arXiv subjects

C. G. Bezerra

Publications and source records attributed to C. G. Bezerra.

15 recordsLinked to original sources

arXiv2026

L\'evy walkers inside spherical shells with absorbing boundaries: Towards settling the optimal L\'evy walk strategy for random searches

The L\'evy flight foraging hypothesis states that organisms must have evolved adaptations to exploit L\'evy walk search strategies. Indeed, it is widely accepted that inverse square L\'evy walks optimize the search efficiency in foraging with unrestricted revisits (also known as non-destructive foraging). However, a mathematically rigorous demonstration of this for dimensions $D \geq 2$ is still lacking. Here we study the very closely related problem of a L\'evy walker inside annuli or spherical shells with absorbing boundaries. In the limit that corresponds to the foraging with unrestricted revisits, we show that inverse square L\'evy walks optimize the search. This constitutes the strongest formal result to date supporting the optimality of inverse square L\'evy walks search strategies.

cond-mat.stat-mech↗

arXiv2025

Physics-Informed Neural Network for Elastic Wave-Mode Separation

Mode conversion in non-homogeneous elastic media makes it challenging to interpret physical properties accurately. Decomposing these modes correctly is crucial across various scientific areas. Recent machine learning approaches have been proposed to address this problem, utilizing the Helmholtz decomposition technique. In this paper, we investigate the capabilities of a physics-informed neural network (PINN) in separating P and S modes by solving a scalar Poisson equation. This scalar formulation offers a dimensionally scalable reduction in computational cost compared to the traditional vector formulation. We verify the proposed method in both homogeneous and realistic non-homogeneous elastic models as showcases. The obtained separated modes closely match those from conventional numerical techniques, while exhibiting reduced transverse wave leakage.

physics.comp-ph↗

arXiv2025

Intermediate statistics: addressing the Landau diamagnetism problem

Quantum groups and quantum algebras have received considerable attention in the last decades because they are very useful as mathematical tools of research. Existing proposals for quantum groups have always suggested the idea of deforming a classical object. Motivated by the possibility of anyons in three dimensions ($d=3$), with important consequences to a wide range of fields of physics, in the present work we investigate how the magnetization and other thermodynamic quantities, associated to the Landau diamagnetism problem, depend on the deforming parameter of two models with intermediate statistics: (i) $q$-fermions and (ii) $F$-anyons, and make {\it comparisons between both cases}. In particular, we extend the results from the literature for $q$-fermions by considering {\it second order terms} in the expansion of the grand partition function. Also, we find that for $F$-anyons statistics the magnetization shows a stronger response with respect to magnetic fields compared to magnetization for $q$-fermions statistics. This theoretical outcome may be experimentally verified for instance in superconductors, that are perfect diamagnetic materials with strong magnetic susceptibility, by adjusting impurities or pressure. The latter can be associated to the deforming parameter $q$.

cond-mat.stat-mech↗

arXiv2024

Intermediate statistics: addressing the thermoelectric properties of solids

We study the thermodynamics of a crystalline solid by applying intermediate statistics obtained by deforming known solid state models using the mathematics of $q$-analogs. We apply the resulting $q$-deformation to both the Einstein and Debye models and study the deformed thermal and electrical conductivities and the deformed Debye specific heat. We find that the $q$-deformation acts in two different ways -- but not necessarily as independent mechanisms. First, it acts as an effective factor of disorder or impurity, modifying the characteristics of a crystalline structure, which are phenomena described by q-bosons. Second, it also manifests intermediate statistics, namely, the B-anyons (or B-type systems). For the latter case, we have identified the Schottky effect, normally associated with high-$T_c$ superconductors in the presence of rare-earth-ion impurities. We also find that it increases the specific heat of the solids beyond the Dulong-Petit limit at high temperature. Such an effect is usually related to anharmonicity of interatomic interactions. Alternatively, since in the $q$-bosons case the statistics are in principle maintained, the effect of the deformation acts more slowly due to a small change in the crystal lattice. On the other hand, B-anyons that belong to modified statistics are more sensitive to the deformation. The results reported here may be verified experimentally, for instance, in experimental samples by inserting impurities, or changes in pressure or temperature if one assumes these tuning quantities are related with the q-deformation parameter.

cond-mat.stat-mech↗

arXiv2020

The connection between Jackson and Hausdorff derivatives in the context of generalized statistical mechanics

