3.10 Tesis doctorado

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Browsing 3.10 Tesis doctorado by browse.metadata.categoria "Matemática física y química"

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    Amorphous materials under stresses: understanding critical behavior
    (2022) Villarroel Cortés, Carlos Javier; Düring, Gustavo; Pontificia Universidad Católica de Chile. Facultad de Física
    Gran parte de los materiales que utilizamos a diario no se comportan como un sólido elástico o un fluido newtoniano cuando se les aplica deformación. Dentro de la extensa lista de estos materiales que presentan características no lineales en cantidades macroscópicas, podemos encontrar muchos alimentos que consumimos o incluso la piel humana. Comprender estos comportamientos particulares actualmente representa un desafóo importante con aplicaciones en la industria y la medicina. Para responder algunas de las preguntas que estos materiales particulares presentan hoy en día, en esta tesis, utilizando simulaciones numéricas de alto nivel, estudiamos dos fenómenos no lineales críticos, el fenómeno de “Yielding” y el fenómeno de “Strain-Stiffening”. En particular, la transición de “Yielding” se observa en materiales donde, dependiendo de la tensión aplicada, es posible pasar de un estado mecánicamente estable a uno que fluye como un líquido. En este contexto, mediante simulaciones de partículas blandas, se realiza el cálculo de los exponentes críticos que gobiernan el régimen fluido para dos escenarios de esfuerzos aplicados, y se estudia cómo las estadísticas de avalanchas pueden caracterizar el flujo. Finalmente, para el fenómeno “Strain-Stiffening”, se propone un nuevo modelo de redes semi-flexibles capaces de replicar este comportamiento, donde un sistema blando se transforma en uno rígido mediante la aplicación de una deformación. A su vez, este modelo es capaz de explicar y predecir de buena manera los exponentes críticos que gobiernan la transición.
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    Aspects of quantum gravity in AdS3/CFT2
    (2019) Reyes Raffo, Ignacio Andrés; Erdmenger, Johanna; Koch, Benjamin; Bañados, Máximo; Ströhmer, Raimund; Pontificia Universidad Católica de Chile. Facultad de Física
    The quest for finding a unifying theory for both quantum theory and gravity lies at the heart of much of the research in high energy physics. Although recent years have witnessed spectacular experimental confirmation of our expectations from Quantum Field Theory and General Relativity, the question of unification remains as a major open problem. In this context, the perturbative aspects of quantum black holes represent arguably the best of our knowledge of how to proceed in this pursue. In this thesis we investigate certain aspects of quantum gravity in 2 + 1 dimensional anti-de Sitter space (AdS3), and its connection to Conformal field theories in 1 + 1 dimensions (CFT2), via the AdS/CFT correspondence. We study the thermodynamics properties of higher spin black holes. By focusing on the spin-4 case, we show that black holes carrying higher spin charges display a rich phase diagram in the grand canonical ensemble, including phase transitions of the Hawking-Page type, first order inter-black hole transitions, and a second order critical point. We investigate recent proposals on the connection between bulk codimension-1 volumes and computational complexity in the CFT. Using Tensor Networks we provide concrete evidence of why these bulk volumes are related to the number of gates in a quantum circuit, and exhibit their topological properties. We provide a novel formula to compute this complexity directly in terms of entanglement entropies, using techniques from Kinematic space. We then move in a slightly different direction, and study the quantum properties of black holes via de Functional Renormalisation Group prescription coming from Asymptotic safety. We avoid the arbitrary scale setting by restricting to a narrower window in parameter space, where only Newton’s coupling and the cosmological constant are allowed to vary. By one assumption on the properties of Newton’s coupling, we find black hole solutions explicitly. We explore their