Highly degenerate Fermi gases

The aim of this work is to study a dilute Fermi gas, whether it has a spin 1/2 or it has a high degeneracy. The starting point is to calculate the energy of the system. However, as we are dealing with a many body system, a perturbation series method will be applied. R. F. Bishop in reference [1] wro...

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Autor: Pera i Ferreruela, Jordi|||0000-0002-9313-9073
Tipo de documento: dissertação
Data de publicação:2020
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2117/349399
Acesso em linha:https://hdl.handle.net/2117/349399
Access Level:Acceso aberto
Palavra-chave:Gases
Fermi
gas
degeneracy
polarization
Gasos
Àrees temàtiques de la UPC::Física
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spelling Highly degenerate Fermi gasesPera i Ferreruela, Jordi|||0000-0002-9313-9073GasesFermigasdegeneracypolarizationGasosÀrees temàtiques de la UPC::FísicaThe aim of this work is to study a dilute Fermi gas, whether it has a spin 1/2 or it has a high degeneracy. The starting point is to calculate the energy of the system. However, as we are dealing with a many body system, a perturbation series method will be applied. R. F. Bishop in reference [1] wrote the terms of the expansion up to fourth order in the gas parameter, which is defined as the Fermi momentum times the S-wave scattering length, but only for the case of a non-polarized gas. What we do in this present work is the generalization of that expansion up to third order including any possible polarization. The universal expansion, that is up to second order, have been computed analytically. For the third order terms was not possible, but thanks to numerical calculation we have obtained the energy for different polarizations. Therefore, this work will contain a combination of both analytical and numerical calculus. The final expression obtained for the energy depends on the polarization, the gas parameter and the degeneracy and stands for low density gases. Afterwards, thanks to knowing the relation between the energy and the polarization, the study of the ferromagnetic phase transition is presented. We see how the transition point changes due to the degeneracy and what kind of phase transition we obtain. For spin 1/2 a continuous transition is observed, while a discontinuous transition happens for higher degeneracy. To complement the phase transition study, different physical properties have been computed, such as, the magnetic susceptibility, and the Tan?s constant. Our study is extended to highly degenerate Fermi gases which are now realized in cold Fermi labs.Universitat Politècnica de CatalunyaBoronat Medico, Jordi20202020-10-0920212021-07-15master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2117/349399reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3493992026-05-27T15:37:01Z
dc.title.none.fl_str_mv Highly degenerate Fermi gases
title Highly degenerate Fermi gases
spellingShingle Highly degenerate Fermi gases
Pera i Ferreruela, Jordi|||0000-0002-9313-9073
Gases
Fermi
gas
degeneracy
polarization
Gasos
Àrees temàtiques de la UPC::Física
title_short Highly degenerate Fermi gases
title_full Highly degenerate Fermi gases
title_fullStr Highly degenerate Fermi gases
title_full_unstemmed Highly degenerate Fermi gases
title_sort Highly degenerate Fermi gases
dc.creator.none.fl_str_mv Pera i Ferreruela, Jordi|||0000-0002-9313-9073
author Pera i Ferreruela, Jordi|||0000-0002-9313-9073
author_facet Pera i Ferreruela, Jordi|||0000-0002-9313-9073
author_role author
dc.contributor.none.fl_str_mv Boronat Medico, Jordi
dc.subject.none.fl_str_mv Gases
Fermi
gas
degeneracy
polarization
Gasos
Àrees temàtiques de la UPC::Física
topic Gases
Fermi
gas
degeneracy
polarization
Gasos
Àrees temàtiques de la UPC::Física
description The aim of this work is to study a dilute Fermi gas, whether it has a spin 1/2 or it has a high degeneracy. The starting point is to calculate the energy of the system. However, as we are dealing with a many body system, a perturbation series method will be applied. R. F. Bishop in reference [1] wrote the terms of the expansion up to fourth order in the gas parameter, which is defined as the Fermi momentum times the S-wave scattering length, but only for the case of a non-polarized gas. What we do in this present work is the generalization of that expansion up to third order including any possible polarization. The universal expansion, that is up to second order, have been computed analytically. For the third order terms was not possible, but thanks to numerical calculation we have obtained the energy for different polarizations. Therefore, this work will contain a combination of both analytical and numerical calculus. The final expression obtained for the energy depends on the polarization, the gas parameter and the degeneracy and stands for low density gases. Afterwards, thanks to knowing the relation between the energy and the polarization, the study of the ferromagnetic phase transition is presented. We see how the transition point changes due to the degeneracy and what kind of phase transition we obtain. For spin 1/2 a continuous transition is observed, while a discontinuous transition happens for higher degeneracy. To complement the phase transition study, different physical properties have been computed, such as, the magnetic susceptibility, and the Tan?s constant. Our study is extended to highly degenerate Fermi gases which are now realized in cold Fermi labs.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-10-09
2021
2021-07-15
dc.type.none.fl_str_mv master thesis
http://purl.org/coar/resource_type/c_bdcc
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/349399
url https://hdl.handle.net/2117/349399
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya
publisher.none.fl_str_mv Universitat Politècnica de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,228081

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