Triatomic molecules in two-dimensional layers
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações do ITA |
Texto Completo: | http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2056 |
Resumo: | We found universal laws for the spectrum of two-dimensional three-body systems, composed by two identical particles and a distinct one (AAB). These universal laws appear when the potential range (r_0) is much smaller than the size of the system. In two dimensions this condition is formulated as (E2 is the two-body energy and ? is the reduced mass). The zero range model, which is very appropriated to establish the universal laws, is introduced through the ?-Dirac potential. We derive the corresponding two-dimensional Faddeev equations for the three-body system and solve them numerically in momentum space. Our results showed that the three-body binding energy monotonically increases with the two-body binding energy, and such dependence is more pronounced than the mass variations. We found that the three-body energy depends logarithmic on the two-body energy for large values. Furthermore, been m=mB/mA the ratio between the masses of the B and A particles, the three-body energy is mass-independent for m ? ? and increase without bounds for m ?0. The limit of two non-interacting identical particles is also studied in the AAB system. We found that the two-dimensional three-body system always support at least two bound states and more bound states appear for m<0.22. Finally, we analyze the particular limit of m ?0 using the adiabatic approximation. This approximation can be used to study the three-body system in two-dimensions with an accuracy better than 10% compared to the solutions of the Faddeev equations, for m ? 0.01. |
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Biblioteca Digital de Teses e Dissertações do ITA |
spelling |
Triatomic molecules in two-dimensional layersProblema de poucos corposProblema de três corposMoléculas triatômicasGasesBaixa temperaturaEnergiaFísica molecularFísica nuclearWe found universal laws for the spectrum of two-dimensional three-body systems, composed by two identical particles and a distinct one (AAB). These universal laws appear when the potential range (r_0) is much smaller than the size of the system. In two dimensions this condition is formulated as (E2 is the two-body energy and ? is the reduced mass). The zero range model, which is very appropriated to establish the universal laws, is introduced through the ?-Dirac potential. We derive the corresponding two-dimensional Faddeev equations for the three-body system and solve them numerically in momentum space. Our results showed that the three-body binding energy monotonically increases with the two-body binding energy, and such dependence is more pronounced than the mass variations. We found that the three-body energy depends logarithmic on the two-body energy for large values. Furthermore, been m=mB/mA the ratio between the masses of the B and A particles, the three-body energy is mass-independent for m ? ? and increase without bounds for m ?0. The limit of two non-interacting identical particles is also studied in the AAB system. We found that the two-dimensional three-body system always support at least two bound states and more bound states appear for m<0.22. Finally, we analyze the particular limit of m ?0 using the adiabatic approximation. This approximation can be used to study the three-body system in two-dimensions with an accuracy better than 10% compared to the solutions of the Faddeev equations, for m ? 0.01.Instituto Tecnológico de AeronáuticaTobias FredericoFilipe Furlan Bellotti2012-06-14info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2056reponame:Biblioteca Digital de Teses e Dissertações do ITAinstname:Instituto Tecnológico de Aeronáuticainstacron:ITAenginfo:eu-repo/semantics/openAccessapplication/pdf2019-02-02T14:03:48Zoai:agregador.ibict.br.BDTD_ITA:oai:ita.br:2056http://oai.bdtd.ibict.br/requestopendoar:null2020-05-28 19:38:08.288Biblioteca Digital de Teses e Dissertações do ITA - Instituto Tecnológico de Aeronáuticatrue |
dc.title.none.fl_str_mv |
Triatomic molecules in two-dimensional layers |
title |
Triatomic molecules in two-dimensional layers |
spellingShingle |
Triatomic molecules in two-dimensional layers Filipe Furlan Bellotti Problema de poucos corpos Problema de três corpos Moléculas triatômicas Gases Baixa temperatura Energia Física molecular Física nuclear |
title_short |
Triatomic molecules in two-dimensional layers |
title_full |
Triatomic molecules in two-dimensional layers |
title_fullStr |
Triatomic molecules in two-dimensional layers |
title_full_unstemmed |
Triatomic molecules in two-dimensional layers |
title_sort |
Triatomic molecules in two-dimensional layers |
author |
Filipe Furlan Bellotti |
author_facet |
