Models of quantum walks which admit continuous time and continuous spacetime limits have recently led to quantum simulation schemes for simulating fermions in relativistic and non relativistic regimes (Di Molfetta and Arrighi, 2020). This work continues the study of relationships between discrete time quantum walks (DTQW) and their ostensive continuum counterparts by developing a more general framework than was done in (Di Molfetta and Arrighi, 2020) to evaluate the continuous time limit of these discrete quantum systems. Under this framework, we prove two constructive theorems concerning which internal discrete transitions ("coins") admit nontrivial continuum limits in 1D+1. We additionally prove that the continuous space limit of the continuous time limit of the DTQW can only yield massless states which obey the Dirac equation. We also demonstrate that for general coins the continuous time limit of the DTQW can be identified with the canonical continuous time quantum walk (CTQW) when the coin is allowed to transition through the continuum limit process. Finally, we introduce the Plastic Quantum Walk, or a quantum walk which admits both continuous time and continuous spacetime limits and, as a novel result, we use our 1D+1 results to obtain necessary and sufficient conditions concerning which DTQWs admit plasticity in 2D+1, showing the resulting Hamiltonians. We consider coin operators as general 4 parameter unitary matrices, with parameters which are functions of the lattice step size 𝜖. This dependence on 𝜖 encapsulates all functions of 𝜖 for which a Taylor series expansion in 𝜖 is well defined, making our results very general.

Resumo: O método de segunda quantificação é utilizado para construir o operador espalhamento S no espaço de Fock, no contexto de Thermofield Dynamics (TFD), para o campo de Dirac sujeito a um potencial eletromagnético externo dependente do tempo. Esta descrição é baseada na abordagem construtiva do espaço de Fock, a qual é aplicada ao sistema original e a seu dual. Seguindo a prescrição de TFD, o operador S é utilizado para avaliar o processo de produção de pares elétron-pósitron à temperatura finita, e uma análise do limiar de produção é feita a partir do cálculo da probabilidade total de transição. / Abstract: The second quantization methods is used to build the scattering operator S in Fock space, in the contex of Thermofield Dynamics (TFD), for the Dirac field subject to an external time-dependent electromagnetic potential. This description is based on the constructive approach to the Fock space, wich is applied to the original system and to its dual. Following TFD prescription, the operator S is used to estimate the process of electron-positron pair production at finite temperature, and an analysis of the production threshold is done based on the calculation of the total transition probability. / Orientador: Jeferson de Lima Tomazelli / Coorientador: Bruto Max Pimentel Escobar / Banca: José David Mangueira Vianna / Banca: Ademir Eugênio de Santana / Banca: Fernando Luiz de Campos Carvalho / Banca: Maria Cristina Batoni Abdalla / Doutor

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Orientador: Julio Marny Hoff da Silva / Banca: Saulo Henrique Pereira / Banca: Marco André Ferreira Dias / Banca: José Abdalla Helayel-Neto / Banca: Alexis Roa Aguirre / Resumo: Na presente tese apresentaremos de forma detalhada o estudo sistemático de uma teoria quântica com férmions de dimensão de massa um que obedecem as estatísticas de Fermi-Dirac, abordando essencialmente sua construção, quantização do campo, análise dos observáveis físicos e aplicações quânticas. Forneceremos todos os detalhes de uma descoberta teórica inesperada da partícula de spin $1/2$ que compõe um conjunto completo de autoespinores com helicidade dual do operador conjugação de carga. Esses espinores recebem o nome de Elko, um acrônimo proveniente do Alemão \textit{Eigenspinoren des Ladungskonjugationsoperators}. Veremos que o elo entre os espaços de representação $(1/2, 0)$ e $(0, 1/2)$ não é dado pela simetria de paridade mas sim pela 'Mágica das matrizes de Pauli', e, portanto, como consequência a dinâmica de tais campos será regida única e exclusivamente pela dinâmica de Klein-Gordon. Tal fato faz com que o propagador associado ao Elko guarde muita similaridade com o propagador do campo escalar. Intrinsicamente, em sua formulação embrionária, as somas de spin para o Elko mostram um termo que quebra explicitamente a covariância relativística, levando então à apreciação da \textit{Very Special Relativity}, que nada mais é do que um subgrupo do grupo de Lorentz, cuja álgebra deixa as somas de spin invariantes ou covariantes. Entretanto, mostraremos que existe uma liberdade na definição da estrutura dual, a qual permite que seja construída uma teoria local e invariante p... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The present thesis covers in details a systematic study of a quantum theory based on mass dimension one fermions which satisfy the Fermi-Dirac statistics, essentially addressing its construction, field quantization, analysis of physical observables and quantum applications. We provide all the details of an unexpected theoretical discovery of a spin 1/2 particle which composes a complete set of dual helicity spinors of the charge conjugation operator. Such spinors are called Elko, an acronym for the German word Eigenspinoren des Ladungskonjugationsoperators. We show that the relation between the representation spaces (1/2,0) and (0,1/2) is given by the "Magic of Pauli matrices" rather than parity symmetry, therefore, as a consequence the dynamic of such fields is governed solely and exclusively by the Klein-Gordon dynamic. Such fact makes the Elko propagator to be very similar to the scalar field propagator Intrinsically, in its embryonic formulation, Elko spin sums shows up a term that explicitly breaks relativistic covariance, leading to the appreciation of Very Special Relativity, a theory which is based on a subgroup of the Lorentz group, whose algebra leaves the spin sums invariant or covariant. However, we show a freedom in the dual structure definition, which allows the construction of a local and Lorentz invariant theory, thus, leading to a very interesting and promising new physics / Doutor