thermodynamical properties, and discover that very large black holes exhibit very unusual features.The quest for finding a unifying theory for both quantum theory and gravity lies at the heart of much of the research in high energy physics. Although recent years have witnessed spectacular experimental confirmation of our expectations from Quantum Field Theory and General Relativity, the question of unification remains as a major open problem. In this context, the perturbative aspects of quantum black holes represent arguably the best of our knowledge of how to proceed in this pursue. In this thesis we investigate certain aspects of quantum gravity in 2 + 1 dimensional anti-de Sitter space (AdS3), and its connection to Conformal field theories in 1 + 1 dimensions (CFT2), via the AdS/CFT correspondence. We study the thermodynamics properties of higher spin black holes. By focusing on the spin-4 case, we show that black holes carrying higher spin charges display a rich phase diagram in the grand canonical ensemble, including phase transitions of the Hawking-Page type, first order inter-black hole transitions, and a second order critical point. We investigate recent proposals on the connection between bulk codimension-1 volumes and computational complexity in the CFT. Using Tensor Networks we provide concrete evidence of why these bulk volumes are related to the number of gates in a quantum circuit, and exhibit their topological properties. We provide a novel formula to compute this complexity directly in terms of entanglement entropies, using techniques from Kinematic space. We then move in a slightly different direction, and study the quantum properties of black holes via de Functional Renormalisation Group prescription coming from Asymptotic safety. We avoid the arbitrary scale setting by restricting to a narrower window in parameter space, where only Newton’s coupling and the cosmological constant are allowed to vary. By one assumption on the properties of Newton’s coupling, we find black hole solutions explicitly. We explore their thermodynamical properties, and discover that very large black holes exhibit very unusual features.The quest for finding a unifying theory for both quantum theory and gravity lies at the heart of much of the research in high energy physics. Although recent years have witnessed spectacular experimental confirmation of our expectations from Quantum Field Theory and General Relativity, the question of unification remains as a major open problem. In this context, the perturbative aspects of quantum black holes represent arguably the best of our knowledge of how to proceed in this pursue. In this thesis we investigate certain aspects of quantum gravity in 2 + 1 dimensional anti-de Sitter space (AdS3), and its connection to Conformal field theories in 1 + 1 dimensions (CFT2), via the AdS/CFT correspondence. We study the thermodynamics properties of higher spin black holes. By focusing on the spin-4 case, we show that black holes carrying higher spin charges display a rich phase diagram in the grand canonical ensemble, including phase transitions of the Hawking-Page type, first order inter-black hole transitions, and a second order critical point. We investigate recent proposals on the connection between bulk codimension-1 volumes and computational complexity in the CFT. Using Tensor Networks we provide concrete evidence of why these bulk volumes are related to the number of gates in a quantum circuit, and exhibit their topological properties. We provide a novel formula to compute this complexity directly in terms of entanglement entropies, using techniques from Kinematic space. We then move in a slightly different direction, and study the quantum properties of black holes via de Functional Renormalisation Group prescription coming from Asymptotic safety. We avoid the arbitrary scale setting by restricting to a narrower window in parameter space, where only Newton’s coupling and the cosmological constant are allowed to vary. By one assumption on the properties of Newton’s coupling, we find black hole solutions explicitly. We explore their thermodynamical properties, and discover that very large black holes exhibit very unusual features.
