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Edilberto O. Silva

Publications and source records attributed to Edilberto O. Silva.

At least 91 records · Page 5Linked to original sources
arXiv2023

Quantum heat machines enabled by twisted geometry

In this paper, we analyze the operation of an Otto cycle heat machine driven by a non-interacting two-dimensional electron gas on a twisted geometry. We show that due to both the energy quantization on this structure and the adiabatic transformation of the number of complete twists per unit length of a helicoid, the machine performance in terms of output work, efficiency, and operation mode can be altered. We consider the deformations as in a spring, which is either compressed or stretched from its resting position. The realization of classically inconceivable Otto machines with an incompressible sample can be realized as well. The energy-level spacing of the system is the quantity that is being either compressed or stretched. These features are due to the existence of an effective geometry-induced quantum potential which is of pure quantum-mechanical origin.

quant-ph↗
arXiv2023

Applications of the Klein-Gordon equation in the Feshbach-Villars representation in the non-inertial cosmic string space-time

We study the relativistic quantum motion of a spineless particle using the Feshbach-Villars (FV) formalism in the spinning cosmic string spacetime. The movement equations are derived using the first-order FV formulation of the Klein-Gordon (KG) equation. We apply the equation of motion (a) to study the motion of the particle confined to a rigid-wall potential, (b) motion in the presence of a Coulomb-type potential, and (c) particle interacting with the Feshbach-Villars oscillator (FVO). The energy levels and wave functions are obtained for the three cases. Our study focused on the impact of rotation and curvature on the energy levels of the particle

hep-th↗
arXiv2023

Exact and approximate bound state solutions of the Schrödinger equation with a class of Kratzer-type potentials in the global monopole spacetime

This work investigates the motion of a non-relativistic charged particle within the spacetime of a global monopole. We introduce the Schrödinger equation to describe the particle's motion with two interactions by considering the Kratzer and the screened modified Kratzer potential. The problem's eigenfunctions and eigenvalues are obtained by deriving and solving the radial equation. The effective potential encompasses both the Kratzer and electrostatic self-interaction potential and leads to bound states solutions. The energy spectrum is investigated, particularly emphasizing its dependence on the system's physical parameters. The screened modified Kratzer potential and the screened self-interaction potential reveal an important role in influencing both the effective potential and the energy spectrum. Additionally, it also accommodates the existence of bound states. All these behaviors are illustrated with graphs and discussed in detail.

quant-ph↗
arXiv2023

Optical and electronic properties of a two-dimensional quantum ring under rotating effects

This work presents a study on the nonrelativistic quantum motion of a charged particle in a rotating frame, considering the Aharonov-Bohm effect and a uniform magnetic field. We derive the equation of motion and the corresponding radial equation to describe the system. The Schrödinger equation with minimal coupling incorporates rotation effects by substituting the momentum operator with an effective four-potential. Additionally, a radial potential term, dependent on the average radius of the ring, is introduced. The analysis is restricted to motion in a two-dimensional plane, neglecting the degree of freedom in the $z$-direction. By solving the radial equation, we determine the eigenvalues and eigenfunctions, allowing for an explicit expression of the energy. The probability distribution is analyzed for varying rotating parameter values, revealing a shift of the distribution as the rotation changes, resulting in a centrifugal effect and occupation of the ring's edges. Furthermore, numerical analysis demonstrates the significant rotational effects on energy levels and optical properties, including optical absorption and refractive coefficients.

cond-mat.mes-hall↗
arXiv2023

Approximate analytical solutions of the Schrödinger equation with Hulthén potential in the global monopole spacetime

In this paper, we study the nonrelativistic quantum mechanics of an electron in a spacetime containing a topological defect. We also consider that the electron is influenced by the Hulthén potential. In particular, we deal with the Schrödinger equation in the presence of a global monopole. We obtain approximate solutions for the problem, determine the scattering phase shift and the $S$-matrix, and analyze bound states.

quant-ph↗
arXiv2022

Modification of Landau levels in a two-dimensional ring due to rotation effects and edge states

