We investigate the employment of a non-perturbative regularization scheme – the spectral regularization, which is based on the gauge technique, previously implemented in the context of chiral quark models – in the study of the gauge symmetry preservation within the Schwinger model and violation in the chiral Schwinger model. We show that the spectral regularization provides mathematical consistent and ambiguity free solutions for the two-point functions of both Schwinger and chiral Schwinger models in exact (1+1) dimensions, correctly displaying the gauge invariance in the Schwinger model and the axial anomaly in the chiral Schwinger model. The employment of the spectral regularization avoids any dependence on ambiguous amplitudes and/or unconventional γ5 algebra. Our results reinforce the strength of the spectral regularization as a mathematical consistent, divergence free, and ambiguity free regularization scheme that correctly implements symmetry conservation or violation in each case.

Through non-linear generalizations of Maxwell's Electrodynamic Theory (TEM) it is possible to build a mathematical tool capable of reproducing certain phenomena described in the General Theory of Relativity (GRT). Therefore, such generalizations constitute excellent mental laboratories for the study of physical systems subject to geometrization. In particular, using the effective metric technique, we can describe the evolution of light rays in these theories in terms of typical tools of general relativity. On the other hand, we can produce solutions, involving only the electromagnetic field, capable of totally or partially imitating certain phenomena typical of the gravitational field. Such an approach constitutes a particular example of the so-called analogous models of gravitation. In this work we will study the effective metrics in models of non-linear electrodynamics, investigating the possibility of building step-by-step solutions whose Lagrangian depends only on the invariant F and we will show important aspects of the interaction of light with light, and we will try to reproduce a horizon of events by the effective metric.

The Schwinger model, i.e. quantum electrodynamics (QED) in two dimensions with massless fermions, is the simplest model for fermionic fields that implements several features also observed in other more realistic 4D gauge models. It is also an interesting feature of the model that, being two-dimensional, vector and axial fermionic currents are not independent of each other. Thus, the chiral Schwinger model polarization model is related to the same possible Schwinger model tree. Finally, the solution of the action in divergences in the fits within the model, Schwinger model is finite, in other words, is free of divergences. Despite the results when the regularization schemes are used, being recognized, therefore, as an indeterminate quantity, we intend to investigate the same phenomenon (fin ambiguities in the same phenomenon) Schwinger), from the perspective of the Spectral Model of quarks.

Dark matter is one of the great mysteries of the Universe that we still haven’t been able to
unravel, despite all the success in describing the fundamental constituents of matter, only
15% is described by the Standard Model. We know about the existence of this large amount of
matter because of cosmological observations, in which for certain structures in the Universe
to exist in the way we observe, the existence of a mass that we cannot see is necessary. There
are varied approaches to looking for dark matter, and given the success of the Standard Model
in describing known matter in terms of fundamental particles, we believe that dark matter
must be made up of particles that can be accommodated by a model that is an extension
of the Standard Model. In our work, the search for dark matter is linked to the LHC particle
collider and the characteristics of its ATLAS detector and due to the huge amount of data
generated in particle collisions, we use Artificial Intelligence software to help us in this search.
We use artificial deep neural networks, implementing a binary classifier in TensorFlow in
order to separate the events that are from the standard model from the possible dark matter
events, with data generated in CalcHep implementing the ZP-TP-DM model.

Nano beams are special devices, which can confine both optical and mechanical modes. Starting from the equation of the classical beam, we find the normal modes of vibration of an isolated beam. From there, we were able to quantize the Hamiltonian of the beam, similarly quantization of the electromagnetic field, to begin a study of the nanobeams.

The influence of zinc doping in high-temperature superconducting cuprates is studied. It is known experimentally that Tc decrease linearly with the zinc density. We model the effect of zinc as impurities that both modify the intensity of the superconducting interaction and reduce the velocity of charge carriers in a recent model for these materials.

Statistical physics, compared to other areas, is extremely new. Statistical physics is a formalism that establishes a link between the microscopic properties of a physical system and the macroscopic properties, which can usually be called thermodynamic properties. Currently, Statistical Physics has found application in several areas besides Physics. The present work aims to make a bibliographic review of some models with application in biological systems. We start by doing an analysis of processes in balance and out of balance. Subsequently, we studied the contact process and its application, for example, in the behavior of epidemics. Then, we show that by adding more than one species, we can use the contact process to describe ecological interactions, such as commensalism, parasitism and symbiosis.

At the beginning of the 19th century, works such as those by Faraday and Maxwell established the rules of classical electromagnetism. Using vector formalism, the set of differential equations composed of Maxwell's equations and Lorentz's law of force established a solid basis for several experiments carried out in their time. At the end of the 19th century, experiments such as the double slit, the photoelectric effect, the Michaelson experiment, among others, brought us to the need for a better theoretical explanation for the results. In the 20th century, Albert Einstein proposed in his works some new postulates and thus built a basis for a "new" physics. Through concepts such as the invariance of the speed of light and the independence of the adopted coordinate system, a theory for gravitation emerges, where we adopt a tensor formalism through which we can observe a series of similarities between the electromagnetic theory and the theory of gravitation. Knowing the main tensors responsible for the description of the electromagnetic and gravitational fields, we will describe some of the main algebraic characteristics, and through this characterization we will classify both the Faraday tensor and the Weyl tensor. We will be particularly concerned with gravitation through the Weyl tensor and the so-called Petrov classification. We will qualitatively discuss this classification and its physical interpretation, and briefly see how it can help us in current experiments proposed by observational cosmology, such as the generation and propagation of gravitational waves, fields generated by massive static and uncharged objects, or with rotation around some axis is loaded and the torsional forces in the so-called tidal effects.