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    Control of wave-particle duality via atom-field interaction in double-slit schemes
    (2022) Miranda Rojas, Mario Ernesto Brayan; Orszag Posa, Miguel; Pontificia Universidad Católica de Chile. Instituto de Física
    The dual nature of light and matter represents an important challenge for science. Since the origins of quantum mechanics, several theoretical and experimental works have studied the wave and corpuscular properties of photons, atoms, electrons, etc. The main model that has been considered in the development of them has been the Young's double-slit scheme, by means of which the wave nature of light was demonstrated. However, it also can be used to obtain the particle-like properties of the systems. In case of considering identical slits, this model allows to obtain total fringe visibility on a screen located at a certain distance from the double-slit, and thus, null knowledge about the path followed by the object that crosses the scheme. Therefore, the system shows a wave behavior. In order to obtain information about the path taken by the objects (photons, atoms, electrons, etc), several authors have studied the coupling of external systems to double-slit schemes, which allows to know the path followed by the particle. As a consequence, the implementation of any type of path-detector results in the loss of fringe visibility, according to the principle of complementarity postulated by Bohr. In this research, we have considered the use of double-slit schemes and atom-field interactions to control the balance between fringe visibility and which-path information. We consider field cavities which act as path-detectors and they are represented by different quantum states. Instead of photons, our schemes are crossed by atoms, whose internal levels are correlated to the paths of the schemes. Therefore, based on the peparation of both, field and atom, we can study the balance between distinguishability, visibility and the concurrence present in the system. Our results show that the wave-particle duality can be controlled by atomic and field parameters, depending on the behavior that the experimenter wishes to observe, wave-like or particle-like. Additionally, we present a model in which a classical field can control the quantum atom-field interaction. Therefore, the amplitude of the classical field can also be considered as a controlling parameter of the wave-particle duality. Finally, based on our results, we propose a theoretical model to be implemented in quantum eraser and delayed choice experiments, which nowadays arouses great interest among researchers. Our results suggest that the wave-particle duality can be controlled even at times after the atom is registered on a screen, which allows us to choose the behavior of the system, wave-like or particle-like, at any moment.
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    Delving into the phenomenology of very special relativity: from subatomic particles to binary stars
    (2024) Santoni, Alessandro; Muñoz Tavera, Enrique; Koch, Benjamin; Pontificia Universidad Católica de Chile. Facultad de Física
    En esta tesis, se investigan las implicaciones de las teorías de violación de Lorentz (LV), enfocándose en Very Special Relativity (VSR) y sus consecuencias fenomenológicas. Presentada inicialmente como un mecanismo alternativo para las masas de los neutrinos, VSR se ha convertido en una parte significativa del marco general de la LV, distinguida por su estructura de grupo y la presencia de operadores no locales.Después de una introducción exhaustiva a los principios de la LV y VSR, presentamos sus modificaciones a la ecuación de Dirac. Una parte significativa de la tesis está dedicada al desarrollo de un formalismo Hamiltoniano dentro del contexto de VSR, abordando sus no-localidades. Este enfoque se extiende al límite no relativista, conectándolo al esquema de Schrödinger.Luego establecemos límites superiores en los parámetros de VSR, examinando sus correcciones a una amplia gama de sistemas y escenarios físicos, como los niveles de Landau de partículas cargadas, el factor g de los electrones, el espectro de energía de neutrones ultrafríos en el campo gravitatorio terrestre, y la emisión gravitacional de estrellas binarias. Este último análisis nos llevó a la construcción de una teoría de campo en VSR para partículas de espín-2, que resultó acomodar una masa del gravitón gauge-invariante.Mediante este estudio, conectamos varias predicciones teóricas con datos experimentales, allanando el camino para futuras exploraciones en teorías de LV y evidenciando su potencial para abordar preguntas no resueltas en la física moderna.