We investigate the properties of a two-dimensional quantum ring under rotating and external magnetic field effects. We initially analyse the Landau levels and inertial effects on them. Among the results obtained, we emphasize that the rotation lifted the degeneracy of Landau levels. When electrons are confined in a two-dimensional ring, which is modeled by a hard wall potential, the eigenstates are described by Landau states as long as the eigenstates are not too close to the edges of the ring. On the other hand, near the edges of the ring, the energies increase monotonically. These states are known as edge states. Edge states have an important effect on the physical properties of the ring. Thus, we analyze the Fermi energy and magnetization. In the specific case of magnetization, we consider two approaches. In the first, we obtain an analytical result for magnetization but without considering rotation. Numerical results showed the de Haas-Van Alphen (dHvA) oscillations. In the second, we consider rotating effects. In addition to the dHvA oscillations, we also verify the Aharonov-Bohm-type (AB) oscillations, which are associated with the presence of edge states. We discuss the effects of rotation on the results and find that rotation is responsible for inducing Aharonov-Bohm-type oscillations.

cond-mat.mes-hall↗
arXiv2021

Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem

In this work, we investigate how both rotation and a Coulomb potential affect the quantum mechanical description of a spin-$1/2$ particle in the presence of the Aharonov-Bohm effect. We employ the method of the self-adjoint extensions in the framework of the Pauli-Schrödinger equation. We discuss the role of the spin degree of freedom on this problem, find the energy spectrum, and investigate the results in detail.

quant-ph↗
arXiv2021

Self-adjoint extension approach for singular Hamiltonians in (2+1) dimensions

In this work, we review two methods used to approach singular Hamiltonians in (2+1) dimensions. Both methods are based on the self-adjoint extension approach. It is very common to find singular Hamiltonians in quantum mechanics, especially in quantum systems in the presence of topological defects, which are usually modelled by point interactions. In general, it is possible to apply some kind of regularization procedure, as the vanishing of the wave function at the location of the singularity, ensuring that the wave function is square-integrable and then can be associated with a physical state. However, a study based on the self-adjoint extension approach can lead to more general boundary conditions that still gives acceptable physical states. We exemplify the methods by exploring the bound and scattering scenarios of a spin 1/2 charged particle with an anomalous magnetic moment in the Aharonov-Bohm potential in the conical space.

math-ph↗
arXiv2020

On the Dirac oscillator in a spinning cosmic string spacetime in external magnetic fields: Investigation of energy spectrum and connection with the condensed matter physics

In this article, we study topological and noninertial effects on the motion of the two-dimensional Dirac oscillator in the presence of a uniform magnetic field and the Aharonov-Bohm potential. We obtain the Dirac equation that describes the model. Expressions for the wave functions and energy spectrum are derived. The energy spectrum of the oscillator as a function of the various physical parameters involved in the problem is rigorously studied. Finally, we present some analogies between our results and others of the condensed matter physics.

hep-th↗
arXiv2020

Tripartite entanglement: Foundations and applications

We review some current ideas about tripartite entanglement, the case representing the next level of complexity beyond the simplest one (though far from trivial), namely the bipartite. This kind of entanglement has an essential role in the understanding of foundations of quantum mechanics. Also, it allows several applications in the fields of quantum information processing and quantum computing. In this paper, we make a revision about the main foundational aspects of tripartite entanglement and we discuss the possibility of using it as a resource to execute quantum protocols. We present some examples of quantum protocols in detail.

quant-ph↗
arXiv2020

Relativistic quantum motion of an electron in spinning cosmic string spacetime in the presence of uniform magnetic field and Aharonov-Bohm potential

In this manuscript, we study the relativistic quantum mechanics of an electron in external fields in the spinning cosmic string spacetime. We obtain the Dirac equation, write the first and second-order equations from it, and then we solve these equations for bound states. We show that there are bound states solutions for the first-order equation Dirac. For the second-order equation, we show that its wave functions are given in terms of the Kummer functions and we determine the energies of the particle. We examine the behavior of the energies as a function of the physical parameters of the model, such as rotation, curvature, magnetic field, Aharonov-Bohm flux, and quantum numbers. Our study reveals that both curvature and rotation influence more intensely when these parameters have values smaller than 0.3. We also find that, depending on the values of these parameters, there are energy nonpermissible levels.

hep-th↗
arXiv2020

Quantum particle motion on the surface of a helicoid in the presence of harmonic oscillator

The geometric potential in quantum mechanics has been attracted attention recently, providing a formalism to investigate the influence of curvature in the context of low-dimensional systems. In this paper, we study the consequences of a helicoidal geometry in the Schrödinger equation dealing with an anisotropic mass tensor. In particular, we solve the problem of an harmonic oscillator in this scenario. We determine the eigenfunctions in terms of Confluent Heun Functions and compute the respective energy levels. The system exhibit several different behaviors, depending on the adjustment on the mass components.

