/PhysRevB.68.014406>. Acesso em: 23 fev. 2015. |
dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufop.br/handle/123456789/4482 |
dc.identifier.issn.none.fl_str_mv |
1550-235X |
dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.1103/PhysRevB.68.014406 |
identifier_str_mv |
NUNES, M. E. S.; FLORENCIO JUNIOR, J. Effects of disorder on the dynamics of the XY chain. Physical Review B - Solid State, v. 68, p. 14406-14411, 2003. Disponível em: <http://journals.aps.org/prb/pdf/10.1103/PhysRevB.68.014406>. Acesso em: 23 fev. 2015. 1550-235X |
url |
http://www.repositorio.ufop.br/handle/123456789/4482 https://doi.org/10.1103/PhysRevB.68.014406 |
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eng |
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eng |
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