Theory and application of Fermi pseudo-potential in one dimension

The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential and two Fermi pseudo-potentials, one odd under space reflection and the other even. The odd one gives the proper interpretation for the delta'(x) potential, while the even one is unexpected and more interesting. Among the many applications of these Fermi pseudo-potentials, the simplest one is described. It consists of a superposition of the delta-function potential and the even pseudo-potential applied to two-channel scattering. This simplest application leads to a model of the quantum memory, an essential component of any quantum computer.Comment: RevTeX4, 32 pages, no figure

Theory of Transmission of Light by Sub-wavelength Cylindrical Holes in Metallic Films

This paper presents theory and finite-difference time-domain (FDTD) calculations for a single and arrays of sub-wavelength cylindrical holes in metallic films presenting large transmission. These calculations are in excellent agreement with experimental measurements. This effect has to be understood in terms of the properties exhibited by the dielectric constant of metals which cannot be treated as ideal metals for the purpose of transmission and diffraction of light. We discuss the cases of well-differentiated metals silver and tungsten. It is found that the effect of surface plasmons or other surface wave excitations due to a periodical set of holes or other roughness at the surface is marginal. The effect can enhance but also can depress the transmission of the arrays as shown by theory and experiments. The peak structure observed in experiments is a consequence of the interference of the wavefronts transmitted by each hole and is determined by the surface array period independently of the material. Without large transmission through a single hole there is no large transmission through the array. We found that in the case of Ag which at the discussed frequencies is a metal there are cylindrical plasmons at the wall of the hole, as reported by Economu et al 30 years ago, that enhanced the transmission. But it turns out, as will be explained, that for the case of W which behaves as a dielectric, there is also a large transmission when compared with that of an ideal metal waveguide. To deal with this problem one has to use the measured dielectric function of the metals. We discuss thoroughly all these cases and compare with the data.Comment: 13 pages and 9 figure

Are any Growth Theories Robust?

The recent growth literature has seen an explosion of work exploring the role of new and fundamental theories of growth such as geography, institutions, ethnic fractionalization, and religion. Nevertheless, claims about the empirical validity of these new growth theories are typically made within very particular specifications of the growth model. In this paper, we investigate the robustness of these theories when the researcher appropriately accounts for model uncertainty. We first consider the robustness of these theories within the canonical growth regression framework. We then deviate from this framework to explore the impact of these new growth theories on the components of growth – TFP growth and physical and human accumulation rates – derived from a growth accounting exercise. We find very little evidence to support the contention that any of the new growth theories play an important and robust role in explaining growth and its components. We find instead that variation in growth may be robustly explained by differences in macroeconomic policies and unknown heterogeneity associated with regional groupings. We also find that, consistent with endogenous growth models, physical and human capital externalities are the main determinants of TFP growth.

Is God in the details? A reexamination of the Role of Relegion in Economic

Barro and McCleary (2003) is a key research contribution in the new literature exploring the macroeconomic effects of religious beliefs. This paper represents an effort to evaluate the strength of their claims. We evaluate their results in terms of replicability and robustness. While we find that their analysis meets the standard of statistical replicability, we do not find that the results are robust to changes in their baseline statistical specification. Taken together, we conclude that their analysis cannot be taken to provide useable evidence on how religion might affect aggregate outcomes.

Waveform Design for Secure SISO Transmissions and Multicasting

Wireless physical-layer security is an emerging field of research aiming at preventing eavesdropping in an open wireless medium. In this paper, we propose a novel waveform design approach to minimize the likelihood that a message transmitted between trusted single-antenna nodes is intercepted by an eavesdropper. In particular, with knowledge first of the eavesdropper's channel state information (CSI), we find the optimum waveform and transmit energy that minimize the signal-to-interference-plus-noise ratio (SINR) at the output of the eavesdropper's maximum-SINR linear filter, while at the same time provide the intended receiver with a required pre-specified SINR at the output of its own max-SINR filter. Next, if prior knowledge of the eavesdropper's CSI is unavailable, we design a waveform that maximizes the amount of energy available for generating disturbance to eavesdroppers, termed artificial noise (AN), while the SINR of the intended receiver is maintained at the pre-specified level. The extensions of the secure waveform design problem to multiple intended receivers are also investigated and semidefinite relaxation (SDR) -an approximation technique based on convex optimization- is utilized to solve the arising NP-hard design problems. Extensive simulation studies confirm our analytical performance predictions and illustrate the benefits of the designed waveforms on securing single-input single-output (SISO) transmissions and multicasting

