The interaction between a partially coherent field with a one-dimensional periodic photonic environment is investigated within the framework of Floquet-Bloch modes. To this end, we describe the interplay between lattice properties and field fluctuations by considering the optical beam as a linear combination of Floquet-Bloch modes, whose coefficients are described by a stationary random process. It is demonstrated that the propagation of partially coherent beams depends not only on the average of the excitation of each band but also on the correlations existent among the various bands supported by the lattice.

Trivalent rare earth ions have been shown to be extremely efficient in absorbing and emission of different wavelengths. This is because the optically active electrons are not the outermost, which weakens the ion bond when doped into a host material, due to partial shielding of the 4f state. In this text, the fluorescent efficiency of Nd3+ (neodymium) in NdxY1.00-xAl3(BO3)4 particles under a non-resonant Anti-Stokes type excitation (1064 nm) starting from the ground state to the 4F3/2 level was shown. Even with a non-resonant excitation, intensities were observed in the very broad photoluminescent spectrum, from visible to infrared, which is explained by the photon avalanche (AF) type excitation mechanism, which very efficiently favored the level population. 4F3/2 along with phonon annihilation to initially populate the 4F3/2 level. In the interaction between an excited ion (4F3/2) and another in the ground state (4I9/2), the excited ion performs a cross-relaxation (non-radiative) interacting with an ion in the ground state in such a way that the first relaxes from the level 4F3/2 to 4I15/2 and the second is excitedly promoted from 4I9/2 to 4I15/2. Due to the proximity to the lower levels, these ions relax non-radiatively to the 4I13/2 and 4I11/2 levels. Once at the 4I11/2 level, ions can absorb radiation from the excitation beam that is resonant with the 4I11/2 🡪 4F3/2 transition. Thus, an ion initially excited at the 4F3/2 level by a
low probability at room temperature, takes two ions to the 4F3/2 state and after the sequence of events: phonon-assisted ground state absorption; cross relaxation; non-radiative relaxations and resonant excited state absorption. The two ions at the 4F3/2 level can transfer energy to two neighbors in the ground state and take four ions to the 4F3/2 level. The repetition of this set of events leads to an excitation that follows a geometric progression of excited ions, abruptly increasing the absorption of photons at 1064 nm. With large numbers of ions at the 4F3/2 level we can observe transitions that characterize upconversion and downconversion of energy covering the
visible and infrared spectrum. The influence of neodymium concentrations for different samples was also investigated, and a strong dependence on cross-relaxation was found for the photon avalanche mechanisms, due to the proximity of the ions, and with this, an energy looping mechanism was proposed for concentrations of 5% to 20% of Nd3+, and for concentrations greater than 20%, the photon avalanche is established. The results of this dissertation are published in the journals: Applied Physics Letters with the title “Photon-avalanche-like upconversion in NdAl3(BO3)4 nanoparticles excited at 1064nm” and Optical Materials with the title “Energy-looping and photon-avalanche-like phenomena in NdxY1 .00-xAl3(BO3)4 powders excited at 1064 nm”.

This study is dedicated to investigating the thermo-optical and nonlinear response of complex fluids such as liquid crystals, carbon quantum dots, and dyes in various solvents. Using the time-resolved z-scan technique, we explore the impact of adding carbon quantum dots derived from dansyl chloride (CD-DsCl) on the nonlinear refractive coefficient in planar liquid crystal samples. In the study of CD-DsCl addition in liquid crystals, we analyze the dependence of the nonlinear optical response on temperature, especially near the smectic-A to nematic and nematic to isotropic phase transitions. We also investigate the effects of an external electric field on these samples. Our preliminary results indicate that liquid crystal samples doped with carbon quantum dots may exhibit an enhanced nonlinear optical response, depending on the intensity of the applied external field. This study contributes to the understanding of nonlinear optical phenomena in liquid crystal systems doped with carbon quantum dots. We also investigate the effect of solvents on the nonlinear optical properties of the tautomeric forms of methyl orange through experimental approaches. Our results show that in the presence of different solvents, methyl orange exhibits a negative nonlinear optical behavior, and a red shift in its linear absorption is observed as the solvent polarity increases. This work contributes to advancing the understanding of the basic physics of organic compounds.

This study is dedicated to investigating the thermo-optical and nonlinear response of complex fluids such as liquid crystals, carbon quantum dots, and dyes in various solvents. Using the time-resolved z-scan technique, we explore the impact of adding carbon quantum dots derived from dansyl chloride (CD-DsCl) on the nonlinear refractive coefficient in planar liquid crystal samples. In the study of CD-DsCl addition in liquid crystals, we analyze the dependence of the nonlinear optical response on temperature, especially near the smectic-A to nematic and nematic to isotropic phase transitions. We also investigate the effects of an external electric field on these samples. Our preliminary results indicate that liquid crystal samples doped with carbon quantum dots may exhibit an enhanced nonlinear optical response, depending on the intensity of the applied external field. This study contributes to the understanding of nonlinear optical phenomena in liquid crystal systems doped with carbon quantum dots. We also investigate the effect of solvents on the nonlinear optical properties of the tautomeric forms of methyl orange through experimental approaches. Our results show that in the presence of different solvents, methyl orange exhibits a negative nonlinear optical behavior, and a red shift in its linear absorption is observed as the solvent polarity increases. This work contributes to advancing the understanding of the basic physics of organic compounds.