In literature one can find many generalizations of the usual Leibniz derivative, such as Jackson derivative, Tsallis derivative and Hausdorff derivative. In this article we present a connection between Jackson derivative and recently proposed Hausdorff derivative. On one hand, the Hausdorff derivative has been previously associated with non-extensivity in systems presenting fractal aspects. On the other hand, the Jackson derivative has a solid mathematical basis because it is the $\overline{q}$-analog of the ordinary derivative and it also arises in quantum calculus. From a quantum deformed $\overline{q}$-algebra we obtain the Jackson derivative and then address the problem of $N$ non-interacting quantum oscillators. We perform an expansion in the quantum grand partition function from which we obtain a relationship between the parameter $\overline{q}$, related to Jackson derivative, and the parameters $ζ$ and $q$ related to Hausdorff derivative and Tsallis derivative, respectively.

cond-mat.stat-mech↗

arXiv2017

Tuning the Fano factor of graphene via Fermi velocity modulation

In this work we investigate the influence of a Fermi velocity modulation on the Fano factor of periodic and quasi-periodic graphene superlattices. We consider the continuum model and use the transfer matrix method to solve the Dirac-like equation for graphene where the electrostatic potential, energy gap and Fermi velocity are piecewise constant functions of the position x. We found that in the presence of an energy gap, it is possible to tune the energy of the Fano factor peak and consequently the location of the Dirac point, by a modulations in the Fermi velocity. Hence, the peak of the Fano factor can be used experimentally to identify the Dirac point. We show that for higher values of the Fermi velocity the Fano factor goes below 1/3 in the Dirac point. Furthermore, we show that in periodic superlattices the location of Fano factor peaks is symmetric when the Fermi velocity $v_A$ and $v_B$ is exchanged, however by introducing quasi-periodicity the symmetry is lost. The Fano factor usually holds a universal value for a specific transport regime, which reveals that the possibility of controlling it in graphene is a notable result.

cond-mat.mes-hall↗

arXiv2014

Quantifying magnetic anisotropy dispersion: Theoretical and experimental study of the magnetic properties of anisotropic FeCuNbSiB ferromagnetic films

The Stoner-Wohlfarth model is a traditional and efficient tool to calculate magnetization curves and it can provides further insights on the fundamental physics associated to the magnetic properties and magnetization dynamics. Here, we perform a theoretical and experimental investigation of the quasi-static magnetic properties of anisotropic systems. We consider a theoretical approach which corresponds to a modified version of the Stoner-Wohlfarth model to describe anisotropic systems and a distribution function to express the magnetic anistropy dispersion. We propose a procedure to calculate the magnetic properties for the anisotropic case of the SW model from experimental results of the quadrature of magnetization curves, thus quantifying the magnetic anisotropy dispersion. To test the robustness of the approach, we apply the theoretical model to describe the quasi-static magnetic properties of amorphous FeCuNbSiB ferromagnetic films. We perform calculations and directly compare theoretical results with longitudinal and transverse magnetization curves measured for the films. Thus, our results provide experimental evidence to confirm the validity of the theoretical approach to describe the magnetic properties of anisotropic amorphous ferromagnetic films, revealed by the excellent agreement between numerical calculation and experimental results.

cond-mat.mtrl-sci↗

arXiv2012

Anomalous Magnetoresistance in Fibonacci Multilayers

The present paper theoretically investigates magnetoresistance curves in quasiperiodic magnetic multilayers for two different growth directions, namely [110] and [100]. We considered identical ferromagnetic layers separated by non-magnetic layers with two different thicknesses chosen based on the Fibonacci sequence. Using parameters for Fe/Cr multilayers, four terms were included in our description of the magnetic energy: Zeeman, cubic anisotropy, bilinear and biquadratic couplings. The minimum energy was determined by the gradient method and the equilibrium magnetization directions found were used to calculate magnetoresistance curves. By choosing spacers with a thickness such that biquadratic coupling is stronger than bilinear coupling, unusual behaviors for the magnetoresistance were observed: (i) for the [110] case there is a different behavior for structures based on even and odd Fibonacci generations; and more interesting, (ii) for the [100] case we found magnetic field ranges for which the magnetoresistance increases with magnetic field.

cond-mat.mes-hall↗

arXiv2010

A renormalization group study of the three-color Ashkin-Teller model on a Wheatstone hierarchical lattice