Optimization of Dimples in Microchannel Heat Sink with Impinging Jets—Part B: the Influences of Dimple Height and Arrangement

The combination of a microchannel heat sink with impinging jets and dimples (MHSIJD) can effectively improve the flow and heat transfer performance on the cooling surface of electronic devices with very high heat fluxes. Based on the previous work by analysing the effect of dimple radius on the overall performance of MHSIJD, the effects of dimple height and arrangement were numerically analysed. The velocity distribution, pressure drop, and thermal performance of MHSIJD under various dimple heights and arrangements were presented. The results showed that: MHSIJD with higher dimples had better overall performance with dimple radius being fixed; creating a mismatch between the impinging hole and dimple can solve the issue caused by the drift phenomenon; the mismatch between the impinging hole and dimple did not exhibit better overall performance than a well-matched design

Temperature-dependent Cross Sections for Charmonium Dissociation in Collisions with Pions and Rhos in Hadronic Matter

Meson-charmonium dissociation reactions governed by the quark interchange are studied with temperature-dependent quark potentials. Quark-antiquark relative-motion wave functions and masses of charmonia and charmed mesons are determined by the central spin-independent part of the potentials or by the central spin-independent part and a smeared spin-spin interaction. The prominent temperature dependence of the masses is found. Based on the potentials, the wave functions, and the meson masses, we obtain temperature-dependent cross sections for fifteen pion-charmonium and rho-charmonium dissociation reactions. The numerical cross sections are parametrized for future applications in hadronic matter. The particular temperature dependence of the J/psi bound state leads to unusual behavior of the cross sections for endothermic J/psi dissociation reactions. The quantum numbers of psi' and chi_c can not make their difference in mass in the temperature region 0.6T_c < T < T_c, but can make the psi' dissociation different from the chi_c dissociation.Comment: 52 pages, 23 figures, 6 table

Unsteady Aerodynamic Interaction Between Rotor and Ground Obstacle

The mutual aerodynamic interaction between rotor wake and surrounding obstacles is complex, and generates high compensatory workload for pilots, degradation of the handling qualities and performance, and unsteady force on the structure of the obstacles. The interaction also affects the minimum distance between rotorcrafts and obstacles to operate safely. A vortex-based approach is then employed to investigate the complex aerodynamic interaction between rotors and ground obstacle, and identify the distance where the interaction ends, and this is also the objective of the GARTEUR AG22 working group activities. In this approach, the aerodynamic loads of the rotor blades are described through a panel method, and the unsteady behaviour of the rotor wake is modelled using a vortex particle method. The effects of the ground plane and obstacle are accounted for via a viscous boundary model. The method is then applied to a “Large” and a “Wee” rotor near the ground and obstacle, and compared with the earlier experiments carried out at the University of Glasgow. The results show that the predicted rotor induced inflow and flow field compare reasonably well with the experiments. Furthermore, at certain conditions the tip vortices are pushed up and re-injected into the rotor wake due to the effect of the obstacle resulting in a recirculation. Moreover, contrary to without the obstacle case, the peak and thickness of the radial outwash near the obstacle is smaller due to the barrier effect of the obstacle, and an up-wash is observed. Additionally, as the rotor closes to the obstacle, the rotor slipstreams impinge directly on the obstacle, and the up-wash near the obstacle is faster, indicating a stronger interaction between the rotor wake and the obstacle. Also, contrary to the case without the obstacle, the fluctuations of the rotor thrust, rolling and pitching moments are obviously strengthened. When the distance between the rotor and the obstacle is larger than 3R, the effect of the obstacle is small

Quantum-defect theory of resonant charge exchange

We apply the quantum-defect theory for $-1/R^4$ potential to study the resonant charge exchange process. We show that by taking advantage of the partial-wave-insensitive nature of the formulation, resonant charge exchange of the type of $^1$S+$^2$S can be accurately described over a wide range of energies using only three parameters, such as the \textit{gerade} and the \textit{ungerade} $s$ wave scattering lengths, and the atomic polarizability, even at energies where many partial waves contribute to the cross sections. The parameters can be determined experimentally, without having to rely on accurate potential energy surfaces, of which few exist for ion-atom systems. The theory further relates ultracold interactions to interactions at much higher temperatures.Comment: 8 pages, 7 figure