The objective of this dissertation is to analyze, with a certain level of detail, the scattering of monochromatic electromagnetic radiation by an isotropic and linear dielectric material having $\mathcal{PT}$ symmetry in the Born approximation. Studying the light scattered by a specific material can give us useful information about the nature of the material. Thus, we verify how light scattering behaves in a material that has $\mathcal{PT}$ symmetry and how the presence of gain and loss within the material can affect the spectral density of the scattered field. Spectral density is a quantity that can be measured directly in the laboratory. We verified that, for certain gain and loss distributions, the scattered field direction can be varied without changing the scatterer geometry. The non-Hermitian character of the refractive index of the scatterer is also reflected in the scattered intensity pattern, which now becomes asymmetric with respect to the scattering angle.

We begin in chapter 1 with a brief motivation about the development of the work. Chapter 2 presents the fundamental concepts of $\mathcal{PT}$ symmetry and their respective applications in the field of quantum mechanics, discussing the most important properties that describe this symmetry. We will also make the connection of such symmetry with the research field of optics.
Chapter 3 presents the classical theory of scattering and the wave equation satisfied by the electric field in the scalar approximation, starting from the set of Maxwell's equations. The formal theory of scattering for scalar fields and the representation of multiple scattering with the Born series will also be exposed. We will discuss how such approximations are given and their applications of interest to our work. In chapter 4, we will deal with the scattering of light by a $\mathcal{PT}$-symmetric material in the first Born approximation. Our main conclusion is that the scattered field directions can undergo changes depending on the presence of gain and loss in the scattering material. Finally, in chapter 5, we discuss our conclusions and some future perspectives.

Ascorbic acid, known as vitamin C, plays a crucial role in human health, and it is necessary to develop sensitive and selective sensors for its detection in complex samples. In order to enhance electrical responses and interaction with biomolecules, nanomaterials are incorporated into the surface of sensors. Titanium dioxide (TiO2) and graphene oxide (GO) nanocrystals have interesting properties, such as high surface area, catalytic activity and ability to amplify electrical signals, making them excellent candidates for electrochemical sensors. Thus, their synergism can enhance these properties. Therefore, this work investigated the synergism between nanocrystals of TiO2 doped with nickel (Ni) and GO and its application in the detection of ascorbic acid. The optical, structural and vibrational properties of the samples were investigated using optical absorption spectroscopy (AO), X-ray diffraction (XRD), Raman spectroscopy and cyclic voltammetry (VC). In the AO spectra, it confirmed the absorption in the ultraviolet of the TiO2 nanocrystals and that with the doping it altered the band gap. XRD and Raman data confirmed the presence of the anatase phase of the TiO2 nanocrystals, the lattice distortions with doping and the formation of GO. In the results of voltammetry and application in sensors for detection of ascorbic acid, it confirmed that nanocrystals of TiO2 doped with Ni and GO presented a high sensitivity and selectivity in the detection of ascorbic acid, with linear response in the concentration range, enhancing the sensitivity of the sensor . The synergistic effect of the two nanomaterials further enhanced the detection signal. Therefore, these results contribute to the advancement of knowledge in the field of nanomaterials and their application in sensitive and selective detection systems of bioactive compounds, such as ascorbic acid.

In this dissertation we investigate spontaneous Lorentz symmetry breaking in a 4-fermion derivative model. The essence of the spontaneous Lorentz symmetry breaking mechanism consists in the coupling of tensor fields through potentials in such a way that, in the minima of the potentials, these fields acquire expected values of non-trivial vacuum, thus introducing privileged space-time directions. For this model we calculate the effective potential in the context of zero temperature and finite temperature, we also investigate the conditions for symmetry restoration. Next, we calculate the corresponding effective action and show that the resulting potential is positively defined and has a continuous set of minima, as well as performing the induction of the second order kinetic action in the auxiliary field.

The present study is devoted to characterizing the optical and interfacial properties of chitosan films doped with carbon quantum dots. In particular, carbon nanoparticles are synthesized from the hydrothermal method, using methyl red dye as a precursor.
Using UV-Vis spectroscopy and optical tensiometry techniques, the photostability and wettability of polymeric films are analyzed, emphasizing the effects associated with photoexcitation of the samples with a laser in the UV region. The obtained results show that the addition of a small percentage of carbon quantum dots does not modify the wettability of the films but increases the photostability of the samples to UV radiation. Using glycerol as a test liquid during the contact angle measurements, one can observe that the wetting dynamics is not affected by the addition of carbon quantum dots, which act as an absorber center for electromagnetic radiation. Using the kinetic-molecular theory to analyze the wetting dynamics, the physical-chemical parameters that characterize the wetting phenomenon are determined. The results obtained in this work show that the addition of quantum dots can be used to improve the stability of biocompatible polymer films, making them less susceptible to UV radiation from the medium.