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    Desarrollo de hidrogeles a base de óxido de grafeno y cobre para usos en tratamiento de aguas
    (2022) Acuña Porras, Camilo; Díaz, Donovan; Pontificia Universidad Católica de Chile. Instituto de Física
    En el presente trabajo se modificó químicamente (grado de oxidación) y morfológicamente (tamaño de lámina) láminas de óxido de grafeno (GO) en solución sintetizado por método de Hummers modificado, además se sintetizó partículas de cobre (PCu) como refuerzo, posteriormente se crecieron hidrogeles con GO (GOH) y PCu (Cu-GOH) por vía hidrotermal. Con los hidrogeles se realizaron pruebas de adsorción de azul de metileno (AM) disuelto en agua, con el fin de determinar correlaciones entre las características químicas, estructurales y morfológicas de los hidrogeles con la capacidad y cinética de adsorción del AM como impureza del agua. La modificación química se realizó variando la cantidad del agente oxidante y el tipo de grafito de partida en la síntesis de GO. Esta modifico el grado oxidación y la distribución de grupos funcionales del GO, estudiado por espectroscopía XPS. Se encontró una reducción de los grupos funcionales oxigenados (OFG) al variar la cantidad de KMnO4, además de un punto de saturación en que el KMnO4 no influía en la química del GO. También se observó el efecto del tipo de grafito en la formación de hidrogeles, cuando se usó grafito amorfo este no se formó en contraposición a el grafito laminado donde se formó el hidrogel. La modificación morfológica consistió en un pretratamiento de sonicación a distintos intervalos de tiempo 30min, 60min, 90min, 120min, 180min y 240min en la síntesis de GO (in-situ). Y postratamiento de sonicación a distintas potencias comprendidas entre 50 y 200 W, y a tiempos de exposición de 5 y 10 minutos del GO sintetizado en solución (Post síntesis). El grado de oxidación y OFG se analizaron por los espectros de alta resolución (C1s y O1s) XPS, determinando que la sonicación del GO no presenta modificaciones significativas en la distribución de OFG y una consistencia en su grado de oxidación (relación C:O). Adicionalmente, el tamaño de lámina promedio se obtuvo por procesamiento de imágenes AFM, Para la solución de GO base encontró un valor entre 25040 - 33516 nm2 ; Para pretratamiento in-situ 57120 - 37220 nm2 ; Y post síntesis 5410 - 13620nm2 . Se observó que el tiempo de sonicación afecta el tamaño de lámina para el tratamiento in-situ como para el post síntesis. Los hidrogeles crecidos vía hidrotermal mostraron una estructura porosa (entrecruzamiento de láminas de GO) en la superficie por imágenes SEM. Químicamente se observó por los espectros de alta resolución C1s y O1s de XPS un proceso de reducción de los OFG por la síntesis hidrotermal. También la incorporación PCu afecto la morfología (interacción de láminas de GO con CuP), estructura (cambios de fases cristalinas de PCu) y química (Oxidación de PCu y reducción del GO) del hidrogel. Las pruebas de adsorción de AM se hicieron con dos concentraciones iniciales una de 1.2 mg⁄L para los hidrogeles modificados y con PCu Y de 100 mg⁄Lpara hidrogeles con la solución GO base (sin modificación morfológica y química), y condiciones de agitación y temperatura. El hidrogel con GO base y con PCu adsorben el AM eficientemente comparado a los modificados. Los hidrogeles bajo condiciones de temperatura y agitación tienen una capacidad de adsorción entre 21.99—38.45 mg⁄g. Estos hidrogeles, se analizó la cinética de adsorción mediante dos modelos, Pseudo-First Order (PFO) y Pseudo-Second Order (PSO), inicialmente la adsorción mostro que la remoción del tinte se produce por fisisorción dado los valores termodinámicos (entalpia, energía libre de Gibbs y entropía).
