In this work, we study the propagation of a massless scalar field in a
Schwarzschild spacetime modified by a background Kalb-Ramond field, which induces
spontaneous Lorentz symmetry breaking via a non-minimal coupling to gravity. The
Klein-Gordon equation is solved analytically by mapping its radial equation onto the
confluent Heun equation. Near the event horizon, we analyze the thermal spectrum and
the Hawking temperature perceived by stationary observers, examining how geometric
modifications influence the emission flux. In the asymptotic region, the radial equation
reduces to a Coulomb-like form in the low-frequency limit, allowing us to obtain
analytical expressions for the phase shifts and scattering cross sections. Furthermore, we
discuss the conditions for the polynomial truncation of confluent Heun solutions and
their relation to the numerical quasinormal mode spectrum computed via Leaver’smethod and the WKB approximation. Finally, the analysis of the effective potentialallows us to verify the modal stability of the scalar field. The results indicate thatspontaneous Lorentz symmetry breaking alters the geometrical, thermodynamical, andwave properties of the black hole while preserving overall linear spacetime stability.

We investigate the renormalization and calculation of critical exponents in the scalar field theory of the λϕ3 type, formulated inspacetimes with explicit Lorentz-symmetry violation (LV). The starting point is the canonical theory in d = 6 − ε dimensions, the uppercritical dimension at which the cubic interaction is marginally relevant. Building on the foundational concepts of quantum field theory,we systematically construct the renormalization constants Zϕ, Zm2 , and Zλ up to two loops, employing dimensional regularization inthe minimal subtraction (MS) scheme. For the general case of an N-component field with the Potts-model interaction tensor dijk,we derive the relevant tensor contractions bα = (N + 1)2(N − 1), bβ = (N + 1)2(N − 2), and bγ = (N + 1)6 − 6(N + 1)5 + 10(N + 1)4,and obtain the beta function together with the anomalous dimensions. The non-trivial fixed point u∗(ε) yields the universal critical
exponents η(ε) and ν(ε). The special cases N = 1 (Yang–Lee edge singularity) and N → 0 (percolation) are examined individually,and numerical estimates in physical dimensions are obtained via Padé approximants [1, 1], with a discussion of the limitations imposedby the asymptotic nature of the ε-expansion. The extension to the LV scenario is performed by introducing a small, symmetric,
constant background tensor Kμν, with |Kμν| ≪ 1. The modified propagator admits a perturbative expansion in Kμν; we show that eachindependent loop-momentum integration introduces a multiplicative factor Π ≡ 1 − 12Kμνδμν, so that an L-loop diagram carries ΠL.
Consequently, the LV renormalization constants satisfy ZLV = ZLI(u → uΠ1/2), and the non-trivial fixed point shifts to u∗2LV = u∗2LI/Π.The central result of the dissertation is that, upon evaluating the anomalous dimensions at the shifted fixed point, all factors of Π cancelexactly, yielding critical exponents identical to those of the Lorentz-invariant theory: ηLV = ηLI and νLV = νLI, to two-loop order and for
|Kμν| ≪ 1. This outcome is interpreted as a direct consequence of the universality principle: the kinetic-sector Lorentz violation doesnot modify the internal symmetry that defines the universality class and is therefore irrelevant at the critical fixed point.

In this work, a theoretical study based on Density Functional Theory
(DFT) was carried out on linear hydrogen-saturated carbon chains (CₙH₂, with
n = 4, 6, and 8) confined inside single-walled carbon nanotubes of the zigzag
(8,0) and armchair (5,5) types under the influence of a transverse external
electric field. The structural and electronic properties of these systems were
investigated, with emphasis on bond length alternation (BLA), transverse
deformation, charge transfer, and the electronic response to the applied field.
The results showed that systems based on the (8,0) nanotube exhibit a more
pronounced structural and electronic response compared to the (5,5) systems,
including greater charge redistribution, stronger BLA reduction, and higher
sensitivity of the electronic band gap. Despite these modifications, all systems
preserved the polyyne character of the chains and maintained a finite band gap
throughout the investigated field range. The analysis of the band structure and
projected density of states revealed that the electronic response is
predominantly governed by the host nanotube, while the carbyne chain acts as
a secondary electronic perturbation. An essentially reversible structural
behavior was also observed after removal of the electric field.
Additionally, the effects of substitutional boron and nitrogen doping on two-
dimensional carbon allotropes of the tripentaphene (TPH) type were
investigated. The results indicated that doping significantly modifies the
electronic properties of these systems, promoting transitions between metallic
and semiconducting behaviors, as well as modulation of the band gap. The
obtained results highlight the potential of these hybrid materials, as well as two-
dimensional allotropes, for applications in nanoelectronics and the engineering
of materials with tunable electronic properties.