In this present work, we study the dynamics of an electron in two-dimensional systems (2D) under the effect of an external electric field. In both cases we investigate the time evolution of an initially localized wave packet, using a Taylor formalism to solve the set of Schrödinger equations. In the first case, we consider a square lattice with the hopping terms distributed aperiodically. The obtained results suggest that fast propagation of electrons (ballistic dynamics) is found for a range of values of the degree of aperiodicity ν of the system. By inserting the effect of a static electric field in the model, it is verified the existence of an oscillatory behavior similar to the electronic dynamics in crystalline systems, or that is, where they exhibit “ Bloch oscillations”. The frequency ω and the size LE of these oscillations are investigated and the results found are compared with the semi-classical approach, resulting in good agreement with default behavior. In the second case, we consider a square lattice with the hopping terms with correlated disorder. Our results indicated that the correlated disorder promotes a fast electronic propagation fast for intermediate times. When we insert an electric field, we also observe behavior similar to “Bloch oscillations”. The frequency obtained for this second case is also in good agreement with those predicted by the semi-classical approach. Despite the absence of extended states and based on the disorder inserted in the model, we discuss the stability of these apparent “Bloch oscillations”. We also investigated the quantum state transfer (QST) in a channel with diagonally uncorrelated disorder, connected to an sender (S) and a receiver (R). We use some measures of the degree of localization in order to evaluate the localization or non-localization properties of the proposed channel for QST. The results revealed that within a certain limit of weak disorder, the transfer of quantum states occurs with good fidelity.

In this work, we carried out a spectroscopic study of glass based on Tellurium and Zinc oxides (xTeO2:yZnO) doped and co-doped with Dy3+, Pr3+, Eu3+ and Ho3+ ions under UV and blue excitation. The analysis of this investigation were based on measurements of optical absorption and excitation, luminescence, time-resolved luminescence and energy transfer efficiency parameters. The results show that under UV/blue excitation the co-doped systems generate well-defined emission bands in the visible region, and the behavior of the emission intensity as a function of the co-dopant concentration indicated the presence of energy transfer mechanisms Dy3+ → Pr3+, Pr3+ → Dy3+, Eu3+ → Ho3+ e Ho3+ → Eu3+, which were later confirmed by lifetime measurements. The analysis of energy transfer efficiencies indicated that transfers according to Dy3+ → Pr3+ e Ho3+ → Eu3+ Dy3+ → Pr3+ and Ho3+ → Eu3+ mechanisms are more efficient and, therefore, are more likely to occur. It was also observed that the emissions are sensitive to the excitation wavelengths used, and furthermore, these excitations are responsible for altering the sensitizer/acceptor relationship in the energy transfer process, showing, therefore, that the spectral profile of the emissions is a function not only of the concentration of the ions, but also of the excitation used and consequently of the energy transfer. The results presented here may impact studies that explore the optical properties of devices based on the light emitted by Dy3+/ Pr3+ and Eu3+/ Ho3+ ion pairs

In this work, we investigate topological orders and quantum phase transitions in distinct interacting spin models using numerical methods. We introduce the finite-size tangential scaling method, where we demonstrate its validation in the characterization of topological phase transitions between Haldane and Large-D phases in an anisotropic Heisenberg chain of spin S = 1. Our results were validated by theoretical theories of the critical exponent of the correlation length ν originated from a non-linear effective field theory σ. Next, we investigate the quantum phases and topological phase transitions for a class of tetramer ferrimagnetic models (S1 − S1 − S2 − S2) with isotropic and alternating Heisenberg interactions. We first investigate the case S1 = 1 2 and S2 = 5 2 where we obtain the phase diagram of the model and investigate the quantum phases from different magnetization curves. We characterize a critical point of the phase diagram using the finite-size tangential scaling method, where we have a topological phase transition of critical exponent ν = 2 3 . Next, we investigate the universality of topological phase transitions for a class of ferrimagnetic chains where we demonstrate that the zero-field critical points that arise in this class of models are universal and belong to the universality class SU(2) Wess-Zumino-Witten with ν = 2 3 . Finally, we investigated another tetramer ferrimagnetic chain with S1 = 1 and S2 = 3 2 , obtaining a rich phase diagram of the model showing successive transitions of topological phases at zero field. We investigate these transitions again implementing the finite size tangential scaling method, where we demonstrate that these transitions are also universal and belong to the SU(2) Wess-Zumino-Witten class with ν = 2 3 . Finally, we investigate the role of distinct dissipations in the symmetry-protected topological order given by the Affleck-Kennedy-Lieb-Tasaki model in one dimension using tensor network methods. We show that for asymmetric dissipations with respect to time-reversal symmetry the nontrivial topological ordering is destroyed with increasing dissipation intensity γ. For the case of symmetric dissipation, we saw that the model’s symmetry-protected topological phase is maintained, validated by measurements of the order parameter string, purity Γn, and analyzing the Schmidt spectrum. It is worth mentioning that we identified the degeneracy pattern in the Schmidt spectrum of the model’s density matrix in the steady state, as it is possible to observe in the entanglement spectrum in the case of non-trivial topological phases for pure states. Our results validate the argument that we obtained a dissipative symmetry-protected topological phase and that can be characterized by tools also used for the case of pure states.

The manipulation of particles or microstructures without contamination, either due to the environment or direct contact is of great interest for studies focused on biotechnology and the development of new drugs and applications aimed at diagnosis. In this context, it is necessary to study techniques that make this process more effective. In recent decades there has been a movement in order to remedy this need. In the present work, we will explore techniques for manufacturing acoustofluidics devices, which combine microfluidics techniques coupled with ultrasonic systems, with this capability, as well as advantages and disadvantages. We will study the physical quantities involved in these devices, and how their behavior affects/implies the aggregated features. We will demonstrate the manufacture of these devices, with project development based on analytical simulation, 3D modeling and manufacturing via additive manufacturing, using a printer with DLP technology based on photopolymerizable resin. This device will be able to levitate and standardize objects or beings of the order of µm, we will evaluate its operation, in addition to indicating pioneering applications for the evaluation of microorganisms such as the causes of leishmaniasis and also Raman spectroscopy, reducing the analysis time, increasing practicality, and amplifying the captured signal through improvements in the focusing system used.