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    Dinámica de espín electrónico y nuclear en diamante
    (2021) Duarte Portilla, Héctor; Maze Ríos, Jerónimo; Pontificia Universidad Católica de Chile. Instituto de Física
    Durante los últimos años los centros de color o defectos ópticos en sólidos han emergido como potenciales candidatos para aplicaciones en metrología cuántica y transmisión y procesamiento de información cuántica. El modelamiento de las propiedades ópticas y de otros grados de libertad asociados a estos defectos es crucial para la implementación exitosa de estas aplicaciones o tecnologías. Muchas de estas propiedades como, por ejemplo, la coherencia de espines tanto electrónicos como nucleares, asociados a los defectos, son afectadas en gran medida por su interacción con el medio ambiente. Recientemente se ha encontrado experimentalmente que los espines nucleares aledaños pueden ser polarizados utilizando la dinámica del espín electrónico central del centro NV. La descripción y entendimiento de este fenómeno es crucial tanto para mitigar la decoherencia causados por el medio ambiente o baño de espines nucleares, como para el desarrollo de memorias nucleares y procesamiento de información ocupando espines nucleares. En esta tesis, en primer lugar, se realiza un estudio sobre evoluciones coherentes y se presenta un nuevo término no adiabático que permite entender fases acumuladas en evoluciones no adiabáticas. Logrando resolver de manera exacta la evolución no adiabática de un espín electrónico en presencia de un campo magnético oscilante. Luego se propone como utilizar las secuencias de Ramsey y Espín-ECHO sobre el centro NV para encontrar interferencia producto de una fase geométrica. Además, describimos la polarización de espines nucleares en el medio ambiente del centro de color NV bajo bombeo óptico de un espín central y radiaciónde microonda resonante con un espín electrónico central asociado a los centros de color NV. Se utiliza el formalismo matemático basado en la ecuación maestra para describir la dinámica del espín electrónico central en presencia de un baño radiativo fotónico y la acción de un bombeo óptico mediante un láser. Con ello se caracteriza la dinámica de polarización de espines nucleares acoplados coherentemente mediante interacción hiperfina con el espín electrónico central para varias condiciones de campo magnético externo (magnitud y orientación). Y se introduce la técnica de marco rotante y aproximación de marco rotante para caracterizar el rol de la radiación de microonda resonante con el espín electrónico central. Logramos ejemplificar cómo los acoplamientos por componente de interacción hiperfina posibilitan la polarización de espines nucleares, y como afecta o contribuye a este objetivo la magnitud de las componentes anisotrópicas de esta interacción. Se muestra además, para cuatro modelos de tasas de transición, como la tasas de cruce internos del sistema y las transiciones que no preservanespín reducen la polarización electrónica, lo que a su vez reduce la polarización nuclear. Por un lado, los resultados de esta tesis permitirán modelar evoluciones no adiabáticas, y por otro lado, muestran un camino para lograr validar el modelo de tasas de transición que mejor se ajuste al centro NV y polarizar un gran número de espines nucleares y a su vez habilitar aplicaciones en metrología como magnetometría con un bajo ruido magnético y por ende aumentando su sensibilidad.
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    Exploring the landscape of very special relativity
    (2020) Soto Villarroel, Alex; Alfaro Solís, Jorge Luis; Pontificia Universidad Católica de Chile. Instituto de Física
    In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.In this thesis we study the Very Special Relativity (VSR) framework. In particular we put the emphasis in the QED sector. We present the basics of the Lorentz group and the subgroup SIM(2), which is the symmetry of nature in this framework instead of the full Lorentz group. This symmetry allows introducing terms like n.p/n.q, where n transforms with a phase under SIM(2) transformations. With this construction, we can explain the neutrino mass without the addition of new particles. We explore VSR in two dimensions, showing that the Lorentz group allows VSR terms. This fact shows that we can revisit QED2. We compute the photon self-energy and the axial anomaly, finding differences from the standard result. In addition, in four dimensions, we review the electron self-energy, and we discuss the importance of a prescription to regulate infrared divergencies in the VSR integrals. We present a prescription to use when we introduce a possible gauge-invariant photon mass in the electron self-energy computation. The Coulomb scattering is presented as an example of a simple process that can be computed, showing a small signal of the vector n.
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    Loops in Holographic Correlators
    (2023) Muñoz Sandoval, Iván Ignacio; Bañados, Máximo; Pontificia Universidad Católica de Chile. Instituto de Física
    In the context of the Anti de-Sitter (AdS)/Conformal Field Theory (CFT) correspondence, we investigate the computation of holographic correlation functions for quantum fields in the bulk. Unlike the semi-classical approach, quantum computations involve Infra-Red (IR) and Ultra-Violet (UV) divergences. However, consistent with the semiclassical approximation, we find that IR infinities correspond to boundary divergences, while UV divergences correspond to the bulk. We present a systematic procedure for solving the perturbative quantum problem in the bulk. To illustrate our approach, we consider a Φ4 scalar field on a fixed AdS background and obtain the boundary correlation function in position and momentum space. In position space, we use two approximations: (i) we assume that the field is composed of the classical solution plus a quantum fluctuation, and we solve the classical part before using the holographic dictionary to obtain the quantum correction to the 2- and 4-point functions, requiring UV and IR renormalizations;(ii) using the quantum effective action, we renormalize the UV divergence from the equation of motions and then use the holographic dictionary to obtain the dual correlation function. Both formulations lead to the same conclusions and demonstrate that the bulk theory is renormalizable up to AdS7. Meanwhile, in momentum space, we use the background field method and renormalize the two-point function up to one loop, finding exact agreement with the position space computation. Finally, we provide a general set-up for obtaining the off-shell graviton bulk propagator, which is crucial for obtaining correlation functions for more realistic models.