The search for new two-dimensional carbon allotropes has
intensified due to the potential of these materials in nanoelectronics,
especially as alternatives to graphene, whose absence of a band gap limits its
applications in semiconductors. Graphyne-like structures, characterized by
the coexistence of and sp sp2 hybridizations, allow the modulation of
electronic properties through structural variations. With the synthesis of the
biphenylene monolayer (BPN), it becomes possible to theoretically investigate
new structures derived from its crystalline network with incorporated
acetylenic linkages. The objective of this thesis is to theoretically investigate,
through the formalism of Density Functional Theory (DFT), the structural,
electronic, and mechanical properties of a new two-dimensional carbon
allotrope derived from BPN, which we denote as ɑ-BPNGY or BPN graphyne,
as well as its quasi-one-dimensional systems, such as nanoribbons and
nanotubes. In this context, we propose to evaluate the structural and
mechanical stability, anisotropy, band structure, density of states (DOS), and
the spatial distribution of the wave functions, as well as the influence of
width, diameter, and chirality in the quasi-1D systems. The results indicate
that the proposed two-dimensional structure is metallic in the non-spin-
polarized (NP) state, but becomes semiconducting in the antiferromagnetic
(AFM) state when the bipartition of the lattice into spin sublattices is
considered, with the opening of a gap on the order of 0.15 eV. The mechanical
stability of ɑ-BPNGY was confirmed by the absence of negative frequencies in
the phonon dispersion, and its thermal stability was evidenced by ab initio
Born–Oppenheimer molecular dynamics (BO-MD) simulations. It was
observed that increasing the number of acetylenic units ( = 1, 2, and 3; n
where indicates the number of acetylenic links) directly influences the n
mechanical properties, imparting anisotropy to the investigated systems (ɑ-
BPNGY, ɑ-BPNGY-2, and ɑ-BPNGY-3). In the quasi-1D systems, the electronic
behavior of nanotubes depends on chirality and diameter, whereas that of
nanoribbons depends on width. The evaluated nanoribbons are
semiconducting, with gaps ranging from 0.07 to 0.46 eV. Most of these one-
dimensional systems exhibit a spin-polarized semiconducting state similar to
that observed in the two-dimensional system. These findings highlight the
possibility of fine-tuning the electronic properties, emphasizing the potential
of these materials for nanoelectronic applications.

O monitoramento de íons metálicos em altas concentrações industriais
é frequentemente limitado pela saturação de sinal e pela não linearidade
inerentes aos sensores ópticos convencionais. Este trabalho propõe uma
plataforma de sensoriamento baseada em Pontos de Carbono (PCs) sintetizados
a partir do mesocarpo de Orbignya speciosa, integrando as espectroscopias de
Fluorescência (FL) e Espectrometria de Lente Térmica (TLS) a algoritmos de
Aprendizado de Máquina. A abordagem multitécnica revelou assinaturas físico-
químicas distintas para cada analito: o cobre (Cu2+) induziu supressão estática
dominada por agregação e espalhamento de luz; o cobalto (Co2+) ativou
mecanismos dinâmicos de esfera de ação em regime de lente térmica forte; e o
níquel (Ni2+) apresentou comportamento regido por acessibilidade fracionada. O
modelo Random Forest (RF) alcançou precisão máxima (100%) na classificação
e superou modelos lineares e SVR na etapa de quantificação, demonstrando
robustez ao interpretar distorções cinéticas e espectrais complexas. Em síntese,
a convergência entre nanomateriais sustentáveis e inteligência artificial viabiliza
diagnósticos precisos em regimes de alta concentração, superando gargalos
analíticos tradicionais do sensoriamento óptico.

