Bound state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system

In this work, we study of the (2+1)-dimensional Dirac oscillator in the presence of a homogeneous magnetic field in an Aharonov-Bohm-Coulomb system. To solve our system, we apply the $left$-$handed$ and $right$-$handed$ projection operators in the Dirac oscillator to obtain a biconfluent Heun equation. Next, we explicitly determine the energy spectrum for the bound states of the system and their exact dependence on the cyclotron frequency $\omega_c$ and on the parameters $Z$ and $\Phi_{AB}$ that characterize the Aharonov-Bohm-Coulomb system. As a result, we observe that by adjusting the frequency of the Dirac oscillator to resonate with the cyclotron half-frequency the energy spectrum reduces to the rest energy of the particle. Also, we determine the exact eigenfunctions, angular frequencies, and energy levels of the Dirac oscillator for the ground state ($n=1$) and the first excited state ($n=2$). In this case, the energy levels do not depend on the homogeneous magnetic field, and the angular frequencies are real and positive quantities, increase quadratically with the energy and linearly with $\omega_{c}$.Comment: 13 pages, no figur

Exact solutions of the Dirac oscillator under the influence of the Aharonov-Casher effect in the cosmic string background

In this work, we study the Aharonov-Casher effect in the $(2+1)$-dimensional Dirac oscillator coupled to an external electromagnetic field. We set up our system in two different scenarios: in the Minkowski spacetime and the cosmic string spacetime. In both cases, we solve exactly the Dirac oscillator and we determine the energy spectrum and the eigenfunctions for the bound states. We verify that in the Minkowski spacetime, the Dirac oscillator spectrum depends linearly on the strength of the magnetic field $B$, and on the Aharonov-Casher phase. In addition, we explicitly obtain the corrections on the Dirac spinors and the energy levels due to the curvature effects in the cosmic string background. Finally, we investigate the nonrelativistic limit and compare our results with those found in the literature.Comment: 15 pages, no figur

Optoelectronic properties of zinc oxide: A first-principles investigation using the Tran-Blaha modified Becke-Johnson potentia

In this work we use density functional theory (DFT) to investigate the influence of semi-local exchange and correlation effects on the electronic and optical properties of zinc oxide. We find that the inclusion of such effects using the Tran-Blaha modified Becke-Johnson potential yields an excellent description of the electronic structure of this material giving energy band gap which is systematically larger than the one obtained with standard local functionals such as the generalized gradient approximation. The discrepancy between the experimental and theoretical band gaps is then significantly reduced at a computational low cost. We also calculated the dielectric functions of ZnO and find a violet shift to the absorption edge which is in good agreement with experimental results.Comment: 12 pages, 2 figure

The relativistic Aharonov-Bohm-Coulomb system with position-dependent mass

In this work, we study the Aharonov-Bohm-Coulomb (ABC) system for a relativistic Dirac particle with position-dependent mass (PDM). To solve our system, we use the left-handed and right-handed projection operators. Next, we explicitly obtain the eigenfunctions and the energy spectrum of the particle. We verify that these eigenfunctions are written in terms of the generalized Laguerre polynomials and the energy spectrum depends on the parameters Z, $\Phi_{AB}$ and $\kappa$. We notice that the parameter $\kappa$ has the function of increasing the values of the energy levels of the system. In addition, the usual ABC system is recovered when one considers the limit of constant mass ($\kappa\to{0}$). Moreover, also we note that even in the absence of ABC system ($Z=\Phi_{AB}=0$), the particle with PDM still has a discrete energy spectrum.Comment: 9 page

Spacetime as a deformable solid

In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction. We simulate the spacetime manifold by a very specific congruence of curves and use the Landau-Raychadhuri equation to study the behavior of such a congruence. The lattice appears because we are forced to associate to each curve of the congruence a sort of fundamental "particle". The world-lines of these particles should be identified with the congruence fulfilling the spacetime manifold. The conclusion is that when describing the deformations of the spacetime the Einstein equations emerge and the spacetime metric should be treated as a secondary (not fundamental) object of the theory.Comment: 5 pages, RevTex