Many researches are related to the use of organic compounds markers by dansyl chloride (DNS-Cl), which can be a flexible and sensitive means for fluorescence detection. Widely used in areas such as pharmacology, toxicology, organic synthesis and biochemistry. There are no reports on the theoretical study of the DNS-Cl molecule in crystalline form. The crystal structure of DNS-Cl was calculated and analyzed to the following structural properties, electronic, optical and normal modes of vibration, infrared and Raman spectra, as well as thermodynamic properties. It is investigated by simulation using first principle calculations in one approach pseudopotential within the formalism of density functional theory (DFT). We consider the generalized gradient approximation with dispersion correction (GGA + TS) and the local density approximation (LDA-CAPZ) implemented in the CASTEP code. In the calculation of the band structure, a direct gap of 1.83 eV for GGA + TS and a direct gap of 1.73 eV for LDA was found. Optical properties were calculated considering the polarization along the 100, 010, 001 direction and for a polycrystalline sample. Infrared spectra and Raman thermodynamic properties were also obtained and analyzed. The crystal has characteristics of a semiconductor material proven by the band structure, if synthesized with great potential in organic crystal applications, or placed in the crystallographic data blank used as a reference for future research on the studied crystal structure.

We introduce a model for the interaction between a Gaussian beam and a dielectric structure composed of three isotropic layerswith balanced gain and loss, satisfyingthePT symmetry condition,with the central layerbeinga passive one (no gain or loss). Our objective is to calculate the reflection and transmission coefficients of the system and verity their dependence on the geometrical and gain/loss properties of the materials. The size of the central layer can be controlled, varying from zero (by-layer) to a finite value (tri-layer) and the gain/loss rate of the active layers can also be controlled by varying the imaginary part of the refractive index. We compare the results obtained with the Gaussian beam with the usual plane wave model and the differences found between both models are discussed.

Titaniumdioxide (TiO₂) is a semiconductorthatpresentsabsorptionandemission in the ultravioletregion, photostability, catalyticandosseointegratingpropertiesthatallow its use in varioustechnologicaland medical applications, such as catalysts, photovoltaic devices andosseointegratingagents. The incorporationoftransition metal ions (MT) in semiconductorsgenerates magneto-opticalpropertiesthatcanbetuned as a functionof the dopantconcentration. Fewworks in the literaturestudy the structural, opticalandmorphologicalpropertiesof MT-doped TiO₂. Therefore, in ordertounderstandhow the physicalandchemicalpropertiescanbeinfluenced as a functionof the dopantconcentration, in thisworkwesynthesizedandcharacterizednanocrystals (NCs) of TiO₂dopedwithincreasingconcentrationsofmanganeseions (Mn⁺²) by the methodofchemicalprecipitation. Structuralpropertieswereinvestigatedusing X-Ray Diffraction (XRD) and Raman Spectroscopy. OpticalpropertieswereinvestigatedusingOpticalAbsorptionSpectroscopy (AO) andapplicationof the Crystal Field Theory (CCT) model. The morphologicalpropertieswereinvestigatedusingScanningElectronMicroscopy (SEM). In the XRD and Raman spectradiffractionpatterns, the XRD diffractionpatternsand the bands correspondingto the characteristicvibrationalmodesof TiO₂NCs in the anatasephasewereobserved, respectively, notbeingalteredwith the doping concentration. In the AO spectra, the absorption band characteristicof TiO₂NCswasobservedandthatwithincreasing doping therewas a red shift, whichisrelatedto the strongsp-d exchangeinteraction, confirming the incorporationof Mn2+ ions in the NCs. of TiO₂. In the applicationof TCC andwith the aidofTanabe-Suganodiagrams, it wasshownthat Mn²⁺ionsweresubstituted for thoseof Ti⁴⁺ in tetrahedralandoctahedral sites of TiO₂nanocrystals, dependingon the doping concentration. Therefore, basedontheseresults, the successfulgrowthofpureand Mn²⁺-doped TiO₂NCs in the anatasephasewasconfirmedandthat, dependingon the concentration, it ispossibleto tune the site where the Mn²⁺ions are, stronglyaltering the opticalproperties.

In this work we use force curves obtained through the atomic force microscope (AFM) to
study the influence of probes, substrates and media on tip-substrate adhesions. The probes
HYDRA – 100NG, ACCESS – EFM and ACT – SS were used, whose tips are made of silicon (Si)
and silicon coated with Platinum (Pt). The experiments were carried out in three stages. In
the first step, we carried out experiments by interacting the probes on a glass substrate in
air, and, through the force curves obtained, it was observed that there was a greater
adhesion in the interaction of the HYDRA - 100NG and ACT -SS probes with Si tips. In the
second step, for each probe used, measurements of the interaction with two different
substrates were performed: glass and mica, in air. For this case, the AFM force curves
showed that the adhesion of the HYDRA – 100NG and ACT –SS probes on the mica
decreased while the adhesion on the mica of the probe with Pt coated tip, ACCESS – EFM,
increased. In the third stage of the experiment, for each probe and for each substrate,
measurements were carried out in air and in liquid, and in all the curves obtained, a
decrease in the adhesive force was observed in relation to the measurements made in air.
These results are important, since many studies using AFM need to know how the behavior
of adhesion forces in tip-substrate interactions, such as the functionalization of tips and
substrates for the construction of nanobiosensors based on AFM. And, as perspectives,
taking into account the results obtained, the next steps will be towards the fabrication of a
nanobiosensor based on AFM starting from the functionalization of a HYDRA - 100NG probe
and a mica substrate, performing measurements in liquid medium.