Os efeitos relativísticos associados ao movimento não inercial
desafiam a preservação da informação quântica, induzindo a criação de
partículas dependentes do observador e ambientes térmicos cujo impacto nas
medições quânticas ainda não é totalmente compreendido. Motivados por isso,
o principal objetivo desta tese é analisar como a aceleração, as propriedades
do campo, a estrutura de interação e a cinemática do detector afetam a
coerência quântica, a dinâmica de transição e a dualidade onda-partícula no
contexto da informação quântica proveniente de detectores acelerados. A
metodologia baseia-se na evolução perturbativa do sistema detector-campo,
empregando o operador de evolução temporal para obter a matriz de
densidade reduzida após interações de tempo finito. Medidas de coerência
quântica, probabilidades de transição, visibilidade interferométrica
e relações de complementaridade são utilizadas para caracterizar a
degradação da informação em regimes acelerados. Os sistemas estudados
incluem qubits acelerados e circuitos interferométricos sujeitos a vácuo
dispersivo, ruído de fundo de ondas gravitacionais, campos escalares
massivos, acoplamentos não lineares e trajetórias não triviais. Os resultados
mostram que o efeito Unruh atua como um ambiente térmico eficaz que induz a
perda de informação quântica. Mecanismos que amplificam essa degradação,
como vácuo dispersivo, ondas gravitacionais e acoplamentos quadráticos, são
identificados, enquanto mecanismos de mitigação associados a campos
massivos e configurações cinemáticas específicas também são observados. A
tese conclui que a degradação da informação em sistemas quânticos
relativísticos não é universal, mas fortemente dependente do modelo, e
destaca perspectivas para extensões a espaços-tempos curvos, sistemas de
detectores multipartidos e teorias quânticas de campos alternativas.

Este trabalho investiga as propriedades estruturais, mecânicas e eletrônicas do
molibidato duplo N aCe(MoO 4 ) 2 sob condições de alta pressão, utilizando simulações ab
initio baseadas na Teoria do Funcional da Densidade (DFT). A metodologia empregada
adota uma estratégia híbrida: inicialmente, utiliza-se a Aproximação do Cristal Virtual
(VCA) para modelar a resposta da rede sob pressão hidrostática. Para superar as
limitações do VCA na descrição de distorções locais, aplicou-se o método de
supercélula (2 × 1 × 1), no qual os sítios virtuais foram substituídos explicitamente por
íons de Na e Ce em proporção estequiométrica. Essa abordagem permitiu o relaxamento
das coordenadas internas com parâmetros de rede fixos, capturando com certa precisão
as relaxações iônicas e a desordem catiônica. Para descrever corretamente os estados
fortemente correlacionados 4f do cério, utilizou-se o formalismo DFT+U com um
potencial efetivo de 5,0 eV. Os resultados demonstram uma transição de fase estrutural
da fase scheelita (I41/a) para a fase monoclínica M’-fergusonita (P21/c) entre 10 e 12
GPa. Essa transição é caracterizada pela mudança na coordenação do molibdênio de
tetraédrica (MoO 4 ) para octaédrica (MoO 6 ). Eletronicamente, a supercélula revelou um
band gap indireto de 2,845 eV, validando a eficácia da aliança entre VCA e o método de
supercélula para o estudo de molibdatos complexos.