We have investigated the three-color Ashkin-Teller model (3AT), on the Wheatstone bridge hierarchical lattice, by means of a Migdal-Kadanoff renormalization group approach. We have obtained the exact recursion relations for the renormalized couplings, which have been used to investigate the phase diagram and to study the corresponding critical points. The phase diagram, represented in terms of the dual transmissivity vector, presents four magnetic phases and nine critical points. We have also numerically calculated the correlation length ($ν_T$) and crossover ($ϕ$) critical exponents, which show that seven of the critical points are in the Potts model universality class ($q=2$, 4 e 8). The remaining critical points are in a universality class which may belong to the Baxter's line. Our results are exact on the hierarchical lattice used in the present work and the phase diagram can be considered as an approximation to more realistic Bravais lattices.

cond-mat.stat-mech↗

arXiv2001

Influence of the biquadratic interlayer coupling in the specific heat of Fibonacci magnetic multilayers

A theoretical study of the specific heat C(T) as a function of temperature in Fibonacci magnetic superlattices is presented. We consider quasiperiodic structures composed of ferromagnetic films, each described by the Heisenberg model, with biquadratic and bilinear coupling between them. We have taken the ratios between the biquadratic and bilinear exchange terms according to experimental data recently measured for different regions of their regime. Although some previous properties of the spin wave specific heat are also reproduced here, new features appear in this case, the most important of them being an interesting broken-symmetry related to the interlayer biquadratic term.

cond-mat.stat-mech↗

arXiv2001

Magnetization in quasiperiodic magnetic multilayers with biquadratic exchange and uniaxial anisotropy

A theoretical study is made of the magnetization versus applied field curves of ferromagnetic/nonmagnetic multilayers constructed according to a Fibonacci quasiperiodic sequence. The ferromagnetic films are assumed to have uniaxial anisotropy and are coupled by both bilinear and biquadratic effective exchange. The effects of quasiperiodicity in the magnetic phases are illustrated numerically for Fe/Cr systems.

cond-mat.mtrl-sci↗

arXiv2001

The anisotropic Ashkin-Teller model: a renormalization group study

The two-dimensional ferromagnetic anisotropic Ashkin-Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recover all the known exacts results for the square lattice. The correlation length $(ν_T)$ and crossover $(ϕ)$ critical exponents are also calculated. With the only exception of the four-state Potts critical point, the entire phase diagram belongs to the Ising universality class.

cond-mat.stat-mech↗

arXiv2001

Spin wave specific heat in quasiperiodic Fibonacci structures

The energy spectra of a variety of collective modes on quasiperiodic structures exhibit a complex fractal profile. Among the modes that have attracted particular attention in this context, are the spin wave spectra of quasiperiodic magnetic multilayers that obey a substitutional sequence of the Fibonacci type. They are described within the framework of the Heisenberg theory. In order to have a deep insight on the relevant thermodynamical implications of the above mentioned energy spectra's fractal profile, we have performed analytical and numerical calculations of the spin wave specific heat associated with successive hierarchical sequences of the Fibonacci quasiperiodic structures. The spectra show interesting oscillatory behavior in the low-temperature region, which can be traced back to the spin wave's self-similar energy spectrum.

cond-mat.stat-mech↗

arXiv2001

Magnetization in quasiperiodic magnetic multilayers with biquadratic exchange coupling

A theoretical study of the magnetization curves of quasiperiodic magnetic multilayers is presented. We consider structures composed by ferromagnetic films (Fe) with interfilm exchange coupling provided by intervening nonferromagnetic layers (Cr). The theory is based on a realistic phenomenological model, which includes the following contributions to the free magnetic energy: Zeeman, cubic anisotropy, bilinear and biquadratic exchange energies. The experimental parameters used here are based on experimental data recently reported, which contain sufficiently strong biquadratic exchange coupling.

cond-mat.str-el↗

arXiv1999

Self-similar magnetoresistance of Fibonacci ultrathin magnetic films

We study numerically the magnetic properties (magnetization and magnetoresistance) of ultra-thin magnetic films (Fe/Cr) grown following the Fibonacci sequence. We use a phenomenological model which includes Zeeman, cubic anisotropy, bilinear and biquadratic exchange energies. Our physical parameters are based on experimental data recently reported, which contain biquadratic exchange coupling with magnitude comparable to the bilinear exchange coupling. When biquadratic exchange coupling is sufficiently large a striking self-similar pattern emerges.

cond-mat.str-el↗