Local temperature and correlations in quantum many-body systems

Quantum Mechanics was established as the theory of the microscopic world, which allowed to understand processes in atoms and molecules. Its emergence led to a new scientific paradigm that quickly spread to different research fields. Two relevant examples are Quantum Thermodynamics and Quantum Many-B...

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Detalhes bibliográficos
Autor: Hernández Santana, Senaida
Tipo de documento: tese
Data de publicação:2019
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:2117/132775
Acesso em linha:https://hdl.handle.net/2117/132775
https://dx.doi.org/10.5821/dissertation-2117-132775
Access Level:Acceso aberto
Palavra-chave:Àrees temàtiques de la UPC::Física
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dc.title.none.fl_str_mv Local temperature and correlations in quantum many-body systems
title Local temperature and correlations in quantum many-body systems
spellingShingle Local temperature and correlations in quantum many-body systems
Hernández Santana, Senaida
Àrees temàtiques de la UPC::Física
title_short Local temperature and correlations in quantum many-body systems
title_full Local temperature and correlations in quantum many-body systems
title_fullStr Local temperature and correlations in quantum many-body systems
title_full_unstemmed Local temperature and correlations in quantum many-body systems
title_sort Local temperature and correlations in quantum many-body systems
dc.creator.none.fl_str_mv Hernández Santana, Senaida
author Hernández Santana, Senaida
author_facet Hernández Santana, Senaida
author_role author
dc.contributor.none.fl_str_mv Acín dal Maschio, Antonio
Gogolin, Christian
dc.subject.none.fl_str_mv Àrees temàtiques de la UPC::Física
topic Àrees temàtiques de la UPC::Física
description Quantum Mechanics was established as the theory of the microscopic world, which allowed to understand processes in atoms and molecules. Its emergence led to a new scientific paradigm that quickly spread to different research fields. Two relevant examples are Quantum Thermodynamics and Quantum Many-Body Theory, where the former aims to characterize thermodynamic processes in quantum systems and the latter intends to understand the properties of quantum many-body systems. In this thesis, we tackle some of the questions in the overlap between these disciplines, focusing on the concepts of temperature and correlations. Specifically, it contains results on the following topics: locality of temperature, correlations in long-range interacting systems and thermometry at low temperature. The problem of locality of temperature is considered for a system at thermal equilibrium and consists in studying whether it is possible to assign a temperature to any of the subsystems of the global system such that both local and global temperatures are equal. We tackle this problem in two different settings, for generic one-dimensional spin chains and for a bosonic system with a phase transition at non-zero temperature. In the first case, we consider generic one-dimensional translation-invariant spin systems with short-range interactions and prove that it is always possible to assign a local temperature equal to the global one for any temperature, including at criticality. For the second case, we consider a three-dimensional discretized version of the Bose-Einstein model at the grand canonical ensemble for some temperature and particle density, and characterize its non-zero-temperature phase transition. Then, we show that temperature is locally well-defined at any temperature and at any particle density, including at the phase transition. Additionally, we observe a qualitative relation between correlations and locality of temperature in the system. Moving to correlations, we consider fermionic two-site long-range interacting systems at thermal equilibrium. We show that correlations between anti-commutative operators at non-zero temperature are upper bounded by a function that decays polynomially with the distance and with an exponent that is equal to the interaction exponent, which characterizes the interactions in the Hamiltonian. Moreover, we show that our bound is asymptotically tight and that the results extend to density-density correlations as well as other types of correlations for quadratic and fermionic Hamiltonians with long-range interactions. Regarding the results on thermometry, we consider a bosonic model and prove that strong coupling between the probe and the system can boost the thermal sensitivity for low temperature. Furthermore, we provide a feasible measurement scheme capable of producing optimal estimates at the considered regime.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-04-12
2019
2019-05-09
dc.type.none.fl_str_mv doctoral thesis
http://purl.org/coar/resource_type/c_db06
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/132775
https://dx.doi.org/10.5821/dissertation-2117-132775
url https://hdl.handle.net/2117/132775
https://dx.doi.org/10.5821/dissertation-2117-132775
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
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rights_invalid_str_mv open access
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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
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instname_str Universitat Politècnica de Catalunya (UPC)