The physical and chemical properties of nanocarbons have attracted the
scientific community’s attention in the last decades. Computational and
theoretical investigations have been indispensable and relevant in the
development of research on these systems. In this context, this thesis presents
a study of the structural, electronic, and magnetic properties of one-dimensional
physical systems conceived via 2D carbon allotropes, recently proposed in the
literature. The me-graphene and ph-graphene are physical systems that present
atoms with hybridized sp 2 and sp 3 states. These structural properties originate a
thickness of angstrom order, differently from atomic thickness associated with
the graphene, characterizing these systems like quasi-2D materials. Through
different chiralities and structural details of edges, nanoribbons were proposed
for each one of these systems. The calculations were developed via density
functional theory (DFT), using the SIESTA computational package. With relation
to the me-graphene nanoribbons (MeGNRs), the results demonstrate that the
confinement and edge effects perform an important role in the investigated
properties. In particular, differently from 2D systems, which are semiconductors
of indirect energy gap, the nanoribbons can display semiconductor behavior of
direct or indirect energy gap, in addition to one of the cases presenting metallic
behavior, exhibiting a low dispersive band around the Fermi level. This last case
shows spin-dependent properties, revealing a phase transition of metal –
semiconductor type between not polarized and polarized states. The ph-
graphene nanoribbons (PHGNRs) can exhibit semiconductor and metallic
electronic behaviors. Once again, confinement and edge effects are crucial to
characterize these systems, which exhibit multiple magnetic states defined by
the spin orientation, which mostly is distributed in the internal atoms of the
structure. In this sense, the energetic stabilization mechanism that occurs from
spin polarization is provenient of internal states of the ribbon, differently from
other systems in the literature, whose central agents are edge atoms.
Therefore, in the PHGNRs case, it was demonstrated that edge effects are
secondary in the electronic and magnetic definitions of the resultant systems,
which made these materials promising for nanoelectronic applications, given
that the synthesis precision in the edge region is not that relevant to the result
properties. Finally, in both cases, it is possible to modulate the system’s
properties by the confinement and edge effects and magnetic ordering of states,
allowing a variety of electronic behaviors and some other characteristics, like
the band profiles and modulation of energy gap, among others.

Neste trabalho filmes finos de poli(2-methoxi-5-(2-etilhexiloxi)-p fenilenovinileno)
(MEH-PPV) foram crescidos pelo método de Langmuir-Blodgett (LB) e Drop Casting para
investigar os efeitos do processamento dos filmes e seu impacto nas propriedades óticas e
elétricas. As propriedades óticas com e sem polarização dos filmes fabricados porespectrofotometria de UV-Vis para explorar o “band-optical gap” e estudar o comportamento dos estados localizados no gap a partir da energia de Urbach e emissão de fluorescência, paraanálise do acoplamento eletron-fonon por meio dos cálculos do parâmetro de Huang-Rhys (S),permitindo assim caracterizar a interação do polímero com o substrato por diferentes métodosde deposição. Primeiramente foi estudada a influência do tratamento por plasma de oxigênionos substratos e sua influência para a deposição das camadas dos filmes poliméricos ondeavaliamos o ângulo de contato, os resultados mostraram que o tempo de exposição aoambiente e a sucessiva aplicação de plasma influenciam diretamente na molhabilidade dossubstratos. Como os filmes e a camada ativa nos dispositivos são processados a partir desoluções, começamos avaliando os efeitos solvatocrômicos na absorção e emissão. A seletividade de cada solvente forma microestruturas e morfologias em solução que podem ser parcialmente mantidas nos filmes produzidos, a partir das alterações nos máximos de absorçãoe emissão e utilizando do deslocamento Stokes, parâmetro de Huang-Rhys (S), comprimento efetivo de conjugação n e experimentos de isoterma de filmes de Langmuir. Com isso foi possível observar a progressão da agregação para cada solvente. Para os filmes LB foi possível distinguir efeitos de interface e de volume, para até 10 camadas há forte influência da interface com Eu duas vezes maior que os valores encontrados para maiores números de camadas depositadas e do que os valores encontrados para os filmes Drop-Casting. Embora Eoptg permaneça essencialmente o mesmo valor, independentemente da direção, o dicroísmo de absorção indica que um número maior de cadeias principais conjugadas estão alinhadas na direção de imersão. Ao mesmo tempo, Eu não apresenta dependência direcional, revelando que a distribuição de defeitos óticos isotrópica. A análise dos parâmetros vibrônicos (fator de Huang-Rhys S, comprimento médio de conjugação n e separação vibrônica E00 − E01) mostraque essas grandezas atuam como marcadores sensíveis da organização estrutural. A caracterização elétrica mostrou que os dois métodos de deposição produzem filmes com perfis de armadilhas marcadamente diferentes. Embora ambos os dispositivos apresentem expoentes de baixo campo semelhantes próximos ao regime ôhmico, o dispositivo LB apresenta transições mais suaves entre as regiões ôhmica, SCLC e TFL. E por final filmes de LB sãoaplicados em dispositivos de Memória, apenas como um estudo introdutório, é observado que os dispositivos LB conseguiram comutar seu estado resistivo com um menor de varreduras I-V.A menor espessura assim como a diferentes organizações desempenham um papel crucial
para as diferenças observadas na Icc.