Le sujet de cette thèse est l'analyse du second champ critique supraconducteur (Hc2) ainsi que l'interaction entre la supraconductivité et les points critiques quantiques (PCQ), pour les composés CeCoIn5, URhGe et UCoGe. Dans le composé CeCoIn5, l'étude par résistivité du domaine de liquide de Fermi a permis la localisation précise du PCQ a pression ambiante. Cette analyse permet d'invalider l'hypothèse d'une coïncidence entre Hc2(0) et le PCQ. Dans une deuxième partie, l'évolution sous pression de Hc2 est analysée. Le dôme supraconducteur de ce composé est non-conventionnel avec deux pressions caractéristiques différentes: à ~1.6GPa, la température de transition supraconductrice est maximum alors que c'est à ~0.4GPa que la plupart des grandeurs physiques (maximum de Hc2(0), maximum de la pente dHc2/dT, maximum du saut de chaleur spécifique DC/C, ...) suggèrent la présence d'un PCQ. Nous expliquons cet antagonisme par l'importance des processus de brisure de pairs liés a la proximité du PCQ. Ces deux observations nous permettent de proposer un nouveau diagramme de phase pour CeCoIn5. Dans une troisième partie, les mesures de conduction thermique sur les composés URhGe et UCoGe sont présentées. Elles nous permettent dans un premier temps d'obtenir la transition "bulk" supraconductrice et de confirmer la forme in-habituelle de Hc2 observée en résistivité. La dépendance en températures et en champs de la conduction thermique nous permet d'identifier une contribution non-électronique au transport de chaleur jusqu'aux plus basses températures. D'autre part, nous identifions deux différents domaines supraconducteurs a bas et hauts champs appliqués selon l'axe b. Ces deux domaines sont compatibles avec un modèle de supraconductivité multigaps. Suivant ces observations et des mesures de pouvoir thermoélectrique, nous proposons un modèle de transition de Lifshitz pour ces deux composés. / The subject of this thesis is the analyze of the superconducting upper critical field (Hc2) and the interaction between superconductivity and quantum critical points (QCP), for the compounds CeCoIn5, URhGe and UCoGe. In CeCoIn5, study by mean of resistivity of the Fermi liquid domain allows us to localize precisely the QCP at ambient pressure. This analyze rule out the previously suggested pinning of Hc2(0) at the QCP. In a second part, the evolution of Hc2 under pressure is analyzed. The superconducting dome is unconventional in this compound with two characteristic pressures: at 1.6GPa, the superconducting transition temperature is maximum but it is at 0.4GPa that physical properties (maximum of Hc2(0), maximum of the initial slope dHc2/dT, maximum of the specific heat jump DC/C,... ) suggest a QCP. We explain this antagonism with pair-breaking effects in the proximity of the QCP. With these two experiments, we suggest a new phase diagram for CeCoIn5. In a third part, measurements of thermal conductivity on URhGe and UCoGe are presented. We obtained the bulk superconducting phase transition and confirmed the unusual curvature of the slope dHc2/dT observed by resistivity. The temperatures and fields dependence of thermal conductivity allow us to identify a non-electronic contribution for heat transport down to the lowest temperature (50mK) and probably associated with magnon or longitudinal fluctuations. We also identified two different domains in the superconducting region, These domains are compatible with a two bands model for superconductivity. Thermopower measurements on UCoGe reveal a strong anisotropy to current direction and several anomaly under field applied in the b direction. We suggest a Lifshitz transition to explain our observations in these two compounds.