Although the Standard Model (SM) is able to explain many phenomena in the world of particles, there are many problems that have not yet been clarified by this model. The nature of dark matter (DM), which makes up about 27% of the entire Universe, is an enigma both from the point of view of Particle Physics and Cosmology. DM does not interact with ordinary matter as we know it, so it cannot be detected in current experimental apparatus, being the perception of its existence only due to its gravitational interaction with ordinary matter. In the Large Hadron Collider (LHC), the search for DM is associated with its signature characterized by missing transverse energy ($\cancel{E}_T$) in experiments. Several theories beyond the SM consider a new DM candidate particle that can be a scalar, vectorial, a fermion of Dirac or Majorana particle. In this work, we consider a scalar DM candidate $\phi$ (with spin 0) predicted by ZP-TP-DM model that come from the decay of a new vector boson $Z'$ (spin 1) into a pair $T' \overline{T'}$ (called top fermionic partners with spin 1/2), giving rise to the final state $t\bar{t}\phi \phi$. Using Machine Learning (AM) techniques, we separate the background events ($pp \longrightarrow t\bar{t} Z $, with $ Z $ decaying in neutrinos and their respective antineutrinos) from the signal events ($ pp \longrightarrow T'\overline{T'} \longrightarrow t\bar{t} \phi\phi $) generated by CalcHEP. We built a deep neural network (DNN) to separate background and signal events and obtained values close to 1 for the Area Under the Receiver Operating Characteristic curve (AUC), indicating that the created classifier efficiently separated the events. However, the results obtained for statistical significance represent an ideal situation, since we did not include in the analysis the decay of the pair $t\bar{t}$.

This master's thesis was a search for subdiffusion in worker termites of the genus Cornitermes Cumulans, also known as termites of the pasto. The experiments were carried out on plates 10 cm indiameter and 1 cm in height and were based on single-particle tracking. Termite movement was captured by a camera, initially for a period of 30 minutes. Data were collected by a program developed by professor Sidiney Geraldo Alves in Python language and using Fortran as a tool, algorithms were developed to analyze the series. The first tests were carried out in Petri dishes without traps or geometric restrictions, an exponent was found that matches with anomalous diffusion, but of the superdiffusive type. After these first experiments, we used a maze of the same size and height as the Petri dish. Several experiments were carried out and an exponent was found that also matches superdiffusion, but a slightly smaller exponent.

This work aimed to study some of the ways used to characterize the classicality of quantum states, with a focus on Roughness (R), it is a measure recently presented to indicate how quantum a state is by means of interesting way with respect to of the Wigner Function, and Husimi. The study carried out was based on the analysis of the Roughness graphically and as reflections of quantum behaviors in the Wignere function consequently of R, thus the state of cat, thermal esquezed were exhaustively studied. Were observed graphically the behaviors for the status of odd and even cat and the manifestations in the quasi-probability distributions that could be associated and thus representing the overlapping of the states and how the difference between the two manifested. In the case of the behavior of the thermal state, the trend of a uniform distribution was observed when the state tended to the condition that queR → 0. For the squeezed states, reflections were observed in the graphs of the functions W, Q, W − Qe | W − Q | esu and the relationship with ∆q∆p. Through these observations, we will be able to visualize the potentialities and advantages of using Roughness in classifying how quantum a state is.

The bouncer model consists of a classic particle, subject to the acceleration of gravity, which collides with a wall that behaves like a piston, oscillating with time. This model was proposed as an alternative system to study the Fermi acceleration, a phenomenon that consists of the unlimited energy gain of the particle due to collisions with the moving wall. In this work we study a version of the bouncer model in which the field in which the particle is inserted is not homogeneous. The system map was constructed to provide the particle speed and the wall phase after each collision. For certain combinations of parameter values and initial conditions, the dynamics presents a chaotic behavior. This non-linear phenomenon was quantified by means of Lyapunov exponents for the regions with the lowest energy. The x points and their stability were also found numerically for different parameter values. Finally, we study the transition from the integrable to the non-integrable regime using scale analysis. We show that the average energy, the roughness (variance of the average speed) and the average speed of a set of non-interacting particles obey scale functions. The scale description was found for the chaotic regions below the first invariant curve.

Discovered in 1911 by Kamerlingh Onnes, supercondictivity took 46 years to be describedwith a microscopic approach. It happened in 1957, when the group formed by Bardeen, Cooperand Schrieffer published their article. However, the theory, called BCS Theory, could onlydescribe metallic superconductors with one conduction band. Some materials, which presentedanomalous behavior, were not adequately described by the theory.Thus, it is needed to change the theory and to confirm if it is able to describe more advancedrelations than the one which involves only one conduction band. An example of this situationis the case of an alloy, which can present more than one conduction band in its electronicdistribution. It will be done a change in the Hamiltonian which describes the BCS Theory,aiming to describe interactions caused by hybridization.It will be considered the cases that these bands are formed by electronic orbitals with an-gular momentum, thus, the hybridization between then may be symmetric on anti-symmetric.Only attractive interactions intra-bands in two conduction bands and the emergence of an in-duction inter-band will be considered, what will result in a pairing of the gaps. It will beshown that superconductors interactions (inter-bands), are induced in the total absence of at-tractive interactions between two bands, which turns out to be completely dependent on thehybridization between then.