On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Revista Brasileira de Ensino de Física (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172016000300410 |
Resumo: | A similarity transformation is an equivalence relation between square matrices which preserves determinant, trace and eigenvalues, playing a key role in quantum mechanics in simplifying complex hamiltonian systems and improving analytical results attainable from the use of perturbation theory. As a prototypical example, the conventional BCS theory of superconductivity is usually derived from a similarity transformation of the original electron-phonon hamiltonian, written in second quantized version. Here we discuss the general method for writing the similarity transformation operator in second quantized form, allowing one to recast a hamiltonian describing an interacting fermion-boson system into an effective theory in which only the desired degrees of freedom are kept after the transformation. |
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On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theoryfermion-boson systemssimilarity transformationsecond quantizationsuperconductivityA similarity transformation is an equivalence relation between square matrices which preserves determinant, trace and eigenvalues, playing a key role in quantum mechanics in simplifying complex hamiltonian systems and improving analytical results attainable from the use of perturbation theory. As a prototypical example, the conventional BCS theory of superconductivity is usually derived from a similarity transformation of the original electron-phonon hamiltonian, written in second quantized version. Here we discuss the general method for writing the similarity transformation operator in second quantized form, allowing one to recast a hamiltonian describing an interacting fermion-boson system into an effective theory in which only the desired degrees of freedom are kept after the transformation.Sociedade Brasileira de Física2016-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172016000300410Revista Brasileira de Ensino de Física v.38 n.3 2016reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/1806-9126-RBEF-2015-0032info:eu-repo/semantics/openAccessDartora,C.A.Campos,Fillipi Klos Rodrigues deeng2016-06-02T00:00:00Zoai:scielo:S1806-11172016000300410Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2016-06-02T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory |
title |
On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory |
spellingShingle |
On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory Dartora,C.A. fermion-boson systems similarity transformation second quantization superconductivity |
title_short |
On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory |
title_full |
On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory |
title_fullStr |
On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory |
title_full_unstemmed |
On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory |
title_sort |
On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory |
author |
Dartora,C.A. |
author_facet |
Dartora,C.A. Campos,Fillipi Klos Rodrigues de |
author_role |
author |
author2 |
Campos,Fillipi Klos Rodrigues de |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Dartora,C.A. Campos,Fillipi Klos Rodrigues de |
dc.subject.por.fl_str_mv |
fermion-boson systems similarity transformation second quantization superconductivity |
topic |
fermion-boson systems similarity transformation second quantization superconductivity |
description |
A similarity transformation is an equivalence relation between square matrices which preserves determinant, trace and eigenvalues, playing a key role in quantum mechanics in simplifying complex hamiltonian systems and improving analytical results attainable from the use of perturbation theory. As a prototypical example, the conventional BCS theory of superconductivity is usually derived from a similarity transformation of the original electron-phonon hamiltonian, written in second quantized version. Here we discuss the general method for writing the similarity transformation operator in second quantized form, allowing one to recast a hamiltonian describing an interacting fermion-boson system into an effective theory in which only the desired degrees of freedom are kept after the transformation. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172016000300410 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172016000300410 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/1806-9126-RBEF-2015-0032 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
dc.source.none.fl_str_mv |
Revista Brasileira de Ensino de Física v.38 n.3 2016 reponame:Revista Brasileira de Ensino de Física (Online) instname:Sociedade Brasileira de Física (SBF) instacron:SBF |
instname_str |
Sociedade Brasileira de Física (SBF) |
instacron_str |
SBF |
institution |
SBF |
reponame_str |
Revista Brasileira de Ensino de Física (Online) |
collection |
Revista Brasileira de Ensino de Física (Online) |
repository.name.fl_str_mv |
Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF) |
repository.mail.fl_str_mv |
||marcio@sbfisica.org.br |
_version_ |
1752122422885089280 |