Das Ziel dieser Doktorarbeit ist die Berechnung, aus ersten Prinzipien, von Niedrigenenergiekonstanten (NEK), welche die chirale Störungsheorie (ChST) parametrisieren, durch Simulationen auf dem Gitter. Diese Arbeit ist eine Pilotstudie und will deshalb nicht zu definitiven und präzisen quantitativen Vorhersagen führen, sondern wir möchten qualitative Leitlinien für zukünftige genauere Erforschungen der epsilon-Entwicklung der ChST geben. Letztere ist ein Gebiet in dem die chirale Symmetrie wiederhergestellt ist und wo die Compton-Wellenlänge der leichtesten Mesonen grösser als die lineare Dimension des endlichen Volumens ist. Die epsilon-Region ist weiterhin durch die wichtige Rolle der topologischen Ladung, nu, charakterisiert, so dass die Untersuchung der mesonischen Zweipunkt-Korrelationsfunktionen in definierten topologischen Sektoren vorzunehmen ist. Aus diesem Grunde haben wir chirale Fermionen auf dem Gitter simuliert, wobei der overlap Formalismus für den Dirac Operator, mit dem gewöhnliches Wilson Dirac Operator als Kern, in der quenched Approximation genommen wurde. Wir demonstrieren dass der Sektor mit neutraler topologischer Ladung, nu = 0, numerisch sehr schwierig zu untersuchen ist, weil die Daten von erheblichen Spitzen beeinflusst werden, die aufgrund sehr kleiner, nicht verschwindender Eigenwerte herrühren. Diese Beobachtung findet eine Übereinstimmung in einer Studie der Random Matrix Theory (RMT), die besagt, dass man eine Statistik von mehr als 10000 Konfigurationen benötigt, falls man auf kleine Eigenwerte empfindlich reagierende physikalische Grössen, im triviale topologische Sektoren simulieren möchte. Weniger Probleme ergeben sich in dem nicht-trivialen Sektoren |nu| > 0: wir präsentieren deshalb unsere Ergebnisse aus dem topologisches Sektor nu = 1 und den Daten aus das Sektor mit nu = 2 nur als Gegenprobe. Wir zeigen die Existenz einer unteren Schranke für das physikalisches Volumen bei V > 1 fm zur vierten Potenz für die Gültigkeit der ChST, übereinstimmend mit einer vorherigen Beobachtung aus der RMT. Wir beschränken deshalb unsere Untersuchung auf ein grösseres Gitter, wo wir die Daten des axialen Korrelators mit den Vorhersagen der ChST in der Valenzquark-Approximation fitten und eine stabile Bestimmung der gequenchten Pionen-Zerfallskonstante, F, erhalten. Die skalaren und pseudoskalaren Korrelationsfunktionen sind durch mehrere NEK parametrisiert. Dadurch ist der Vergleich mit den Vorhersagen der ChST schwieriger, und deshalb präsentieren wir nur einige Abschätzungen, die mit der entsprechenden Literatur verglichen werden. Zum Schluss präsentieren wir mögliche Implementierungen von verbesserten Algorithmen für die Inversion des overlap Operators, die die Simulationkosten reduzieren. / The aim of this thesis is the computation of Low Energy Constants (LEC) which parameterise Chiral Perturbation Theory (ChPT) from a first principles analysis via lattice simulations. The thesis provides a pilot study and will not give definitive and precise quantitative predictions, but rather our aim is to provide qualitative hints for future accurate investigations of the epsilon-expansion of ChPT, where chiral symmetry is restored and the Compton wavelength of the lightest meson is larger than the linear size of the finite volume. One of the property characterising the epsilon-regime is the important role played by the topological charge, nu, leading to the investigation of the two-point meson correlation functions in distinct topological sectors. To this end, we simulate chiral fermions on the lattice adopting the overlap formalism for the Dirac operator in the quenched approximation, with the kernel provided by the usual Wilson Dirac operator. We demonstrate that the neutral topological sector, nu = 0, is very difficult to explore numerically, as the data are affected by large spikes due to the presence of very small, non-zero eigenvalues. This observation is in agreement with a study of Random Matrix Theory (RMT), which indicates that a statistic of more than 10000 configurations is required when physical quantities sensitive to small eigenvalues are investigated in the neutral topological sector. Therefore, we present our results corresponding to the topological sector nu = 1. Due to the modest statistic, we only use the nu = 2 data as a crosscheck. We find a lower bound on the physical volume V > 1 fm to the four for ChPT to be used, in agreement with a previous observation using RMT. Restricting our attention to a larger lattice, we fit the data of the axial correlation function with the predictions of quenched ChPT, obtaining a stable determination of the quenched pion decay constant, F. The scalar and pseudoscalar correlation functions are parameterised by a larger number of LEC, rendering the comparison with ChPT predictions much more difficult and hence we present only some estimates that are compared with other determinations in the literature. Finally, we present possible implementations of improved algorithms used in the ``inversion'''' of the overlap operator, whose aim is to reduce the computational cost of the simulations.