Coherent light scattering by a disordered media generally produces speckles displaying Rayleigh statistics. Research on speckle patterns has been developed over the years. In the special case of non-Rayleigh speckles, basically their patterns maintain a spatial random granular structure, but the intensity probability distribution deviates from the Rayleigh statistics. In our work, we propose an easy and efficient method to generate a continuous range of contrast values corresponding to sub-Rayleigh and super-Rayleigh. We name this speckle fields exact non-Rayleigh non-diffractive (ENRND). The generated Speckle fields are solutions of the Helmholtz scalar equation. We use a computer to control the relative phases of a plane wave decomposition of the speckle fields. Therefore, it was possible to generate patterns without losing the non-diffractive characteristics and keeping non-Rayleigh statistics during the propagation.

Microfluidics, Passive Micromixers, Unbalanced Colisions

All the questions and situations presented in this thesis are complementary and intermingle to point the discussions towards its theme. We study the properties of transport, quantum entanglement, quantum coherence, superoscillations and the emergence of extreme events in discrete-time quantum walks (DTQWs). For this, it was necessary to insert some elements such as: aperiodicity, non-linearity, noises, disorder and artificial fields. We begin by studying how the localization properties, energy spectrum and quantum entanglement between degrees of freedom of a DTQWs are changed when adding an aperiodic spatial dependence in the quantum coin operator. The aperiodicity is described by coins spatially dependent on the positions in a 1D chain. Within the transport properties, we identified two regimes: delocalized and localized quantum walks mediated by an adequate adjustment of the parameter that controls the degree of aperiodicity of the distribution. Using energy spectra analysis, we show that at the initial stage inhomogeneity leads to a vanishing gap between two main bands, which justifies the predominantly delocalized character. For a sufficiently high degree of aperiodicity, we observe an energy spectrum, which resembles that described by Anderson’s one-dimensional model. Regarding the quantum entanglement of the system, we have shown many configurations where an increase in the ability to generate entanglement is observed. This behavior brings new information about the role of aperiodicity in this correlation between the space of position and the quantum coin for systems with static inhomogeneity, in contrast to what was previously reported, as almost always reducing entanglement when compared to the homogeneous case. Finally, we extend the analysis to show that systems with static heterogeneity are capable of exhibiting an asymptotic limit. Further on, inserting non-linearity, we study the existence and characterization of self-trapping phenomena in DTQWs. When considering a Kerr-type nonlinearity, we associate a probability density-dependent phase acquisition at each time step. Adjusting the nonlinear parameter and the quantum coins, we show the existence of different dynamic regimes, including those with traveling or self-trapping solitons-like structures. After mapping non-linear events in DTQWs, we propose a model to study the consequences of having noise and non-linear interaction associated with a qubit propagating in a circular chain. By employing quantum coherence measures, we report emerging unstable regimes in which quantum walks arise, such as self-focusing and breathing dynamics. Furthermore, we study the dynamics of a quantum walker submitted to independent and time-dependent phases simultaneously. Where such dynamics emulates a quantum particle charged in a lattice subjected to a superposition of static and harmonic electric fields. With appropriate adjustments, we investigated the possibility of inducing Bloch-type superoscillations, resulting from a tuning close to the harmonic phase frequency and that associated with Bloch-type oscillations. Furthermore, we show that under exact resonance conditions it is possible to establish a unidirectional motion. We show that the average drift velocity can be well described within an analog continuous-time model. Finally, we use the general framework of discrete-time quantum walks to study the physical origins of rogue waves through random phase modulation. We reveal its long-tail statistics, distribution profile, and dependence on the degree of randomness of the system. We were able to classify these extreme events as belonging to the Gumbel family of distributions.

The study of Lorentz symmetry violation in field theory has gained a lot of attention in recent years, mainly from the discovery that in string theory we have the possibility of spontaneous breaking of Lorentz symmetry when we take the low energy limit. These studies motivated the construction of the standard model extension (SME), which is, in fact, an extension of the usual standard model (SM), in which all possible terms that violate the Lorentz and CPT symmetries are added, respecting the gauge. The minimal SME contains only renormalizable terms, while the non-minimal SME includes allnon-renormalizable terms. In the first part of this work, we studied the non-minimal extension of Quantum Electrodynamics (QED), considering all Lorentz violation operators (LV) of mass dimension d = 5, and investigated the possibility of generating the Carroll-Field-Jackiw (CFJ) and its higher derivative counterpart on the non-minimal coupling constants. We explicitly demonstrate that there is no generation of the CFJ term when we adopt the dimensional regularization scheme. Furthermore, we show that the divergent parts of the higher derivative terms can be eliminated by considering certain proportionality relationships between the coefficients. In the second part, we consider the Horava-Lifshitz (HL) like QED with z = 3 , in which we include the axial vector b0,i that breaks the CPT symmetry. For this model, we calculated the CFJ term in different regularization schemes and found that the CFJ term is finite, however, ambiguous, since it depends on the regularization scheme used. Finally, we calculate the CFJ term of this model using the functional integral approach, in which we find once again that the CFJ term is finite, but undetermined.

