paper

Trapping Dirac fermions in tubes generated by two scalar fields

arXiv:1307.7579 · doi:10.1103/PhysRevD.89.085036

Abstract

In this work we consider dimensional resonant Dirac fermionic states on tube-like topological defects. The defects are formed by rings in dimensions, constructed with two scalar field and , and embedded in the dimensional Minkowski spacetime. The tube-like defects are attained from a lagrangian density explicitly dependent with the radial distance relative to the ring axis and the radius and thickness of the its cross-section are related to the energy density. For our purposes we analyze a general Yukawa-like coupling between the topological defect and the fermionic field . With a convenient decomposition of the fermionic fields in left- and right- chiralities, we establish a coupled set of first order differential equations for the amplitudes of the left- and right- components of the Dirac field. After decoupling and decomposing the amplitudes in polar coordinates, the radial modes satisfy Schrödinger-like equations whose eigenvalues are the masses of the fermionic resonances. With the Schrödinger-like equations are numerically solved with appropriated boundary conditions. Several resonance peaks for both chiralities are obtained, and the results are confronted with the qualitative analysis of the Schrödinger-like potentials.

arXiv comment6 pages, 9 figures

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