Esta tese investiga a coerência quântica via entropia relativa de coerência e comprimentos de
coerência em posição e momento em estados gaussianos correlacionados mistos de ondas de
matéria, com ênfase em dois cenários: a evolução livre de ondas de matéria de nêutrons
produzidos por fontes parcialmente coerentes e a dinâmica de ondas de matéria de
macromoléculas, como fulerenos, em um banho térmico Markoviano. No primeiro cenário,
analisamos o comprimento de coerência em posição e momento, bem como a entropia relativade coerência, considerando a correlação inicial entre posição e momento, dada em termos doparâmetro γ. Observou-se que o comprimento de coerência em posição e a entropia relativa decoerência crescem com o tempo e dependem de γ, enquanto o comprimento de coerência noespaço de momentos embora dependa de γ é constante no tempo. A função de Wigner reveloucompressão e rotação no espaço de fase, e fontes parcialmente coerentes modulam acompressão do estado. Uma relação entre a entropia relativa de coerência e os comprimentosde coerência foi estabelecida, sugerindo seu uso como quantificadores de coerência quântica.No segundo cenário, estudamos o impacto do acoplamento com um banho térmico e dascorrelações iniciais entre posição e momento sobre coerência e pureza em macromoléculas.Utilizando equações mestras, verificou-se que maiores correlações aumentam a coerência,mas reduzem a pureza, enquanto que menores correlações favorecem a pureza. Além disso,identificamos um fenômeno inusitado de congelamento da coerência em ondas de matéria defulerenos, o qual é inicialmente influenciado pelo valor da correlação posição e momento γ, mastem valor final independente desse parâmetro. Adicionalmente, estabelecemos uma relaçãoentre coerência e pureza, sugerindo a possibilidade de quantificar a entropia relativa decoerência a partir da pureza, uma grandeza independente da base. Por último, mostramos queé possível extrair informações sobre as propriedades do ambiente medindo da entropia relativa
de coerência e pureza via reconstrução da matriz densidade.

The search for new two-dimensional carbon networks with tunable electronic
properties has driven the study of allotropes that combine sp and sp 2
hybridizations. In this context, this work proposes r��GY a novel rectangular
graphyne sheet composed of phenyl blocks connected by acetylenic chains,
similar to hexagonal ��-graphyne This system is arranged on a rectangular
lattice, analogous to the recently synthesized biphenylene network (BPN). The
stability of this bidimensional material was investigated from different
perspectives, and its structural, electronic, and mechanical properties were
studied through calculations based on Density Functional Theory (DFT) and
molecular dynamics simulations. The results indicate that r��G is dynamically
stable, with a phonon spectrum free of imaginary modes and robust behavior
under elevated thermal conditions, as confirmed by simulations showing bond
integrity up to 700 K. In its original form, the rectangular graphyne behaves as
a semiconducting system, presenting pairs of highly localized states. These
features are directly related to the structural anisotropy of the network, since its
electronic states exhibit quasi-one-dimensional behavior embedded in the two-
dimensional structure. In addition, mechanical properties of the 2D sheet were
calculated, revealing elastic anisotropy, with Young’s modulus and Poisson’s
ratio depending on the orientation, which reinforces its potential for applications
in flexible devices. The electronic properties of nanoribbons based on the
r��G structure were also investigated. It was shown how the electronic structure
of these nanoribbons depends on width and edge type (armchair and zigzag).
Nanotubes derived from r��G were analyzed, demonstrating that the band gap
can be tuned by varying the diameter, which expands the electronic versatility of
the system. Therefore, these results highlight r��GY proposed in this work, as
a promising material for future applications, especially in electronic devices, and
encourage further investigations on the properties of 2D allotropes with sp–sp 2
hybridizations.

