arXiv subjects

Edilberto O. Silva

Publications and source records attributed to Edilberto O. Silva.

At least 109 records · Page 6Linked to original sources

arXiv2019

On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries

The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin and the pseudo-spin symmetries. We analyze the presence of cylindrical symmetric scalar potentials which allows us to provide analytic solutions for the resultant field equation. By using an appropriate ansatz, we find that the radial equation is a biconfluent Heun-like differential equation. The solution of this equation provides us with more than one expression for the energy eigenvalues of the oscillator. We investigate these energies and find that there is a quantum condition between them. We study this condition in detail and find that it requires the fixation of one of the physical parameters involved in the problem. Expressions for the energy of the oscillator are obtained for some values of the quantum number $n$. Some particular cases which lead to known physical systems are also addressed.

hep-th↗

arXiv2019

Modifications of electron states, magnetization and persistent current in a quantum dot by controlled curvature

In this work, we use the thin-layer quantization procedure to study the physical implications due to curvature effects on a quantum dot in the presence of an external magnetic field. Among the various physical implications due to the curvature of the system, we can mention the absence of the $m=0$ state is the most relevant one. The absence of it affects the Fermi energy and consequently the thermodynamic properties of the system. In the absence of magnetic fields, we verify that the rotational symmetry in the lateral confinement is preserved in the electronic states of the system and its degeneracy with respect to the harmonicity of the confining potential is broken. In the presence of a magnetic field, however, the energies of the electronic states in a quantum dot with a curvature are greater than those obtained for a quantum dot in a flat space, and the profile of degeneracy changes when the field is varied. We show that the curvature of the surface modifies the number of subbands occupied in the Fermi energy. In the study of both magnetization and persistent currents, we observe that Aharonov-Bohm-type (AB-type) oscillations are present, whereas de Haas-van Alphen-type (dHvA) oscillations are not well defined.

cond-mat.mes-hall↗

arXiv2018

Ground state of a bosonic massive charged particle in the presence of external fields in a Gödel-type spacetime

The relativistic quantum dynamics of a spinless charged particle interacting with both Aharonov-Bohm and Coulomb-type potentials in the Gödel-type spacetime is considered. The dynamics of the system is governed by the Klein-Gordon equation with interactions. We verify that it is possible to establish a quantum condition between the energy of the particle and the parameter that characterizes the vorticist of the spacetime. We rigorously analyze the ground state of the system and determine the corresponding wave functions to it.

hep-th↗

arXiv2018

Curved non-interacting two-dimensional electron gas with anisotropic mass

In the da Costa's thin-layer approach, a quantum particle moving in a 3D sample is confined on a curved thin interface. At the end, the interface effects are ignored and such quantum particle is localized on a curved surface. A geometric potential arises and, since it manifests due to this confinement procedure, it depends on the transverse to the surface mass component. This inspired us to consider, in this paper, the effects due to an anisotropic effective mass on a non-interacting two dimensional electron gas confined on a curved surface, a fact not explored before in this context. By tailoring the mass, many investigations carried out in the literature can be improved which in turns can be useful to better designing electronic systems without modifying the geometry of a given system. Some examples are examined here, as a particle on helicoidal surface, on a cylinder, on a catenoid and on a cone, with some possible applications briefly discussed.

cond-mat.mes-hall↗

arXiv2017

Scattering and bound states of Dirac Equation in presence of cosmic string for Hulthén potential

In this work we study the Dirac equation with vector and scalar potentials in the spacetime generated by a cosmic string. Using an approximation for the centrifugal term, a solution for the radial differential equation is obtained. We consider the scattering states under the Hulthén potential and obtain the phase shifts. From the poles of the scattering $S$-matrix the states energies are determined as well.

hep-th↗

arXiv2017

Scattering and bound states of a spin--1/2 neutral particle in the cosmic string spacetime

In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $μ$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous studies where the interaction between the spin and the line of charge is neglected, here we consider its effects. This interaction gives rise to a point interaction: $\boldsymbol{\nabla} \cdot \mathbf{E}= (2λ/α)δ(r)/r$. Due to the presence of the Dirac delta function, by applying an appropriated boundary condition provided by the theory of self--adjoint extensions, irregular solutions for the Hamiltonian are allowed. We address the scattering problem obtaining the phase shift, S-matrix and the scattering amplitude. The scattering amplitude obtained shows a dependency with energy which stems from the fact that the helicity is not conserved in this system. Examining the poles of the S-matrix we obtain an expression for the bound states. The presence of bound states for this system has not been discussed before in the literature.

