Geometric models of (d+1)-dimensional relativistic rotating oscillators

Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the energy levels and corresponding normalized energy eigenfunctions. An important property is that all these models have the same nonrelativistic limit, namely the usual harmonic oscillator.Comment: 7 pages, Late

The Schr\" odinger picture of the Dirac quantum mechanics on spatially flat Robertson-Walker backgrounds

The Schr\" odinger picture of the Dirac quantum mechanics is defined in charts with spatially flat Robertson-Walker metrics and Cartesian coordinates. The main observables of this picture are identified, including the interacting part of the Hamiltonian operator produced by the minimal coupling with the gravitational field. It is shown that in this approach new Dirac quantum modes on de Sitter spacetimes may be found analytically solving the Dirac equation.Comment: 6 pages 0 figure

Weak Localization and Antilocalization in Topological Insulator Thin Films with Coherent Bulk-Surface Coupling

We evaluate quantum corrections to conductivity in an electrically gated thin film of a three-dimensional (3D) topological insulator (TI). We derive approximate analytical expressions for the low-field magnetoresistance as a function of bulk doping and bulk-surface tunneling rate. Our results reveal parameter regimes for both weak localization and weak antilocalization, and include diffusive Weyl semimetals as a special case.Comment: After publication, we have noticed and corrected two small but potentially misleading typographic errors in Eqs. (2.27) and (2.29), where the definitions of \tau_s and \tau_v were mistakenly switched. Once these typographic errors are fixed, all the results remain unchanged. An Erratum will be published in PR

Dirac-Coulomb scattering with plane wave energy eigenspinors on de Sitter expanding universe

The lowest order contribution of the amplitude of Dirac-Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given energy and helicity. We find that the total energy is conserved in the scattering process.Comment: 9 pages, no figure

Remarks on the spherical waves of the Dirac field on de Sitter spacetime

The Shishkin's solutions of the Dirac equation in spherical moving frames of the de Sitter spacetime are investigated pointing out the set of commuting operators whose eigenvalues determine the integration constants. It is shown that these depend on the usual angular quantum numbers and, in addition, on the value of the scalar momentum. With these elements a new result is obtained finding the system of solutions normalized (in generalized sense) in the scale of scalar momentum.Comment: 7 pages, no figure