Lateral current density fronts in asymmetric double-barrier resonant-tunneling structures

We present a theoretical analysis and numerical simulations of lateral current density fronts in bistable resonant-tunneling diodes with Z-shaped current-voltage characteristics. The bistability is due to the charge accumulation in the quantum well of the double-barrier structure. We focus on asymmetric structures in the regime of sequential incoherent tunneling and study the dependence of the bistability range, the front velocity and the front width on the structure parameters. We propose a sectional design of a structure that is suitable for experimental observation of front propagation and discuss potential problems of such measurements in view of our theoretical findings. We point out the possibility to use sectional resonant-tunneling structures as controllable three-terminal switches.Comment: to appear in J.Appl.Phy

Gravitational instabilities in Kerr space-times

In this paper we consider the possible existence of unstable axisymmetric modes in Kerr space times, resulting from exponentially growing solutions of the Teukolsky equation. We describe a transformation that casts the radial equation that results upon separation of variables in the Teukolsky equation, in the form of a Schr\"odinger equation, and combine the properties of the solutions of this equations with some recent results on the asymptotic behaviour of spin weighted spheroidal harmonics to prove the existence of an infinite family of unstable modes. Thus we prove that the stationary region beyond a Kerr black hole inner horizon is unstable under gravitational linear perturbations. We also prove that Kerr space-time with angular momentum larger than its square mass, which has a naked singularity, is unstable.Comment: 9 pages, 4 figures, comments, references and calculation details added, asymptotic expansion typos fixe

On stochastic switching of bistable resonant-tunneling structures via nucleation

We estimate the critical size of the initial nucleus of the low current state in a bistable resonant tunneling structure which is needed for this nucleus to develop into a lateral switching front. Using the results obtained for deterministic switching fronts, we argue that for realistic structural parameters the critical nucleus has macroscopic dimensions and therefore is too large to be created by stochastic electron noise.Comment: the extended version of the Comment on "Lifetime of metastable states in resonant-tunneling structures" to appear in Phys. Rev.

The Casimir Effect in Spheroidal Geometries

We study the zero point energy of massless scalar and vector fields subject to spheroidal boundary conditions. For massless scalar fields and small ellipticity the zero-point energy can be found using both zeta function and Green's function methods. The result agrees with the conjecture that the zero point energy for a boundary remains constant under small deformations of the boundary that preserve volume (the boundary deformation conjecture), formulated in the case of an elliptic-cylindrical boundary. In the case of massless vector fields, an exact solution is not possible. We show that a zonal approximation disagrees with the result of the boundary deformation conjecture. Applying our results to the MIT bag model, we find that the zero point energy of the bag should stabilize the bag against deformations from a spherical shape.Comment: 24 pages, 3 figures. To appear in Phys. Rev.

Convergence Radii for Eigenvalues of Tri--diagonal Matrices

Consider a family of infinite tri--diagonal matrices of the form $L+ zB,$ where the matrix $L$ is diagonal with entries $L_{kk}= k^2,$ and the matrix $B$ is off--diagonal, with nonzero entries $B_{k,{k+1}}=B_{{k+1},k}= k^\alpha, 0 \leq \alpha < 2.$ The spectrum of $L+ zB$ is discrete. For small $|z|$ the $n$-th eigenvalue $E_n (z), E_n (0) = n^2,$ is a well--defined analytic function. Let $R_n$ be the convergence radius of its Taylor's series about $z= 0.$ It is proved that $$ R_n \leq C(\alpha) n^{2-\alpha} \quad \text{if} 0 \leq \alpha <11/6.$

Dust Emission from Evolved and Unevolved HII Regions in the Large Magellanic Cloud

We present a study of the dust properties of 12 classical and superbubble HII regions in the Large Magellanic Cloud. We use infrared photometry from Spitzer (8, 24, 70, and 160 \mum bands), obtained as part of the Surveying the Agents of a Galaxy's Evolution (SAGE) program, along with archival spectroscopic classifications of the ionizing stars to examine the role of stellar sources on dust heating and processing. Our infrared observations show surprisingly little correlation between the emission properties of the dust and the effective temperatures or bolometric magnitudes of stars in the HII regions, suggesting that the HII region evolutionary timescale is not on the order of the dust processing timescale. We find that the infrared emission of superbubbles and classical HII regions shows little differentiation between the two classes, despite the significant differences in age and morphology. We do detect a correlation of the 24 \mum emission from hot dust with the ratio of 70 to 160 \mum flux. This correlation can be modeled as a trend in the temperature of a minority hot dust component, while a majority of the dust remains significantly cooler.Comment: 15 pages, 5 figures. Accepted to Ap

Dust emission at 8-mic and 24-mic as Diagnostics of HII Region Radiative Transfer

We use the Spitzer SAGE survey of the Magellanic Clouds to evaluate the relationship between the 8-mic PAH emission, 24-mic hot dust emission, and HII region radiative transfer. We confirm that in the higher-metallicity Large Magellanic Cloud, PAH destruction is sensitive to optically thin conditions in the nebular Lyman continuum: objects identified as optically thin candidates based on nebular ionization structure show 6 times lower median 8-mic surface brightness (0.18 mJy arcsec^-2) than their optically thick counterparts (1.2 mJy arcsec^-2). The 24-mic surface brightness also shows a factor of 3 offset between the two classes of objects (0.13 vs 0.44 mJy arcsec^-2, respectively), which is driven by the association between the very small dust grains and higher density gas found at higher nebular optical depths. In contrast, PAH and dust formation in the low-metallicity Small Magellanic Cloud is strongly inhibited such that we find no variation in either 8-mic or 24-mic emission between our optically thick and thin samples. This is attributable to extremely low PAH and dust production together with high, corrosive UV photon fluxes in this low-metallicity environment. The dust mass surface densities and gas-to-dust ratios determined from dust maps using Herschel HERITAGE survey data support this interpretation.Comment: Accepted to ApJ, May 15, 2017. 10 pages, 9 figure

High Frequency Asymptotics for the Spin-Weighted Spheroidal Equation

We fully determine a uniformly valid asymptotic behaviour for large $a \omega$ and fixed $m$ of the angular solutions and eigenvalues of the spin-weighted spheroidal differential equation. We fully complement the analytic work with a numerical study.Comment: The .tar.gz file should contain 1 tex file, 24 figures in .ps format and 1 bibliography file in .bbl format. All these files are located in the same director

Greybody Factors for Brane Scalar Fields in a Rotating Black-Hole Background

We study the evaporation of (4+n)-dimensional rotating black holes into scalar degrees of freedom on the brane. We calculate the corresponding absorption probabilities and cross-sections obtaining analytic solutions in the low-energy regime, and compare the derived analytic expressions to numerical results, with very good agreement. We then consider the high-energy regime, construct an analytic high-energy solution to the scalar-field equation by employing a new method, and calculate the absorption probability and cross-section for this energy regime, finding again a very good agreement with the exact numerical results. We also determine the high-energy asymptotic value of the total cross-section, and compare it to the analytic results derived from the application of the geometrical optics limit.Comment: Latex file, 30 pages, 5 figures, typos corrected, version published in Phys. Rev.