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    On the effects of the modification of the metric in the gravitational context
    (2020) Rubio, Carlos; Alfaro Solís, Jorge Luis; Pontificia Universidad Católica de Chile. Instituto de Física
    This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.This thesis consists of two parts: In the first one, simple generic extensions of isotropic Durgapal–Fuloria stars to the anisotropic domain were presented. These anisotropic solutions were obtained by guided minimal deformations over the isotropic system. When the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors, by means of the minimal geometric deformation approach, were satisfied. Hence, the anisotropic field equations were isolated resulting in a more treatable set of equations. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, the observational effects of such anisotropies when measuring the surface redshift were discussed. To conclude, the consistency of the application of the method over the obtained anisotropic configurations was shown. In this manner, different anisotropic sectors can be isolated from each other and modeled in a simple and systematic way. About 70% of the Universe is Dark Energy, but there is still no consensus in the physics community on what the nature of it is. Delta Gravity (DG) is an alternative theory of gravitation that could solve this cosmological problem. DG is able to explain the SNe data successfully. In this work, we explored the cosmological fluctuations that give rise to the CMB through a hydrodynamic approximation. We calculated the gauge transformations for the metric and the perfect fluid to present the equations of the evolution of cosmological fluctuations, providing the necessary equations to solve, in a semi-analytical way, the scalar TT Power Spectrum. These equations were useful for comparing the DG theory with astronomical observations and thus, being able to restrict the DG cosmology, testing the compatibility with the CMB Planck data, which are currently in contradiction with SNe data.
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    Quantum measurement transition and entanglement of trapped ions and optomechanical systems
    (2024) Araya Sossa, Kevin Jordan; Orszag Posa, Miguel; Pontificia Universidad Católica de Chile. Instituto de Física
    Although quantum mechanics has been able to explain a wide range of physical, chemical, and even biological events with unprecedented accuracy, fundamental problems remain. For instance, the problem of quantum measurement and quantum entanglement, which are the most perplexing problems that have persisted since the foundation of quantum mechanics. Both are crucial quantum resources with broad applications in quantum information science, quantum computing and quantum optics. For this reason, this thesis is devoted to research the quantum measurement from the weakest regime to the strongest one as well as the dynamics of entanglement of different quantum systems. In this work, we study the measurement transition for a coherent-squeezed pointer state through a transition factor Γ that involves a system-pointer coupling by using an arbitrary measured observable A. In addition, we show that the shift in the pointer’s position and momentum establishes a relationship with a new value defined as the transition value, which generalizes the weak value as well as the conditional expectation value. Furthermore, a new strategy is introduced to achieve different measurement regimes by just adjusting the r and ϕξ parameters of the coherent-squeezed pointer state, opening an interesting way to test quantum mechanics foundations. Our scheme has been theoretically applied in a trapped ion illuminated by a bichromatic laser beam, with a high potential to be implemented in future experimental setups. Besides, we propose a method to regulate the quantum entanglement in the system mentioned before as well as a dispersive-hybrid system where a qubit is directly coupled to a cavity and a mechanical resonator. Entanglement can be controlled by only tuning the squeezing parameters associated with the vibrational mode. As the squeezing amplitude becomes larger, the maximal entanglement abruptly falls to zero at specific squeezing phases. For the hybrid system, it is also possible to generate entanglement for bipartitions from the qubit-cavity-resonator system after applying this strategy. Entangled qubit-cavity states are created through squeezing, even though there is no direct interaction between them. We also analyze the effect of atomic, optical, and vibrational losses on the quantum entanglement. We finally discuss our schemes to be implemented in future experimental setups and promote further studies to generalize the concept of “monogamy of entanglement” in tripartite systems outside qubit-composite states, in particular, (2 ⊗ 2 ⊗ n)-dimensional systems.