Resonances on deformed thick branes

In this work we investigate the issue of gravity and fermion localization and resonances in $(4,1)$-branes constructed with one scalar field coupled with gravity in deformed models. Such models give solutions for the scalar field that is the usual kink solution in the extra dimension for a parameter $p=1$ and deformations with a two-kink profile for odd $p>1$. Gravity is localized and resonant modes are found for small values of $p$. The coupling between the scalar field and spinors is a necessary condition for fermions to be localized on such branes. After performing a chiral decomposition of the five-dimensional spinor we found resonances with both chiralities for all odd $p$'s. The correspondence between the spectra for left and right chirality is guaranteed and Dirac fermions are realized on the brane. The increasing of $p$ characterizes the formation of branes with internal structure that turns the gravitational interaction more effective for fermions aside the brane, increasing their lifetime. The influence of the internal structure of the branes and the presence of resonances for gravity and fermionic modes is addressed.Comment: 23 pages, 13 figure

Thermodynamics of Schwarzschild-like black holes in modified gravity models

Over the last decades, many methods were developed to prove Hawking radiation. Recently, a semiclassical method known as the tunneling method has been proposed as a more straightforward way of derivating black hole thermodynamical properties. This method has been widely applied to a vast sort of spacetimes with satisfactory results. In this work, we obtain the black hole thermodynamics in the presence of a Lorentz symmetry breaking (LSB). We apply the Hamilton-Jacobi method to Schwarzschild-like black holes, and we investigate whether the LSB affects their thermodynamics. The results found show that the LSB not only changes the black hole thermodynamic quantities but also makes it necessary to modify the standard first law of thermodynamics.Comment: Title changed, section VI suppressed. Other slight modifications in order to match the accepted version to appears in Annals of Physics. 17 pages, no figure

Graviton resonances on deformed branes

Plane wave solutions of Schrodinger-like equations obtained from the metric perturbations in 5D braneworld scenarios can present resonant modes. The search for those structures is important because they can provide us massive modes with not suppressed couplings with the membrane. We propose in this paper the study of graviton Kaluza-Klein spectrum in a special kind of membrane that possesses internal structure. The interest in study of these deformed defects is because they have a more rich internal structure that has implications in the matter-energy density along the extra dimensions an this produces a space-time background whose curvature has a splitting, if compared to the usual kink-like models. Such models arise from $(4,1)$-branes constructed with one scalar field coupled with gravity where we find two-kink solutions from deformations of a $\phi^4$ potential. The main objective of this work is to observe the effects of deformation process in the resonant modes as well as in the coupling between the graviton massive modes and the brane.Comment: 7 pages, 3 figures. To appear in Europhysics Letters. arXiv admin note: text overlap with arXiv:0912.402

Dualization of non-Abelian B∧ϕB\wedge\phi model

In this work we show a dualization process of a non-Abelian model with an antisymmetric tensor gauge field in a three-dimensional space-time. We have constructed a non-Abelian gauge invariant St\"{u}ckelberg-like master action, and a duality between a non-Abelian topologically massive $B\wedge\phi$ model and a non-Abelian massive scalar action, which leads us to a Klein-Gordon-type action when we consider a particular case.Comment: 4 page

Thermodynamical properties of graphene in noncommutative phase-space

We investigated the thermodynamic properties of graphene in a noncommutative phase-space in the presence of a constant magnetic field. In particular, we determined the behaviour of the main thermodynamical functions: the Helmholtz free energy, the mean energy, the entropy and the specific heat. The high temperature limit is worked out and the thermodynamic quantities, such as mean energy and specific heat, exhibit the same features as the commutative case. Possible connections with the results already established in the literature are discussed briefly.Comment: 12 pages, 6 figures, improvements and changes are added, published versio