In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein-Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin.

We investigate the Schrodinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass V (x) = 0 case whose solutions are hypergeometric functions in tanh 2 x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form V (x) = V0 sinh 2 x. *

We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schrödinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle is very weak, such that makes sense to apply the Schrödinger equation in a curved background whose metric has an off diagonal term which involves time and space. It is also assumed that the particle orbits sufficiently far from the boundary of the region of closed timelike curves which exist around this topological defect. Finally, we find the Landau levels of the particle in the presence of a spinning cosmic string endowed with internal structure, i.e., having finite width and uniformly filled with both material and vacuum energies.

To be published in the Int. J. of Mod. Phys. A (1999). AbstractWe find self-dual vortex solutions in a Maxwell-Chern-Simons model with anomalous magnetic moment. From a recently developed N = 2 supersymmetric extension, we obtain the proper Bogomol'nyi equations together with a Higgs potential allowing both topological and non-topological phases in the theory. * Electronic-addresses: hugo,marcony,helayel,leon

We calculate the renormalized vacuum energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M and radius R. This study will take into account the static and spherically symmetric solution of Hořava-Lifshitz gravity found by Kehagias-Sfetsos (KS), in both weak field and infrared (IR) limits. A slight amplification of the Casimir force between the conducting plates is found. Thermal corrections to the Casimir energy are analyzed. Based on current Casimir effect measurements, a constraint on the ω parameter of KS metric is also obtained.