Filipe Furlan Bellotti |
author_role |
author |
dc.contributor.none.fl_str_mv |
Tobias Frederico |
dc.contributor.author.fl_str_mv |
Filipe Furlan Bellotti |
dc.subject.por.fl_str_mv |
Problema de poucos corpos Problema de três corpos Moléculas triatômicas Gases Baixa temperatura Energia Física molecular Física nuclear |
topic |
Problema de poucos corpos Problema de três corpos Moléculas triatômicas Gases Baixa temperatura Energia Física molecular Física nuclear |
dc.description.none.fl_txt_mv |
We found universal laws for the spectrum of two-dimensional three-body systems, composed by two identical particles and a distinct one (AAB). These universal laws appear when the potential range (r_0) is much smaller than the size of the system. In two dimensions this condition is formulated as (E2 is the two-body energy and ? is the reduced mass). The zero range model, which is very appropriated to establish the universal laws, is introduced through the ?-Dirac potential. We derive the corresponding two-dimensional Faddeev equations for the three-body system and solve them numerically in momentum space. Our results showed that the three-body binding energy monotonically increases with the two-body binding energy, and such dependence is more pronounced than the mass variations. We found that the three-body energy depends logarithmic on the two-body energy for large values. Furthermore, been m=mB/mA the ratio between the masses of the B and A particles, the three-body energy is mass-independent for m ? ? and increase without bounds for m ?0. The limit of two non-interacting identical particles is also studied in the AAB system. We found that the two-dimensional three-body system always support at least two bound states and more bound states appear for m<0.22. Finally, we analyze the particular limit of m ?0 using the adiabatic approximation. This approximation can be used to study the three-body system in two-dimensions with an accuracy better than 10% compared to the solutions of the Faddeev equations, for m ? 0.01. |
description |
We found universal laws for the spectrum of two-dimensional three-body systems, composed by two identical particles and a distinct one (AAB). These universal laws appear when the potential range (r_0) is much smaller than the size of the system. In two dimensions this condition is formulated as (E2 is the two-body energy and ? is the reduced mass). The zero range model, which is very appropriated to establish the universal laws, is introduced through the ?-Dirac potential. We derive the corresponding two-dimensional Faddeev equations for the three-body system and solve them numerically in momentum space. Our results showed that the three-body binding energy monotonically increases with the two-body binding energy, and such dependence is more pronounced than the mass variations. We found that the three-body energy depends logarithmic on the two-body energy for large values. Furthermore, been m=mB/mA the ratio between the masses of the B and A particles, the three-body energy is mass-independent for m ? ? and increase without bounds for m ?0. The limit of two non-interacting identical particles is also studied in the AAB system. We found that the two-dimensional three-body system always support at least two bound states and more bound states appear for m<0.22. Finally, we analyze the particular limit of m ?0 using the adiabatic approximation. This approximation can be used to study the three-body system in two-dimensions with an accuracy better than 10% compared to the solutions of the Faddeev equations, for m ? 0.01. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-06-14 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/masterThesis |
status_str |
publishedVersion |
format |
masterThesis |
dc.identifier.uri.fl_str_mv |
http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2056 |
url |
http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2056 |
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.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Instituto Tecnológico de Aeronáutica |
publisher.none.fl_str_mv |
Instituto Tecnológico de Aeronáutica |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações do ITA instname:Instituto Tecnológico de Aeronáutica instacron:ITA |
reponame_str |
Biblioteca Digital de Teses e Dissertações do ITA |
collection |
Biblioteca Digital de Teses e Dissertações do ITA |
instname_str |
Instituto Tecnológico de Aeronáutica |
instacron_str |
ITA |
institution |
ITA |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações do ITA - Instituto Tecnológico de Aeronáutica |
repository.mail.fl_str_mv |
|
subject_por_txtF_mv |
Problema de poucos corpos Problema de três corpos Moléculas triatômicas Gases Baixa temperatura Energia Física molecular Física nuclear |
_version_ |
1706809279074271232 |