hep-th↗

arXiv2016

Effects of quantum deformation on the integer quantum Hall effect

In this work an application of the $κ$--deformed algebra in condensed matter physics is presented. Starting by the $κ$--deformed Dirac equation we study the relativistic generalization of the $κ$--deformed Landau levels as well as the consequences of the deformation on the Hall conductivity. By comparing the $κ$--deformed Landau levels in the nonrelativistic regime with the energy levels of a two-dimensional electron gas (2DEG) in the presence of a normal magnetic field, upper bounds for the deformation parameter in different materials are established. An expression for the $κ$--deformed Hall conductivity of a 2DEG is obtained as well. The expression recovers the well-known result for the usual Hall conductivity in the limit $\varepsilon=κ^{-1}\to 0$. The deformation parameter breaks the Landau levels degeneracy and due to this, it is observed that deformation gives rise to new plateaus of conductivity in a such way that the plateaus widths of the $κ$--deformed Hall conductivity are less than the usual one. By studying the temperature dependence of the $κ$--deformed Hall conductivity, we show that an increase of the temperature causes the smearing of the plateaus and a diminution of the effect of the deformation, whilst an increase in the magnetic field enhances the effect of the deformation.

hep-th↗

arXiv2016

Influence of a Pseudo Aharonov-Bohm field on the quantum Hall effect in Graphene

The effect of an Aharonov-Bohm (AB) pseudo magnetic field on a two dimensional electron gas in graphene is investigated. We consider it modeled as in the usual AB effect but since such pseudo field is supposed to be induced by elastic deformations, the quantization of the field flux is abandoned. For certain constraints on the orbital angular momentum eigenvalues allowed for the system, we can observe the zero Landau level failing to develop, due to the degeneracy related to the Dirac valleys $K$ and $K^\prime$ which is broken. For integer values of the pseudo AB flux, the actual quantum Hall effect is preserved. Obtaining the Hall conductivity by summing over all orbital angular momentum eigenvalues, the zero Landau levels is recovered. Since our problem is closed related to the case where topological defects on a graphene sheet are present, the questions posed here are helpful if one is interested to probe the effects of a singular curvature in these systems.

cond-mat.mes-hall↗

arXiv2016

Landau quantization, Aharonov-Bohm effect and two-dimensional pseudoharmonic quantum dot around a screw dislocation

In this paper, we investigate the influence of a screw dislocation on the energy levels and the wavefunctions of an electron confined in a two-dimensional pseudoharmonic quantum dot under the influence of an external magnetic field inside a dot and Aharonov-Bohm field inside a pseudodot. The exact solutions for energy eigenvalues and wavefunctions are computed as functions of applied uniform magnetic field strength, Aharonov-Bohm flux, magnetic quantum number and the parameter characterizing the screw dislocation, the Burgers vector. We investigate the modifications due to the screw dislocation on the light interband absorption coefficient and absorption threshold frequency. Two scenarios are possible, depending on if singular effects either manifest or not. We found that as the Burgers vector increases, the curves of frequency are pushed up towards of the growth of it. One interesting aspect which we have observed is that the Aharonov-Bohm flux can be tuned in order to cancel the screw effect of the model.

cond-mat.mes-hall↗

arXiv2016

Relativistic quantum dynamics of vector bosons in an Aharonov-Bohm potential

The Aharonov-Bohm (AB) problem for vector bosons by the Duffin-Kemmer-Petiau (DKP) formalism is analyzed. Depending on the values of the spin projection, the relevant eigenvalue equation coming from the DKP formalism reveals an equivalence to the spin-$1/2$ AB problem. By using the self-adjoint extension approach, we examine the bound state scenario. The energy spectra are explicitly computed as well as their dependencies on the magnetic flux parameter and also the conditions for the occurrence of bound states.

hep-th↗

arXiv2015

Quantum motion of a point particle in the presence of the Aharonov--Bohm potential in curved space

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov--Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The geometry of this line element establishes that the motion of the particle can occur on the surface of a cone or an anti--cone. As a consequence of the nontrivial topology of the cone and also because of two--dimensional confinement, the geometric potential should be taken into account. At first, we establish the conditions for the particle describing a circular path in such a context. Because of the presence of the geometric potential, which contains a singular term, we use the self--adjoint extension method in order to describe the dynamics in all space including the singularity. Expressions are obtained for the bound state energies and wave functions.