In this work, we propose the Octite-sp, derived from the insertion of acetylenic
bridges into Octite SC. This modification changes the structural behavior from
semiconducting to metallic. Furthermore, we investigated the thermodynamic
stability of the structure using the Nosé-Hoover thermostat, and its mechanical
stability using the Born-Huang criterion. The structure showed favorable results,
indicating the possibility of synthesis. We also analyzed the electronic behavior
of nanotubes derived from Octite-sp using the zone folding technique. We found
that for the narrowest nanotube, the results are not accurate when compared to
those obtained through density functional theory (DFT). For larger nanotubes,
zone folding yields more accurate results, and we observed that they exhibit
metallic behavior, consistent with the original 2D structure. As for nanoribbons
of this material, edge geometry effects proved to be relevant, as for a given
cutting direction, it is possible to modulate the energy gap opening or closing it
depending on the nanoribbon type.

In this work, quantum phase transitions in the one-dimensional Axial
Next-Nearest Neighbor Ising (ANNNI) model with transverse field were
investigated, with emphasis on the role of bipartite entanglement as a critical
indicator. The sensitivity of von Neumann entropy to phase changes was
analyzed, and how different choices of bipartitions influence its response in the
transition was evaluated.
Due to the absence of an exact solution for the model with transverse field at
the thermodynamic limit, we applied the Lanczos method to numerically
determine the ground state of finite chains with periodic boundary conditions.
The quantum critical points were estimated using finite-size scaling (FSS)
techniques. In addition, spin correlation functions and the structure factor were
calculated, allowing us to identify magnetic ordering and frustration effects,
including patterns associated with the devil's staircase. The results reinforce
that von Neumann entropy, in addition to adequately identifying the transition
between commensurate phases, is sensitive to spatial modulations originating
from the competition between interactions in the model.

In the present work, the electronic and magnetic properties of
S-graphene, a two-dimensional carbon allotrope, were investigated using the
repulsive Hubbard model solved within the Hartree-Fock approximation
(mean-field theory) and first-principles calculations based on Density Functional
Theory (DFT). Initially, the electronic band structure of S-graphene was
analyzed using the tight-binding model, varying some of the hopping terms,
taking into account the symmetry of the unit cell. We observed that the
modulation of these parameters is crucial for the electronic behavior of the
material, which can exhibit insulating, semiconducting, or metallic phases. We
also identified the presence of flat bands and Dirac cones, evidencing the
influence of the hopping terms on the system's electronic structure. There is a
specific situation where the energy gap disappears, leading the system to a
metallic phase characterized by the overlap of two flat bands at the Fermi level.

The investigation of the magnetic properties was carried out employing the
Hubbard model in the Hartree-Fock approximation. The site-magnetization
curves as a function of the electronic interaction U revealed a continuous phase
transition from a paramagnetic to an antiferromagnetic state, characteristic of a
second-order transition. The phase diagram obtained via mean field identified
three distinct phases: semimetallic (SM), band insulator, and antiferromagnetic
insulator (AFMI). We verified that in these phase transitions, the critical value of
the electronic interaction U can vary between (0.0 − 1.95), demonstrating the
Cinfluence of the hopping terms on specific bonds at the critical thresholds of U .
CWe expect that the variation of the hopping terms can be realized by altering the
distances between the lattice sites, which can be achieved by applying a
uniaxial force (strain) to the cell. The first-principles results, obtained via DFT,
corroborated the mean-field predictions. The analysis of the total energy of the
system as a function of the strain applied in the x-direction of the S-graphene
unit cell revealed that, in an intermediate deformation region, considering spin
polarization (SP) results in a lower energy state compared to the system without
spin polarization (NP). This evidenced the emergence of a magnetically ordered
phase. Additionally, the spatial distribution of magnetization indicated that the
central sites of the S-graphene unit cell are primarily responsible for the
magnetic properties, confirming the mean-field model's predictions. In summary,
this study demonstrated that the application of strain to the S-graphene
structure plays a crucial role in the variation of its electronic and magnetic
properties, with the presence of flat bands and electronic interaction favoring
the emergence of magnetic phases. As a perspective, the Monte Carlo method
can be applied to validate and deepen the understanding of the results obtained
by mean field and DFT.

