Fermions embedded in a scalar-vector kink-like smooth potential

The behaviour of massive fermions is analyzed with scalar and vector potentials. A continuous chiral-conjugation transformation decouples the equation for the upper component of the Dirac spinor provided the vector coupling does not exceed the scalar coupling. It is shown that a Sturm-Liouville perspective is convenient for studying scattering as well as bound states. One possible isolated solution (excluded from the Sturm-Liouville problem) corresponding to a bound state might also come into sight. For potentials with kink-like profiles, beyond the intrinsically relativistic isolated bound-state solution corresponding to the zero-mode solution of the massive Jackiw-Rebbi model in the case of no vector coupling, a finite set of bound-state solutions might appear as poles of the transmission amplitude in a strong coupling regime. It is also shown that the possible isolated bound solution disappears asymptotically as the magnitude of the scalar and vector coupling becomes the same. Furthermore, we show that due to the sizeable mass gain from the scalar background the high localization of the fermion in an extreme relativistic regime is conformable to comply with the Heisenberg uncertainty principle.Comment: arXiv admin note: substantial text overlap with arXiv:1405.0310, arXiv:1310.847

Stationary states of fermions in a sign potential with a mixed vector-scalar coupling

The scattering of a fermion in the background of a sign potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling under the Sturm-Liouville perspective. When the vector coupling and the scalar coupling have different magnitudes, an isolated solution shows that the fermion under a strong potential can be trapped in a highly localized region without manifestation of Klein's paradox. It is also shown that the lonely bound-state solution disappears asymptotically as one approaches the conditions for the realization of spin and pseudospin symmetries.Comment: 4 figure

Scattering and bound states of fermions in a mixed vector-scalar smooth step potential

The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation and chiral-conjugation transformations are discussed and it is shown that a finite set of intrinsically relativistic bound-state solutions appears as poles of the transmission amplitude. It is also shown that those bound solutions disappear asymptotically as one approaches the conditions for the realization of the so-called spin and pseudospin symmetries in a four-dimensional space-time.Comment: 5 figures. arXiv admin note: substantial text overlap with arXiv:1310.847

Polarimetry of Li-rich giants

Protoplanetary nebulae typically present non-spherical envelopes. The origin of such geometry is still controversial. There are indications that it may be carried over from an earlier phase of stellar evolution, such as the AGB phase. But how early in the star's evolution does the non-spherical envelope appear? Li-rich giants show dusty circumstellar envelopes that can help answer that question. We study a sample of fourteen Li-rich giants using optical polarimetry in order to detect non-spherical envelopes around them. We used the IAGPOL imaging polarimeter to obtain optical linear polarization measurements in V band. Foreground polarization was estimated using the field stars in each CCD frame. After foreground polarization was removed, seven objects presented low intrinsic polarization (0.19 - 0.34)% and two (V859 Aql and GCSS 557) showed high intrinsic polarization values (0.87 - 1.16)%. This intrinsic polarization suggests that Li-rich giants present a non-spherical distribution of circumstellar dust. The intrinsic polarization level is probably related to the viewing angle of the envelope, with higher levels indicating objects viewed closer to edge-on. The correlation of the observed polarization with optical color excess gives additional support to the circumstellar origin of the intrinsic polarization in Li-rich giants. The intrinsic polarization correlates even better with the IRAS 25 microns far infrared emission. Analysis of spectral energy distributions for the sample show dust temperatures for the envelopes tend to be between 190 and 260 K. We suggest that dust scattering is indeed responsible for the optical intrinsic polarization in Li-rich giants. Our findings indicate that non-spherical envelopes may appear as early as the red giant phase of stellar evolution.Comment: to be published in A&A, 15 pages, 10 figures. Fig. 3 is available in ftp://astroweb.iag.usp.br/pub/antonio/4270/4270.fig3.pd

Interplay between morphological and shielding effects in field emission via Schwarz-Christoffel transformation

It is well known that sufficiently strong electrostatic fields are able to change the morphology of Large Area Field Emitters (LAFEs). This phenomenon affects the electrostatic interactions between adjacent sites on a LAFE during field emission and may lead to several consequences, such as: the emitter's degradation, diffusion of absorbed particles on the emitter's surface, deflection due to electrostatic forces and mechanical stress. These consequences are undesirable for technological applications, since they may significantly affect the macroscopic current density on the LAFE. Despite the technological importance, these processes are not completely understood yet. Moreover, the electrostatic effects due to the proximity between emitters on a LAFE may compete with the morphological ones. The balance between these effects may lead to a non trivial behavior in the apex-Field Enhancement Factor (FEF). The present work intends to study the interplay between proximity and morphological effects by studying a model amenable for an analytical treatment. In order to do that, a conducting system under an external electrostatic field, with a profile limited by two mirror-reflected triangular protrusions on an infinite line, is considered. The FEF near the apex of each emitter is obtained as a function of their shape and the distance between them via a Schwarz-Christoffel transformation. Our results suggest that a tradeoff between morphological and proximity effects on a LAFE may provide an explanation for the observed reduction of the local FEF and its variation at small distances between the emitter sites.Comment: 8 pages, 7 figures, published versio

The N-Vortex Problem on a Symmetric Ellipsoid: A Perturbation Approach

We consider the N-vortex problem on a ellipsoid of revolution. Applying standard techniques of classical perturbation theory we construct a sequence of conformal transformations from the ellipsoid into the complex plane. Using these transformations the equations of motion for the N-vortex problem on the ellipsoid are written as a formal series on the eccentricity of the ellipsoid's generating ellipse. First order equations are obtained explicitly. We show numerically that the truncated first order system for the three-vortices system on the symmetric ellipsoid is non-integrable.Comment: 14 pages, 1 figur

Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

Experimental Fowler-Nordheim plots taken from orthodoxly behaving carbon nanotube (CNT) field electron emitters are known to be linear. This shows that, for such emitters, there exists a characteristic field enhancement factor (FEF) that is constant for a range of applied voltages and applied macroscopic fields $F_\text{M}$. A constant FEF of this kind can be evaluated for classical CNT emitter models by finite-element and other methods, but (apparently contrary to experiment) several past quantum-mechanical (QM) CNT calculations find FEF-values that vary with $F_\text{M}$. A common feature of most such calculations is that they focus only on deriving the CNT real-charge distributions. Here we report on calculations that use density functional theory (DFT) to derive real-charge distributions, and then use these to generate the related induced-charge distributions and related fields and FEFs. We have analysed three carbon nanostructures involving CNT-like nanoprotrusions of various lengths, and have also simulated geometrically equivalent classical emitter models, using finite-element methods. We find that when the DFT-generated local induced FEFs (LIFEFs) are used, the resulting values are effectively independent of macroscopic field, and behave in the same qualitative manner as the classical FEF-values. Further, there is fair to good quantitative agreement between a characteristic FEF determined classically and the equivalent characteristic LIFEF generated via DFT approaches. Although many issues of detail remain to be explored, this appears to be a significant step forwards in linking classical and QM theories of CNT electrostatics. It also shows clearly that, for ideal CNTs, the known experimental constancy of the FEF value for a range of macroscopic fields can also be found in appropriately developed QM theory.Comment: A slightly revised version has been published - citation below - under a title different from that originally used. The new title is: "Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure