A Novel Method for the Solution of the Schroedinger Eq. in the Presence of Exchange Terms

In the Hartree-Fock approximation the Pauli exclusion principle leads to a Schroedinger Eq. of an integro-differential form. We describe a new spectral noniterative method (S-IEM), previously developed for solving the Lippman-Schwinger integral equation with local potentials, which has now been extended so as to include the exchange nonlocality. We apply it to the restricted case of electron-Hydrogen scattering in which the bound electron remains in the ground state and the incident electron has zero angular momentum, and we compare the acuracy and economy of the new method to three other methods. One is a non-iterative solution (NIEM) of the integral equation as described by Sams and Kouri in 1969. Another is an iterative method introduced by Kim and Udagawa in 1990 for nuclear physics applications, which makes an expansion of the solution into an especially favorable basis obtained by a method of moments. The third one is based on the Singular Value Decomposition of the exchange term followed by iterations over the remainder. The S-IEM method turns out to be more accurate by many orders of magnitude than any of the other three methods described above for the same number of mesh points.Comment: 29 pages, 4 figures, submitted to Phys. Rev.

Spectral efficiency of engineered thermal cloaks in the frequency regime

We analyse basic thermal cloaks designed via different geometric transforms applied to thermal cloaking. We evaluate quantitatively the efficiency of these heterogeneous anisotropic thermal cloaks through the calculation of the standard deviation of the isotherms. The study addresses the frequency regime and we point out the cloak's spectral efficiencies. We find that all these cloaks have comparable efficiency irrespective of whether or not they have singular conductivity at their inner boundary. However, approximate cloaking with multi-layered cloak critically depends upon the homogenization algorithm and a large number of thin layers (at least fifty) is required to reduce substantially the standard deviation of the isotherms.Comment: 13 pages, 7 figures. The results from this article will be presented on a poster at the Metamaterials 2014 Copenhague conferenc

Phase retrieval of reflection and transmission coefficients from Kramers-Kronig relations

Analytic and passivity properties of reflection and transmission coefficients of thin-film multilayered stacks are investigated. Using a rigorous formalism based on the inverse Helmholtz operator, properties associated to causality principle and passivity are established when both temporal frequency and spatial wavevector are continued in the complex plane. This result extends the range of situations where the Kramers-Kronig relations can be used to deduce the phase from the intensity. In particular, it is rigorously shown that Kramers-Kronig relations for reflection and transmission coefficients remain valid at a fixed angle of incidence. Possibilities to exploit the new relationships are discussed.Comment: submitted for publicatio

Optical scatter of quantum noise filter cavity optics

Optical cavities to filter squeezed light for quantum noise reduction require optics with very low scattering losses. We report on measured light scattering from two super-polished fused silica optics before and after applying highly-reflective ion-beam sputtered dielectric coatings. We used an imaging scatterometer that illuminates the sample with a linearly polarized 1064 nm wavelength laser at a fixed angle of incidence and records images of back scatter for azimuthal angles in the plane of the laser beam. We extract from these images the bidirectional reflectance distribution function (BRDF) of the optics with and without coating and estimate their integrated scatter. We find that application of these coatings led to a more than 50% increase of the integrated wide-angle scatter, to 5.00+/-0.30 and 3.38+/-0.20 ppm for the two coated samples. In addition, the BRDF function of the coated optics takes on a pattern of maxima versus azimuthal angle. We compare with a scattering model to show that this is qualitatively consistent with roughness scattering from the coating layer interfaces. These results are part of a broader study to understand and minimize optical loss in quantum noise filter cavities for interferometric gravitational-wave detectors. The scattering measured for these samples is acceptable for the 16 m long filter cavities envisioned for the Laser Interferometer Gravitational-wave Observatory (LIGO), though reducing the loss further would improve LIGO's quantum-noise limited performance.Comment: 10 pages, 3 figure

Spatial depolarization of light from the bulks: electromagnetic prediction

International audienceThe spatial depolarization of light emitted by heterogeneous bulks is predicted with exact electromagnetic theories. The sample microstructure and geometry is connected with partial polarization

Radiative recombination of bare Bi83+: Experiment versus theory

Electron-ion recombination of completely stripped Bi83+ was investigated at the Experimental Storage Ring (ESR) of the GSI in Darmstadt. It was the first experiment of this kind with a bare ion heavier than argon. Absolute recombination rate coefficients have been measured for relative energies between ions and electrons from 0 up to about 125 eV. In the energy range from 15 meV to 125 eV a very good agreement is found between the experimental result and theory for radiative recombination (RR). However, below 15 meV the experimental rate increasingly exceeds the RR calculation and at Erel = 0 eV it is a factor of 5.2 above the expected value. For further investigation of this enhancement phenomenon the electron density in the interaction region was set to 1.6E6/cm3, 3.2E6/cm3 and 4.7E6/cm3. This variation had no significant influence on the recombination rate. An additional variation of the magnetic guiding field of the electrons from 70 mT to 150 mT in steps of 1 mT resulted in periodic oscillations of the rate which are accompanied by considerable changes of the transverse electron temperature.Comment: 12 pages, 14 figures, to be published in Phys. Rev. A, see also http://www.gsi.de/ap/ and http://www.strz.uni-giessen.de/~k