We study three stochastic processes, the majority vote model, the
contact process, and the asynchronous SIR model, with phase transitions in
complex networks. In theory, we use the heterogeneous mean field theory
(HMF), which considers vertices with the same degree as equivalent, to predict
the transition points in each model and the dependence of the order parameter
on the number of vertices in the network. In each model, it was discovered that
this dependence is given by a scaling relationship like a power law. The
exponents related to the transition point deviation and the order parameter, 1/ν
and β/ν, respectively, presented values compatible with the mean field critical
exponents, presenting heterogeneous scaling corrections for the case of power
law networks. Access to finite size dependence was achieved through the use
of external fields in the differential equations of stochastic processes. The
computational simulations carried out using the Monte Carlo method agree with
the scaling relationships obtained in each model.

We study the Gouy phase that arises from the time evolution of
confined matter waves in a harmonic potential. We consider the quantum
dynamics of a particle represented by a Gaussian wavepacket
position-momentum correlated. By tuning the parameters that govern its
evolution, we uncover interesting effects, with a particular focus on squeezing.
During the squeezing process, a Gouy phase contribution of π/4 accumulates,
establishing a direct connection between the Gouy phase and a purely quantum
phenomenon. The interplay between the wavepacket squeezing and spreading
propagation in one dimension contributes to the total Gouy phase accumulation
of π/2. Both, squeezing and Gouy phase have been shown independently
valuable for quantum metrology and state engeenering. By establishing a direct
and controlable link between these two fundamental phenomena, we broaden
the scope for quantum-enhanced technologies, offering potential applications in
precision measurements and quantum communication..

We study continuous phase transitions in a diffusive epidemiological model with permanent immunity in a square lattice. Based on a
reaction-diffusion process, with diffusive rates Ds and Di of healthy and infected individuals, respectively, we verified, from an initial infected
individual, the growth of a cluster formed by activated sites, interpreted as sources of infection. We propose the mapping of this cluster by
percolation theory using the Newman-Ziff algorithm. Numerical simulations in the model, through a kinetic Monte Carlo algorithm, indicate that the
phase transition is controlled by the population density ρ, in order to present the same critical exponents of percolation, regardless of the diffusive
regime. The results obtained indicate that the model in question has the dynamic percolation universality class.

In this work, we present the result of the synthesis and characterization of pure
α-MoO3 and doped with different concentrations of silver (Ag) and aluminum
(Al) by thermal decomposition of ammonium heptamolybdate in the solvents:
acetone, isopropyl alcohol and methyl alcohol, for times of 2, 4 and 6 hours of
calcination at a temperature of 350 oC. The structural analysis performed by X-
ray diffraction (XRD) confirmed the stable and single-phase orthorhombic phase
of the α-MoO3 samples with successful doping. Quantitative analysis of the
diffraction patterns was performed through Rietveld refinement, identifying the
action of the dopant on the lattice parameters of the crystal structure. After the
incorporation of Ag and Al into α-MoO3, changes in vibrational modes were
identified using Raman spectroscopy and Fourier transform infrared
spectroscopy (FTIR), respectively. UV-Vis diffuse reflectance spectroscopy(DRS) was used to evaluate the optical properties, highlighting the bandgap
variation of the samples, which was between 3.1 and 3.4 eV. The electrical
properties demonstrated that the samples behave as semiconductors, with
those with a lower dopant concentration (1.0% Ag and 0.5% Al) presenting a
better electrical response compared to the pure sample.