quant-ph↗

arXiv2015

Lorentz-violating effects in the spin-1/2 Aharonov-Casher problem

The effects of a Lorentz symmetry violating background vector on the Aharonov-Casher bound and scattering scenarios is considered. Using an approach based on the self-adjoint extension method, an expression for the bound state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter. We found that there is an additional scattering for any value of the self-adjoint extension parameter and bound states for negative values of this parameter. By comparing the bound state and scattering results the self-adjoint extension parameter is determined. Expressions for the bound state energies, phase-shift and the scattering matrix are explicitly determined in terms of the self-adjoint extension parameter. The expression obtained for the scattering amplitude reveals that the helicity is not conserved in this scenario.

hep-th↗

arXiv2015

Black hole qubit correspondence from quantum circuits

We consider the black hole qubit correspondence (BHQC) from quantum circuits, taking into account the use of gate operations with base in the formulation of wrapped brane qubits. We interpret these quantum circuits with base on the BHQC classification of entanglement classes and apply in specific examples as the generation of Bell, GHZ states, quantum circuit teleportation and consider the implementation of interchanges in SUSY, black hole configurations, Freudenthal and rank system constructions. These results are discussed from the superstring viewpoint showing that the importance of the construction of the physical states formed by the entanglement of geometrical entities by cohomological operations automatically allows the preservation of different amounts of SUSY in the compactification process given an alternative to the case when fluxes are introduced in the game: the generalized Calabi-Yau of Hitchin.

quant-ph↗

arXiv2015

Generation of geometrical phases and persistent spin currents in 1-dimensional rings by Lorentz-violating terms

We have demonstrated that Lorentz-violating terms stemming from the fermion sector of the SME are able to generate geometrical phases on the wave function of electrons confined in 1-dimensional rings, as well as persistent spin currents, in the total absence of electromagnetic fields. We have explicitly evaluated the eigenenergies and eigenspinors of the electrons modified by the Lorentz-violating terms, using them to calculate the dynamic and the Aharonov-Anandan phases in the sequel. The total phase presents a pattern very similar to the Aharonov-Casher phase accumulated by electrons in rings under the action of the Rashba interaction. Finally, the persistent spin current were carried out and used to impose upper bounds on the Lorentz-violating parameters.

hep-th↗

arXiv2015

Relativistic quantum dynamics of neutral particle in external electric fields: An approach on effects of spin

The planar quantum dynamics of spin-1/2 neutral particle interacting with electrical fields is considered. A set of first order differential equations are obtained directly from the planar Dirac equation with nonminimum coupling. New solutions of this system, in particular, for the Aharonov-Casher effect, are found and discussed in detail. Pauli equation is also obtained by studying the motion of the particle when it describes a circular path of constant radius. We also analyze the planar dynamics in the full space, including the $r=0$ region. The self-adjoint extension method is used to obtain the energy levels and wave functions of the particle for two particular values for the self-adjoint extension parameter. The energy levels obtained are analogous to the Landau levels and explicitly depend on the spin projection parameter.

hep-th↗

arXiv2015

Symplectic Dirac Equation

Symplectic unitary representations for the Poincaré group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Klein-Gordon and Dirac equations are derived in phase space. As an application, we study the Dirac equation with electromagnetic interaction in phase space.

math-ph↗

arXiv2015

2DEG on a cylindrical shell with a screw dislocation

A two dimensional electron gas on a cylindrical surface with a screw dislocation is considered. More precisely, we investigate how both the geometry and the deformed potential due to a lattice distortion affect the Landau levels of such system. The case showing the deformed potential can be thought in the context of 3D common semiconductors where the electrons are confined on a cylindrical shell. We will show that important quantitative differences exist due to this lattice distortion. For instance, the effective cyclotron frequency is diminished by the deformed potential, which in turn enhances the Hall conductivity.

cond-mat.quant-gas↗

arXiv2015

Quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field with scalar and vector couplings

The quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field is analyzed for the general case where scalar and vector couplings are considered. The energy spectra are explicitly computed for different physical situations, as well as their dependencies on the magnetic field strength, spin projection parameter and vector and scalar coupling constants.

hep-th↗