V. B. Bezerra

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.

Hydrogen atom in the gravitational fields of topological defects

We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a pointlike global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the energy levels of the atom. We investigate how the geometric and topological features of these spacetimes lead to shifts in the energy levels as compared with the flat Minkowski spacetime.

Violation of the Nernst heat theorem in the theory of the thermal Casimir force between Drude metals

We give a rigorous analytical derivation of low-temperature behavior of the Casimir entropy in the framework of the Lifshitz formula combined with the Drude dielectric function. An earlier result that the Casimir entropy at zero temperature is not equal to zero and depends on the parameters of the system is confirmed, i.e., the third law of thermodynamics (the Nernst heat theorem) is violated. We illustrate the resolution of this thermodynamical puzzle in the context of the surface impedance approach by several calculations of the thermal Casimir force and entropy for both real metals and dielectrics. Different representations for the impedances, which are equivalent for real photons, are discussed. Finally, we argue in favor of the Leontovich boundary condition which leads to results for the thermal Casimir force that are consistent with thermodynamics.

Non-relativistic quantum systems on topological defects spacetimes

We study the behaviour of non-relativistic quantum particles interacting with different potentials in the spacetimes generated by a cosmic string and a global monopole. We find the energy spectra in the presence of these topological defects and show how they differ from their free-spacetime values.

Global effects due to a chiral cone

Scalar and spinor quantum particles are considered in the background space–time generated by a chiral cosmic string. It is shown that in this chiral conical space–time, the wave functions, the energy spectra, and the scattering amplitude associated with a quantum scalar particle depend on the global features of this space–time. In the case of a spinor particle, we study this dependence on the wave functions, energy, and current. These dependences represent gravitational analogues of the well-known Aharonov–Bohm effect in electrodynamics. Using the Hamilton–Jacobi equations, we also look into the motion of light rays and show how the effective potential depends on the global features of the chiral conical space–time.

Vacuum polarization induced by a cylindrical boundary in the cosmic string spacetime

In this paper we investigate the Wightman function, the renormalized vacuum expectation values of the field square, and the energy-momentum tensor for a massive scalar field with general curvature coupling inside and outside of a cylindrical shell in the generalized spacetime of straight cosmic string. For the general case of Robin boundary condition, by using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density and stresses are investigated in various limiting cases. The generalization of the results to the exterior region is given for a general cylindrically symmetric static model of the string core with finite support.

Advance and prospects in constraining the Yukawa-type corrections to Newtonian gravity from the Casimir effect

We report stronger constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the lateral Casimir force between sinusoidally corrugated surfaces of a sphere and a plate. In the interaction range from 1.6 to 14 nm the strengthening of previously known high confidence constraints up to a factor of

Landau levels in the presence of topological defects

2.4\ifmmode\times\else\texttimes\fi{}{10}^{7}

Correlation of energy and free energy for the thermal Casimir force between real metals

is achieved using these measurements. It is shown that the replacement of a plane plate with a corrugated one in the measurements of the normal Casimir force by means of an atomic force microscope would result in the strengthening of respective high confidence constraints on the Yukawa-type interaction by a factor of

Electromagnetic Casimir densities induced by a conducting cylindrical shell in the cosmic string spacetime

1.1\ifmmode\times\else\texttimes\fi{}{10}^{12}