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    Single Molecules for Quantum Information and Metrology
    (2024) Escalante, Richard; Maze Ríos, Jerónimo; Pontificia Universidad Católica de Chile. Facultad de Física
    Single luminescent molecules provide a unique approach in the development of quantum technologies utilizing single photon sources. This includes quantum metrology by using a molecule’s sensitivity of its emission and magnetic properties to the local environment. In this thesis, we present our investigation of the optical properties of several different classes of luminescent molecules. We begin by providing some theoretical background of single quantum emitters as well as a brief description of the experimental methodologies and equipment. Next, we present an optical investigation of an ensemble of iron phthalocyanines molecules. This molecule possesses a ground state triplet, which is a desirable property for optically active spin qubits, but has a very weak optical emission. Diffraction limited spots displayed photo-instability in the form of blinking and irreversible bleaching. In ensemble form however, their optical stability allowed us to identify a possible Raman peak where we calculated the associated phonon frequency. Next, we present our single molecule study of vanadium phthalocyanine. This molecule has been documented as displaying very long spin coherence times even at room temperatures. We confirmed the presence of a single molecule by measuring the second order correlation function. Additionally, we looked at the intensity and spectral response as a function of the excitation laser polarization. The spectrum was fitted to a two Gaussian function, which may correspond to the two dipole transitions as suggested by theoretical calculations. Lastly, we looked at the optical properties of rare earth europium complexes known for having very sharp optical transitions in the emission spectrum, with each having varying levels of sensitivity to the local environment. Motivated by techniques to investigate non-radiative decay channels, we looked at the optical response of four different europium complexes under two 1 µs pulses of 515 nm laser separated by 1 µs. Each displayed a very different results and allowed us to identify the best candidates for single molecule studies. Finally, we looked at the emission spectrum as well as the optical response under a 6 µs long pulse using time-correlation single photon spectroscopy.
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    Transport phenomena in nontrivial topological materials
    (2023) Bonilla Moreno, Daniel Alejandro; Muñoz Tavera, Enrique; Pontificia Universidad Católica de Chile. Instituto de Física
    In this Ph.D. thesis, we present our work related to electronic quantum transport in materials with nontrivial topology. The fundamental objectives of our work were as follows: Firstly, to study ballistic transport in a nano junction made of a Type I Weyl semimetal material that contains a cylindrical defect created by the application of mechanical strain. In addition to the torsion effect modeled by a pseudo-gauge field, we added an external magnetic field and the repulsive effect of the deformation produced by the mismatch of the crystal lattice. Using the appropriate Landauer ballistic formalism to describe this type of system, we calculated their transport coefficients. Secondly, to study diffusive transport using the linear response regime, of a uniform and diluted concentration of the aforementioned defects through the bulk of a Weyl semimetal slab. For this purpose, we used the standard particle scattering theory, along with Green's functions techniques and diagrammatic methods. Finally, to study the diffusive transport through a single-layer graphene sheet doped with charged impurities, and influenced by the electromagnetic coupling to a topological insulator or a semiconductor. We pursued to investigate the role played by the magneto-electric effect produced by the topological insulator in transport properties, such as electrical conductivity. Here, we also applied a combination of methods based on scattering, linear response, Green's functions, and diagrammatics. We have obtained analytical expressions for the electrical and thermal conductivities, as well as for the Seebeck coefficient. Our results demonstrate the promising nature of these novel topological materials as thermoelectrics for future applications.