Carbon dots constitute a new class of carbon-based nanomaterials that have been the
subject of an increasing number of researches since its discovery in 2004. Presented as an
alternative to the use of metallic and inorganic nanostructures, its uorescent properties,
biocompatibility and low production cost allow its use in several areas. In the present
study, a hydrothermal synthetic method was used to produce carbon dots derived from
5 - (dimethylamino) naphthalene- 1 -sulfonyl (Dansil Chloride) co-doped with Nitrogen
and Sulfur. Through morphological characterization, it was possible to identify the core
crystalline structure and the functional groups attached to the surface of the nanoparticle. Spectroscopy revealed an excitation-dependent uorescence for wavelengths greater
than 400 nm. Thermal analyzes determined the temperature-dependent behavior of the
emission spectrum through an increase in intensity proportional to the increase in the
sample temperature, which was associated with the phenomenon of reverse intersystem
crossing, promoting a thermally activated delayed uorescence. The absolute thermal
sensitivity was determined as 1:04oC-1 and the absolute sensitivity exhibited an increase from 0:45oC-1 to 0:55oC-1 in the temperature range 20oC - 60oC. The possibility
of applying this structure as a raciometric thermal sensor was investigated through the
continuous thermal variation in heating and cooling cycles. Additionally, the quantum
yield of singlet oxygen generation by carbon dots was studied in order to propose its use
in techniques such as Photodynamic therapy

How the brain processes information from external stimuli to perceive and act upon the world is one of the biggest questions in neuroscience. To answer this question, different time series analysis techniques have been employed to characterize the statistical properties of brain signals during cognitive tasks. Usually, specific response processes are addressed by comparing the time course of the average event-related potentials in different types of tests. Here, we analyze data from monkey Local Field Potentials during visual pattern discrimination called the Go/No-Go task in light of quantifiers from information theory. We show that the Bandt-Pompe symbolization methodology for calculating the entropy and complexity of the data is a useful tool for distinguishing response-related differences between Go and No-Go trials. We propose to use an asymmetry index to statistically validate the differences between trial types. Furthermore, by using the multi-scale approach and incorporating time delays to reduce data sampling, we can estimate the important time scales at which relevant information is processed.

Nonlinear phenomena, such as modulational instability (IM) and self-trapping, are present in some physical systems such as in the areas of optics, Bose-Einstein condensate and plasma physics. We can observe IM in nonlinear media with dispersive effects, occurring when we add a small disturbance in the amplitude of the wave function and it is amplified. It is already established for a chain without saturation that the critical non-linear coupling parameter above which occurs IM decays with the inverse of the chain size. With this, using the Holstein model, our goal is to study MI in a one-dimensional nonlinear system, with saturated nonlinearity. To investigate the nature of this phenomenon, we solved the discrete nonlinear Schrödinger equation (DNLSE) numerically with the aid of the eighth-order numerical Runge-Kutta method. In our calculations, we used the participation function, a measure of the degree of localization, and calculated the square module of the wave function, to observe its profile. We solved the nonlinear continuous Schrödinger equation analytically, where we made a theoretical estimative for the critical values of the saturated nonlinearity. We found that when considering saturated nonlinearity, the behavior changes and this critical parameter decays with a term proportional to the inverse of the chain size plus another term that decays with the inverse of the chain size squared. We also show that the increase in saturation promotes the displacement of the critical parameters of intensity of the non-linearity of the transitions already known in the unsaturated case.

A partially coherent polychromatic field was scattered by a PT-symmetric material. We described the scatterer by a gaussian sphere and, we observed the scattered radiation at the far-field. We analyzed this process under the formalism of classical coherence theory, assuming the validity of Born's approximation. Our results show that correlation-induced spectral changes are strongly dependent on the gain and loss properties of the material. For example, the center frequency of the spectral density of the scattered field shows a discontinuous behavior as a function of the non-hermitian parameter characterizing the properties of gain and loss of the material. This discontinuity is due to the introduction of the non-hermiticity to the system generates a root inside of the hermitian spectrum, creating an asymmetrical split in the spectrum. We also observed new scattering directions induced by gain and loss properties of the material who are forbidden in the Hermitian case.

We study the dynamics of entanglement in a one-dimensional coupled-cavity array, with each cavity containing a two-level atom, via the Jaynes-Cummings-Hubbard (JCH) Hamiltonian in the single-excitation sector. The model features a rich variety of dynamical regimes that can be harnessed for entanglement control. The protocol is based on setting an excited atom above the ground state and further letting it evolve following the natural dynamics of the Hamiltonian. Here we focus on the concurrence between pairs of atoms and its relation to atom-field correlations and the involved free-field modes. We show that the extension and distribution pattern of pairwise entanglement can be manipulated through a judicious tuning of the atom-cavity coupling strength. Overall, our work offers a comprehensive account of the machinery of the single-excitation JCH Hamiltonian and contributes to the design of hybrid light-matter quantum networks.

