Claudio Furtado

Landau levels in the presence of disclinations

Abstract This work is an investigation of the influence of a disclination on the spectrum of an electron or hole in a magnetic field in the framework of the theory of defects/three-dimensional gravity of Katanaev and Volovich. The presence of the defect reduces the degeneracy of the Landau levels to a finite value, except for very particular deficit angles. Inclusion of the self-interaction in the study further breaks the degeneracy. Exact wavefunctions and energy eigenvalues are found for special values of the magnetic field.

On the binding of electrons and holes to disclinations

Abstract In this work we study the bound states of electrons and holes to disclinations in the framework of the theory of defects/three- dimensional gravity of Katanaev and Volovich. We find that positive disclinations repel both electrons and holes while negative disclinations act as attractors to both, giving rise to bound states. We compute the wavefunctions and the eigenvalues for these bound states.

Quantum scattering by a magnetic flux screw dislocation

Abstract We investigate the quantum scattering of one electron by a screw dislocation with an internal magnetic flux. The Aharonov–Bohm effect for bound states is analyzed and we demonstrate that the wave function and the energy spectra associated with the particle depend on the Burgers vectors of dislocation and the magnetic flux. We also calculate Berrys phase associated to the dynamics of the electrons in this background. For some specific values of the magnetic flux there is a matching of the effects produced by the flux and by the dislocation in such a way that there is neither scattering nor Berrys phase.

Landau levels in the presence of topological defects

In this paper we study the Landau levels in the presence of topological defects. We analyse the behaviour of electrons moving in a magnetic field in the presence of a continuous distribution of disclinations, a magnetic screw dislocation and a dispiration. We focus on the influence of these topological defects on the spectrum of the electron (or hole) in the magnetic field in the framework of the geometric Katanaev-Volovich theory of defects in solids. The presence of the defect breaks the degeneracy of the Landau levels in different ways depending on the defect. Exact expressions for energies and eigenfunctions are found for all cases. Using Kaluza-Klein theory we solve the Landau level problem for a dispiration and compare the results with the ones obtained in the previous cases.

QUANTUM EFFECTS DUE TO A MAGNETIC FLUX ASSOCIATED TO A TOPOLOGICAL DEFECT

We investigate the quantum scattering of an electron by a topological defect called dispiration, with an externally applied magnetic field along its axis. The Aharonov–Bohm effect for bound states is analyzed and it is demonstrated that the wave function and the energy spectra associated with the particle depend on the features of the dispiration as well as on the magnetic flux. We also calculate Berrys phase associated to the dynamics of electrons in this background.

Aharonov–Bohm effect in the presence of a density of defects

Abstract In this work we study the quantum dynamics of a particle in the presence of a density of defects in continuous media. We solve the Schrodinger equation for a quantum particle in the presence of a distribution of wedge disclination and obtain the eigenfunctions and eigenvalues for this case. We analyze the Aharonov–Bohm effect for bound state.

RELATIVISTIC EINSTEIN–PODOLSKY–ROSEN CORRELATIONS IN COSMIC STRING SPACE–TIME VIA FERMI–WALKER TRANSPORT

We present a geometric approach to study the relativistic EPR correlations in curved space–time background given by the application of the Fermi–Walker transport in the relativistic EPR states and show that its result has the same effect as the applications of successive infinitesimal Lorentz boosts in the relativistic EPR states. We also show that the expression for the Bell inequality due to the Fermi–Walker transport is equivalent to the expression demonstrated by Terashima and Ueda,20 where the degree of violation of the Bell inequality depends on the angle of the Wigner rotation. This geometrical approach for study of the relativistic EPR correlations is a promising formulation to investigate the EPR correlations in the general relativity background.

Aharonov-Bohm effect for bound states in Kaluza-Klein theory

Using Kaluza-Klein theory we study the quantum mechanics of a scalar particle in the background of a chiral cosmic string and of a magnetic cosmic string. We show that the wave functions and the energy spectra associated with the particle depend on the global features of those space–times. These dependences represent the analogs of the well-known Aharonov–Bohm effect. This effect appears as the sum of two contributions, one of gravitational origin and the other of electromagnetic origin.

AHARONOV–BOHM EFFECT AND DISCLINATIONS IN AN ELASTIC MEDIUM

In this work we investigate quasiparticles in the background of defects in solids using the geometric theory of defects. We use the parallel transport matrix to study the Aharonov–Bohm effect in this background. For quasiparticles moving in this effective medium we demonstrate an effect similar to the gravitational Aharonov–Bohm effect. We analyze this effect in an elastic medium with one and N defects.

BOUND STATES IN THE DYNAMICS OF A DIPOLE IN THE PRESENCE OF A CONICAL DEFECT

In this work we investigate the quantum dynamics of an electric dipole in a (2+1)-dimensional conical spacetime. For specific conditions, the Schrodinger equation is solved and bound states are found with the energy spectrum and eigenfunctions determined. We find that the bound states spectrum extends from minus infinity to zero with a point of accumulation at zero. This unphysical result is fixed when a finite radius for the defect is introduced.