Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials

We analytically solve the position-dependent mass (PDM) 1D Schr\"odinger equation for a new class of hyperbolic potentials $V_q^p(x) = -V_0\frac{\sinh^px}{\cosh^qx}, \, p= -2, 0, \dots q$ [see C. A. Downing, J. Math. Phys. 54 072101 (2013)] among which several hyperbolic single- and double-wells. For a solitonic mass distribution, $m(x)=m_0\,\text{sech}^2(x)$, we obtain exact analytic solutions to the resulting differential equations. For several members of the class, the quantum mechanical problems map into confluent Heun differential equations. The PDM Poschl-Teller potential is considered and exactly solved as a particular case.Comment: Some typos corrected. Some references updated. The acronym in the title expanded. 15 pages, 27 figure

Testing excitation models of rapidly oscillating Ap stars with interferometry

Rapidly oscillating Ap stars are unique objects in the potential they offer to study the interplay between a number of important physical phenomena, in particular, pulsations, magnetic fields, diffusion, and convection. Nevertheless, the simple understanding of how the observed pulsations are excited in these stars is still in progress. In this work we perform a test to what is possibly the most widely accepted excitation theory for this class of stellar pulsators. The test is based on the study of a subset of members of this class for which stringent data on the fundamental parameters are available thanks to interferometry. For three out of the four stars considered in this study, we find that linear, non-adiabatic models with envelope convection suppressed around the magnetic poles can reproduce well the frequency region where oscillations are observed. For the fourth star in our sample no agreement is found, indicating that a new excitation mechanism must be considered. For the three stars whose observed frequencies can be explained by the excitation models under discussion, we derive the minimum angular extent of the region where convection must be suppressed. Finally, we find that the frequency regions where modes are expected to be excited in these models is very sensitive to the stellar radius. This opens the interesting possibility of determining this quantity and related ones, such as the effective temperature or luminosity, from comparison between model predictions and observations, in other targets for which these parameters are not well determined.Comment: Accepted for publication in the MNRA

Casimir Effect in the Horava-Lifshitz Gravity with a Cosmological Constant

We calculate the Casimir 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. To this end, we take into account a static and spherically symmetric solution of Ho\v{r}ava-Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant.Comment: 18 pages. Improved conclusions. One figure and several references added. To appear in Annals of Physic

Asteroseismic Theory of Rapidly Oscillating Ap Stars

This paper reviews some of the important advances made over the last decade concerning theory of roAp stars.Comment: 9 pages, 5 figure

Confluent Heun functions in gauge theories on thick braneworlds

We investigate the propagation modes of gauge fields in an infinite Randall-Sundrum scenario. In this model a sine-Gordon soliton represents our thick four-dimensional braneworld while an exponentially coupled scalar acts for the dilaton field. For the gauge-field motion we find a differential equation which can be transformed into a confluent Heun equation. By means of another change of variables we obtain a related Schrodinger equation with a family of symmetric rational (\gamma-\omega z^2)/(1-z^2)^2 potential functions. We discuss both results and present the infinite spectrum of analytical solutions for the gauge field. Finally, we assess the existence and the relative weights of Kaluza-Klein modes in the present setup.Comment: 27 pages, 19 figures. Accepted for publication in Phys. Rev.

Seismic signatures of stellar cores of solar-like pulsators: dependence on mass and age

Useful information from the inner layers of stellar pulsators may be derived from the study of their oscillations. In this paper we analyse three diagnostic tools suggested in the literature built from the oscillation frequencies computed for a set of main sequence models with masses between $1.0\, {\rm M}_{\odot}$ and $1.6\, {\rm M}_{\odot}$, to check what information they may hold about stellar cores. For the models with convective cores ($M \geq 1.2\,{\rm M}_{\odot}$) we find a relation between the frequency slopes of the diagnostic tools and the size of the jump in the sound speed at the edge of the core. We show that this relation is independent of the mass of the models. In practice, since the size of the jump in the sound speed is related to the age of the star, using these seismic tools we may, in principle, infer the star's evolutionary state. We also show that when combining two of the three diagnostic tools studied, we are able to distinguish models with convective cores from models without a convective core but with strong sound-speed gradients in the inner layers