We consider (4, 1)-dimensional branes constructed with two scalar fields φ and χ coupled to a Dirac spinor field by means of a general Yukawa coupling. The equation of motion for the coefficients of the chiral decomposition of the spinor in curved spacetime leads to a Schrödinger-like equation whose solutions allow to obtain the masses of the fermionic modes. The simplest Yukawa couplingΨφχΨ is considered for the Bloch brane model and fermion localization is studied. We found resonances for both chiralities and related their appearance to branes with internal structure.

We discuss the relationship between exact solvability of the Schroedinger equation, due to a spatially dependent mass, and the ordering ambiguity. Some examples show that, even in this case, one can find exact solutions. Furthermore, it is demonstrated that operators with linear dependence on the momentum are nonambiguous. *

Abstract.We proposed a six dimensional string-like braneworld built from a warped product between a 3-brane and the Hamilton cigar soliton space, the string-cigar braneworld. This transverse manifold is a well-known steady solution of the Ricci flow equation that describes the evolution of a manifold. The resulting bulk is an interior and exterior metric for a thick string. Furthermore, the source satisfies the dominant energy condition. It is possible to realize the geometric flow as a result of variations of the matter content of the brane, actually, as its tensions. Furthermore, the Ricci flow defines a family of string-like branes and we studied the effects that the evolution of the transverse space has on the geometric and physical quantities. The geometric flow makes the cosmological constant and the relationship between the Planck masses evolves. The gravitational massless mode remains trapped to the brane and the width of the mode depends on the evolution parameter. For the Kaluza-Klein modes, the asymptotic spectrum of mass is the same as for the thin string-like brane and the analogue Schrödinger potential also changes according to the flow.

A theoretical model supported by experimental results explains the dependence of the Raman scattering signal on the evolution of structural parameters along the amorphization trajectory of polycrystalline graphene systems.Four parameters rule the scattering efficiencies, two structural and two related to the scattering dynamics. With the crystallite sizes previously defined from X-ray diffraction and microscopy experiments, the three other parameters (the average grain boundaries width, the phonon coherence length, and the electron coherence length) are extracted from the Raman data with the geometrical model proposed here. The broadly used intensity ratio between

We analyze the one-dimensional Dirac oscillator in a thermal bath. We found that the heat capacity is two times greater than the heat capacity of the one-dimensional harmonic oscillator for higher temperatures.Comment: 4 pages, 3 figures, to appear in Physics Letters

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One simplified black hole model constructed from a semiclassical analysis of loop quantum gravity (LQG) is called self-dual black hole. This black hole solution depends on a free dimensionless parameter P known as the polymeric parameter and also on the $a_{0}$ area related to the minimum area gap of LQG. In the limit of P and $a_{0}$ going to zero, the usual Schwarzschild-solution is recovered. Here we investigate the quasinormal modes (QNMs) of massless scalar perturbations in the self-dual black hole background. We compute the QN frequencies using the sixth order WKB approximation method and compare them with numerical solutions of the Regge-Wheeler equation. Our results show that as the parameter P grows, the real part of the QN frequencies suffers an initial increase and then starts to decrease while the magnitude of the imaginary one decreases for fixed area gap $a_{0}$. This particular feature means that the damping of scalar perturbations in the self-dual black hole spacetimes are slower, and their oscillations are faster or slower according to the value of P.Comment: 17 pages, 5 figures. Some improvements with respect to the previous version. Final version to appear in Phys. Rev.