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spelling Local temperature and correlations in quantum many-body systemsHernández Santana, SenaidaÀrees temàtiques de la UPC::FísicaQuantum Mechanics was established as the theory of the microscopic world, which allowed to understand processes in atoms and molecules. Its emergence led to a new scientific paradigm that quickly spread to different research fields. Two relevant examples are Quantum Thermodynamics and Quantum Many-Body Theory, where the former aims to characterize thermodynamic processes in quantum systems and the latter intends to understand the properties of quantum many-body systems. In this thesis, we tackle some of the questions in the overlap between these disciplines, focusing on the concepts of temperature and correlations. Specifically, it contains results on the following topics: locality of temperature, correlations in long-range interacting systems and thermometry at low temperature. The problem of locality of temperature is considered for a system at thermal equilibrium and consists in studying whether it is possible to assign a temperature to any of the subsystems of the global system such that both local and global temperatures are equal. We tackle this problem in two different settings, for generic one-dimensional spin chains and for a bosonic system with a phase transition at non-zero temperature. In the first case, we consider generic one-dimensional translation-invariant spin systems with short-range interactions and prove that it is always possible to assign a local temperature equal to the global one for any temperature, including at criticality. For the second case, we consider a three-dimensional discretized version of the Bose-Einstein model at the grand canonical ensemble for some temperature and particle density, and characterize its non-zero-temperature phase transition. Then, we show that temperature is locally well-defined at any temperature and at any particle density, including at the phase transition. Additionally, we observe a qualitative relation between correlations and locality of temperature in the system. Moving to correlations, we consider fermionic two-site long-range interacting systems at thermal equilibrium. We show that correlations between anti-commutative operators at non-zero temperature are upper bounded by a function that decays polynomially with the distance and with an exponent that is equal to the interaction exponent, which characterizes the interactions in the Hamiltonian. Moreover, we show that our bound is asymptotically tight and that the results extend to density-density correlations as well as other types of correlations for quadratic and fermionic Hamiltonians with long-range interactions. Regarding the results on thermometry, we consider a bosonic model and prove that strong coupling between the probe and the system can boost the thermal sensitivity for low temperature. Furthermore, we provide a feasible measurement scheme capable of producing optimal estimates at the considered regime.La Mecánica Cuántica fue establecida como la teoría del mundo microscópico, el cual permitió entender los procesos en átomos y moléculas. Su nacimiento llevo a un nuevo paradigma científico que se propagó rápidamente a otros campos de investigación. Dos ejemplos relevantes son la Termodinámica Cuántica y la Teoría Cuántica de muchos cuerpos, donde la primera pretende caracterizar los procesos termodinamicos en sistemas cuántico y la segunda intenta entender las propiedades de los sistemas cuánticos de muchos cuerpos. En esta tesis, atacamos algunas de las preguntas en la intersección entre estas disciplinas, enfocandonos en los conceptos de la temperatura y las correlaciones. Específicamente, contiene resutlados en os siguientes temas: localidad de la temperature, correlaciones en sistemas interactuantes de largo alcance y termometría a baja temperature. El problema de localidad de la temperatura es considerado para un sistema a equilibrio térmico y consiste en estudiar si es posible asignar temperature a cualquiera de los subsistemas del sistema global tal que la temperature local y global sean equivalentes. Atacamos este problemas en dos casos diferentes, for cadenas de spines genéricas y para un sistema de bosones con una transición de fase a temperature distinta a cero. En el primer caso, consideramos sistemas de espines invarantes traslacional y de una dimensión con interactions de corto alcance y provamos que siempre es posible asignar una temperature local igual a la global para cualquier temperature, incluyendo en la criticalidad. Para el segundo caso, consideramos una versión 3D y discretizada del modelo de Bose-Einstein en el estado gran canónico para alguna temperature y densidad de partículas, y caracterizamos su transición a temperatura distinta a cero. Luego, mostramos que la temperature esta localmente bien definida a cualquier temperature y cualquier densidad de partículas, incluyendo en la transición de fase. Adicionalment, observamos una relación cualitativa entre las correlaciones y la localidad de la temperature en el sistema. Moviéndonos a las correlaciones, consideramos sistemas fermiónicos de con interaction entre dos cuerpos y de largo alcance a equilibrio térmico. Mostramos que las correlations entre los operadores anti-comutativos at temperatura distinta a cero estan acotadas por arriba por una función que decae polinomiamente con la distancia y con un exponent que es igual al exponente de interacción, el cual caracteriza las interacciones en el Hamiltoniano. Además, mostrado que nuestro límite es "ajustado" asintoticamente y que los resultados se extiense a correlations entre operadores de densidad y a otros tipos de correlaciones para Hamiltonianos cuadráticos y fermiónicos con interacciones de largo alcance. Sobre los resultados en termometría, consideramos un modelo bosónico y provamos que el acoplamiento fuerte entre el termómetro y el sistema pueda incrementar la sensibilidad térmica para baja temperatura. Además, explicamos un esquema de medida accesible y capaz de producir estimación óptimas en el régimen que consideramosUniversitat Politècnica de CatalunyaAcín dal Maschio, AntonioGogolin, Christian20192019-04-1220192019-05-09doctoral thesishttp://purl.org/coar/resource_type/c_db06VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/doctoralThesisapplication/pdfhttps://hdl.handle.net/2117/132775https://dx.doi.org/10.5821/dissertation-2117-132775reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1327752026-05-27T15:37:01Z
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