In the present work, we investigate the phase transitions in liquid-crystalline systems involving the smectic-C phase under the effect of an external electric field. Initially, a review of the theoretical model of Maier-Saupe, which describes the nematic-isotropic phase transition was performed, where we determine the behavior of the order parameter, which abruptly goes to zero at the transition temperature. We then approach the McMillan model, which is an extension of the Maier-Saupe model, including the smecticA-nematic transition in our study. With this model we determine the behavior of the order parameters as a function of temperature and reproduce the phases diagrams. In addition, to these two well-known models, we have included in the work a brief review of the model developed by Govind and Madhusudana, which describes the smectic-C -smectic-A phase transition. This model motivated us to further study the smectic-C phase, which made us propose a new theoretical model on the liquid crystalline phase in question. With our model, it was possible to determine the properties of the system, which allowed us a more complete analysis and description of the phase transitions involving the smectic-C phase, in addition to using a smaller amount of descriptive model parameters. Finally, we analyze the effect of an external electric field on phase transitions involving the Sm-C phase, studying the changes in the thermodynamic and statistical properties of the system under such effect.

This thesis investigates surface and finite size effects on the phase transitions of free-standing smectic-C films and electric field effects in the bulk. Initially, a review is given of existing and widely used microscopic models for the description of phase transitions in liquid-crystalline systems presenting nematic and smectic-A phases. We then review the model developed by Govind and Madhusudana, describing the smectic-C–smectic-A phase transition. Motivated by their approach, we propose a new theoretical model to describe phase transitions in systems presenting the smectic-C phase. Using a single-particle mean-field potential, we show that the phase diagram of liquid-crystalline compounds with a small transverse dipole can be reasonably described when the tilt-induced contraction of smectic layers is considered and with a reduced number of model parameters. Aiming to extend the proposed model for freely suspended films, McMillan-Mirantsev’s model for free-standing smectic-A films is reviewed. The model introduced by Mirantsev shows that surface anchoring stabilises the smectic phase for temperatures above the bulk transition temperature. Considering a tilt angle profile and a discrete version of the single-particle mean-field potential, the interplay of surface anchoring and finite size effects affects the behaviour of the order parameters in free-standing smectic-C films. The transition temperature is shown to depend on surface ordering and film thickness. The orientational order imposed by surface anchoring is shown to stabilise the tilt order parameter in the film surface above the bulk smectic-C–smectic-A transition temperature. Surface layers therefore remain in the smectic-C phase, while the central layers undergo a smectic-C–smectic-A phase transition. The effect of an external electric field is considered in smectic-C bulk samples, inducing a reorientation of the director vector and thus enabling the suppression of the isotropic phase and the appearance of residual and field-induced nematic phases.

Synchronization of non-linear systems has been extensively studied in several systems both in physics and biology. In particular, an unusual type of synchronization, called anticipated synchronization (AS), was discovered by Voss, when two dynamic systems were unidirectionally coupled. The AS regime can occur when a dynamic system ("sender") described by a set of ordinary differential equations is coupled unidirectionally to a "receiver" system described by the same equations but subjected to a negative delayed self-feedback. In such cases, AS is characterized by a negative phase difference between the transmitter and the receiver. Recently it was reported that the electrical activity of cortical regions of the monkey brain can display this type of synchronization during the performance of cognitive and motor tasks. In this work, we studied a model of neuron populations of Izhikevich that can display both the AS regime and the usual delayed synchronization regime (DS), characterized by a positive phase difference. In this model each neuron receives an external noise, simulating excitatory synapses coming from other brain regions, which obey a Poisson distribution. We show that for a set of biologically plausible parameters, this model presents a bistable regime between DS and AS. We also found that the properties of this bistability depend on the relationship between the synaptic conductances of the receiving population, the unidirectional coupling, and the external noise in each neuron. We suggest that this motif could represent a toy model for cortical regions during bistable percepetion.

In the last decades, several studies have been carried to analize topolological defects in liquid crystals confined in curved geometries. In this way, we approach the main results of these researches, such as the study of spherical shells of liquid nematic crystals, together with the method of formation of these shells, and the study of nematic shells with variable curvature. We performed the theoretical analysis of the formation of topological defects in liquid crystals confined to nanoscopic shells. For this, we analyze the most frequenttypes of barrier disclination and how to identify the topological charge associated with the defect. There are several factors that can modify topological defects in a shell, such as temperature variation and external field effects. We used Molecular Dynamics to investigate the formation of defects in liquid crystals samples in the nematic phase. In this work, we show the results of the molecular simulation of the director field from the influence of the longitudinal electric field and the transverse electric field.

Recently, luminescent nanoparticles have aroused the researchers' interest in several applications: for fluorescence bioimaging, as efficient biomarkers in tissues of small animals and individual cells, including cancer cells, and as nanothermometers. Among the nanoparticles that are used for nanothermometry, those that are doped with rare earth ions (such as Yb³⁺, Er³⁺, Tm³⁺, Ho³⁺ and Nd³⁺) stand out. But, in general, they have low relative thermal sensitivity. Thus, in order to obtain an increase in the relative thermal sensitivity of nanoparticles doped with rare earth ions, we have proposed here a new way to use their emissions to measure the temperature. The idea is to calculate the emissions ratio associated with four emission peaks, taking the ratio between pairs of peaks, where one of the ratios increases and another ratio decreases with temperature. With this new approach we have showed theoretically, and experimentally, that the effective relative thermal sensitivity will be the sum of the relative thermal sensitivities associated with each pair of emission peak. To prove this proposal, we synthesized seven samples (core-shell and core-shell-shell nanocrystals) doped with Yb³⁺, Tm³⁺, Er³⁺ and Nd³⁺ ions. The LaF₃ core-shell nanoparticle doped with Yb³⁺, Tm³⁺ and Nd³⁺ (LaF₃:YbTm@YbNd) showed the highest value for the maximum relative thermal sensitivity, in this case, 4.0% K^-1 at 29 °C, when compared to the other samples synthesized here. This value obtained is much higher than many other founded in the literature for a system doped with rare earth ions (approximately double). We also obtained a high value for the relative thermal sensitivity of the LaF₃ core-shell-shell nanoparticle doped with Yb³⁺, Tm³⁺, Er³⁺, and Nd³⁺ (LaF₃:YbTm@YbEr@YbNd), whose the value is equal to 3.00% K^-1 at 30 °C. In conclusion, this work has showed a new way to increase the relative thermal sensitivity of nanoparticles doped with rare-earth ions for use in nanothermometry.