The Standard model of particle physics provides a successful theory to understand the experimental results of the electroweak and strong interactions. However, it does not have a satisfactory explanation for the hierarchy problem. Many extensions of the Standard Model that solve the hierarchy problem result in new particles. We will study the phenomenology of vector-like fermions resulting in theories where the Higgs boson is typically a pseudo-Nambu-Goldstone boson. In these theories we study the case where a heavy fermion will be heavier than a heavy gluon, and then the channel of a heavy fermion decaying into a color octet is considered. We study this phenomenology at high energy colliders, both the LHC as well as future machines. / O modelo padrão de física de partículas fornece uma teoria bem-sucedida para entender os resultados experimentais das interações eletrofracas e fortes. No entanto, não tem uma explicação satisfatória para o problema de hierarquia. Muitas extensões do Modelo Padrão que resolvem o problema hierarquia resultam em novas partículas. Estudaremos a fenomenologia de férmions vetoriais resultando em teorias onde o bóson de Higgs é tipicamente um bóson pseudo-Nambu-Goldstone. Nessas teorias, estudaremos o caso em que um férmion pesado será mais pesado do que um glúon pesado, e então o canal de um férmion pesado decaindo em um octeto de cor é considerado. Estudamos esta fenomenologia em colisores de alta energia, tanto para o LHC quanto as futuras máquinas.

The Standard model of particle physics provides a successful theory to understand the experimental results of the electroweak and strong interactions. However, it does not have a satisfactory explanation for the hierarchy problem. Many extensions of the Standard Model that solve the hierarchy problem result in new particles. We will study the phenomenology of vector-like fermions resulting in theories where the Higgs boson is typically a pseudo-Nambu-Goldstone boson. In these theories we study the case where a heavy fermion will be heavier than a heavy gluon, and then the channel of a heavy fermion decaying into a color octet is considered. We study this phenomenology at high energy colliders, both the LHC as well as future machines. / O modelo padrão de física de partículas fornece uma teoria bem-sucedida para entender os resultados experimentais das interações eletrofracas e fortes. No entanto, não tem uma explicação satisfatória para o problema de hierarquia. Muitas extensões do Modelo Padrão que resolvem o problema hierarquia resultam em novas partículas. Estudaremos a fenomenologia de férmions vetoriais resultando em teorias onde o bóson de Higgs é tipicamente um bóson pseudo-Nambu-Goldstone. Nessas teorias, estudaremos o caso em que um férmion pesado será mais pesado do que um glúon pesado, e então o canal de um férmion pesado decaindo em um octeto de cor é considerado. Estudamos esta fenomenologia em colisores de alta energia, tanto para o LHC quanto as futuras máquinas.

Neste trabalho realizamos um estudo de um buraco em um antiferromagneto, como parte de uma revisão de diferentes técnicas de abordagem das fases de “stripes” nos cupratos supercondutores. Estudamos a transição do formalismo de “strings” para um buraco no modelo t - Jz bidimensional, onde existe uma solução analítica, para a solução de pólaron de spin no modelo t - J isotrópico através da aproximação de Born auto-consistente. A forma funcional dos picos de quase-partícula, do peso espectral e do “gap” espectral foi investigada numericamente em detalhe, em função da anisotropia magnética. O movimento de um pólaron de spin na presença de uma parede de domínio antiferromagnética (ADW) em antifase, como uma realização da configuração de “stripes” nos planos CuO dos cupratos de baixa dopagem, também foi analisada.