quant-ph↗
arXiv2020

Study of electronic properties, Magnetization and persistent currents in a mesoscopic ring by controlled curvature

We study the model of a noninteracting spinless electron gas confined to the two-dimensional localized surface of a cone in the presence of external magnetic fields. The localized region is characterized by an annular radial potential. We write the Schrödinger equation and use the thin-layer quantization procedure to calculate the wavefunctions and the energy spectrum. In such a procedure, it arises a geometry induced potential, which depends on both the mean and the Gaussian curvatures. Nevertheless, since we consider a ring with a mesoscopic size, the effects of the Gaussian curvature on the energy spectrum are negligible. The magnetization and the persistent current are analyzed. In the former, we observed the Aharonov-Bohm (AB) and de Haas-van Alphen (dHvA) types oscillations. In the latter, it is observed only the AB type oscillations. In both cases, the curvature increases the amplitude of the oscillations.

cond-mat.mes-hall↗
arXiv2019

Influence of rotation on the electronic states, magnetization and persistent current in 1D quantum ring

Inertial effects can affect several properties of physical systems. In particular, in the context of quantum mechanics, such effects have been studied in diverse contexts. In this paper, starting from the Schrödinger equation for a rotating frame, we describe the influence of rotation on the energy levels of a quantum particle constrained to a one-dimensional ring in the presence of a uniform magnetic field. We also investigate how the persistent current and the magnetization in the ring are influenced by temperature and rotating effects.

quant-ph↗
arXiv2019

Quantum motion of a spinless particle in curved space: A viewpoint of scattering theory

In this work, we study the scattering of a spinless charged particle constrained to move on a curved surface in the presence of the Aharonov-Bohm potential. We begin with the equations of motion for the surface and transverse dynamics previously obtained in the literature (Ferrari G. and Cuoghi G., Phys. Rev. Lett. \textbf{100}, 230403 (2008)) and describe the surface with non-trivial curvature in terms of linear defects such as dislocations and disclinations. Expressions for the modified phase shift, S--matrix and scattering amplitude are determined by applying a suitable boundary condition at the origin, which comes from the self-adjoint extension theory. We also discuss the presence of a bound state obtained from the pole of the S--matrix. Finally, we claim that the bound state, the additional scattering and the dependence of the scattering amplitude with energy are solely due to the curvature effects.

quant-ph↗
arXiv2019

Effects of curvature on the electronic states of a two-dimensional mesoscopic ring

The effects of surface curvature on the motion of electrons in a mesoscopic two-dimensional ring on a cone in the presence of external magnetic fields are examined. The approach follows the thin-layer quantization procedure, which gives rise to a geometry induced potential. Due to the annular geometric shape of the sample, only the mean curvature has relevant effects to the model. Nevertheless, the most significant contribution of the mean curvature occurs in the state $m=0$, which tends to decrease the energies when the magnetic field is null. The effects of curvature are also manifested in the cyclotron frequency as well as in the effective angular momentum through the $α$ parameter, which can be controlled in such a way that the magnitude of these effects becomes explicit. This is verified in the energies and wave functions of the system. A decrease in the number of occupied states in the Fermi energy is observed. As a consequence, there is an alteration in the radial range of the conducting region of the sample. This fact is confirmed by studying the variations in the radii of the states.

cond-mat.mes-hall↗
arXiv2019

Solution of the $κ$-deformed Dirac equation with vector and scalar interactions in the context of spin and pseudospin symmetries

The deformed Dirac equation invariant under the $κ$-Poincaré-Hopf quantum algebra in the context of minimal and scalar couplings under spin and pseudospin symmetries limits is considered. The $κ$-deformed Pauli-Dirac Hamiltonian allows us to study effects of quantum deformation in a class of physical systems, such as an Zeeman-like effect, Aharonov-Bohm effect and an anomalous-like contribution to the electron magnetic moment, between others. In our analysis, we consider the motion of an electron in a uniform magnetic field and interacting with (i) a planar harmonic oscillator and (ii) a linear potential. We verify that the particular choice of a linear potential induces a Coulomb-type term in the equation of motion. Expressions for the energy eigenvalues and wave functions are determined taking into account both symmetries limits. We verify that the energies and wave functions of the particle are modified by the deformation parameter as well as by the element of spin.

hep-th↗