Propriedades de transporte eletrônico em sistemas de elétrons interagentes e um tema central dentro da física de estado sólido. Entretanto, aléem do elevado custo computacional, tais sistemas podem apresentar restrições ao considerar méetodos perturbativos. Neste cenáario, modelos de baixa densidade eletrônica têm se mostrado uma boa alternativa para o estudo mostrando-se capaz de resgatar aspectos importantes presentes em sistemas de muitas partículas interagentes. Um desses fenômenos é o enfraquecimento da localização de Anderson promovido pela interação elétron-eléetron. Tal fenomenologia foi reportada inicialmente em estudos experimentais de correntes persistentes em anéis mesoscópicos. Entretanto, comportamentos semelhantes estão presentes em férmions em redes óticas, condensados ultra frios, modelos de Anderson-Hubbard em 1D, 2D e 3D, e vidros de Coulomb 2D, sugerindo algum grau de competição entre desordem e interação. Entre os trabalhos sobre esta temática, destacamos o trabalho de Dias e Lyra[Physica A 411 (2014) 35-41], que estudaram dois elétrons se movendo em um potencial desordenado unidimensional e mostraram uma influência não monotônica da interação elétron-elétron na localização de Anderson. Outro fenômeno interessante que surge da proposta de baixa densidade eletrônica e o dobramento da frequência de Bloch causado pela interação entre elétrons em sistemas 1D, indo de encontro com resultados de muitos corpos que mostravam que a interação atua destrutivamente nas oscilações de Bloch. O resultado do dobramento foi previsto teoricamente pelo trabalho de Dias e colaboradores[Phys. Rev. B 76 (2007) 155124] e confirmado mais tarde experimentalmente[Science 347 (2015) 1229{1233]. No corpo desta dissertação apresentamos estudos envolvendo os dois cenários. Em um primeiro momento, nos investigamos a existência do caráter não monotônico da localização de Anderson em redes unidimensionais com desordem estrutural. Posteriormente, apresentamos nossos estudos considerando as oscilações de Bloch para sistemas de elétrons interagentes, considerando agora a inclusão de um termo de interação entre as partículas não-local. Os dois sistemas estudados mostram o papel relevante que a interação pode desempenhar sobre a dinâmica dos elétrons. Os resultados revelam aspectos competitivos entre diferentes estados eletrônicos presentes no sistema.

In this work, we investigated the effects of 𝑌b3+ concentration and temperature on the structural and optical properties of nanocrystals (NCs)based on fluorides (𝐶𝑎𝐹2, 𝐿𝑎𝐹3 and 𝑁𝑎𝑌𝐹4) co-doped with 𝑌b3+/ Tm3+ under anti-Stokes excitation at 1064 𝑛𝑚. For that, sets of samples were synthesized varying the 𝑌b3+ concentration (2,10,20 and 40 𝑚𝑜𝑙%) and keeping that of Tm3+ fixed at 0.5 𝑚𝑜𝑙%. We initially analyzed the structural properties by means of X-ray diffraction (XRD) and transmission eléctron microscopy (TEM). Subsequently, the Upconversion (UC) processes in the 400 to 900 𝑛𝑚 spectral region were investigated, Where we observed the effect of the 𝑌b3+ concentration under anti-Stokes excitation. Comparatively, the UC emission spectra of the 𝐶𝑎𝐹2 and 𝑁𝑎𝑌𝐹4 samples had similar behaviors with the 𝑌b3+ concentration increasing, with the samples doped with 10 and 20 𝑚𝑜𝑙% being the best for UC, i.e., these NCs showed concentration quenching, which did not happen with the 𝐿𝑎𝐹3 NC. An important observation was the increase in the UC emissions with temperature for all concentrations, which enhances applications such as fluorescente and termal imaging. Finally,we investigate the potential of the investigated NCs as termal nanosensors based on optical properties, using the fluorescence intensity ratio (FIR) approach, in the temperature range from 313 to 473 K (40 °C to 200 °C), under anti-Stokes excitation. Regarding the results of nanothermometry, all emission bands increased with temperature, and this increasein the UC was attributed to the phonon-assisted anti-Stokes excitation process, which is strongly dependente on temperature. FIRs of several bands were investigated with the purpose of obtaining the best termal sensor and, finally, no major differences were found in the relative termal sensitivity (𝑆𝑟) of the optical nanothermometers, with the increase in the 𝑌b3+ concentration, but obtained diferente evolutions with the temperature. We believe that these results are due to the fact that these NCs have very similar phonon energies (They are all fluorides), although They present very diferente fluorescente yields.