Electromagnetic and Gravitational Radiation of Graviatoms

Graviatom existence conditions have been found. The graviatoms (quantum systems around mini-black-holes) satisfying these conditions contain the following charged particles: the electron, muon, tau lepton, wino, pion and kaon. Electric dipole and quadrupole and gravitational radiations are calculated for the graviatoms and compared with Hawking's mini-hole radiation.Comment: 7 pages, 1 figure, 3 tables; accepted in "Astronomical and Astrophysical Transactions

Stability of the magnetic Schr\"odinger operator in a waveguide

The spectrum of the Schr\"odinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any enlargement of the waveguide produces eigenvalues beneath the continuous spectrum. Also if the waveguide is bent eigenvalues will arise below the continuous spectrum. In this paper a magnetic field is added into the system. The spectrum of the magnetic Schr\"odinger operator is proved to be stable under small local deformations and also under small bending of the waveguide. The proof includes a magnetic Hardy-type inequality in the waveguide, which is interesting in its own

Precision determination of absolute neutron flux

A technique for establishing the total neutron rate of a highly-collimated monochromatic cold neutron beam was demonstrated using a method of an alpha-gamma counter. The method involves only the counting of measured rates and is independent of neutron cross sections, decay chain branching ratios, and neutron beam energy. For the measurement, a target of 10B-enriched boron carbide totally absorbed the neutrons in a monochromatic beam, and the rate of absorbed neutrons was determined by counting 478keV gamma rays from neutron capture on 10B with calibrated high-purity germanium detectors. A second measurement based on Bragg diffraction from a perfect silicon crystal was performed to determine the mean de Broglie wavelength of the beam to a precision of 0.024 %. With these measurements, the detection efficiency of a neutron monitor based on neutron absorption on 6Li was determined to an overall uncertainty of 0.058 %. We discuss the principle of the alpha-gamma method and present details of how the measurement was performed including the systematic effects. We also describe how this method may be used for applications in neutron dosimetry and metrology, fundamental neutron physics, and neutron cross section measurements.Comment: 44 page

Magnetic rings

We study functional and spectral properties of perturbations of the operator −(∂s+ia)2 in L2( 1). This operator appears when considering the restriction to the unit circle of a two-dimensional Schrödinger operator with the Bohm-Aharonov vector potential. We prove a Hardy-type inequality on ℝ2 and, on 1 , a sharp interpolation inequality and a sharp Keller-Lieb-Thirring inequality

Spectral estimates for two-dimensional Schroedinger operators with application to quantum layers

A logarithmic type Lieb-Thirring inequality for two-dimensional Schroedinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers

Eigenvalue bounds for Schr\"odinger operators with a homogeneous magnetic field

We prove Lieb-Thirring inequalities for Schr\"odinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength of the magnetic field, and hence quantifies the diamagnetic behavior of the system. For a harmonic oscillator in a homogenous magnetic field, we obtain the sharp constants in the inequalities.Comment: 12 page

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential $V$ lie in the disjoint union of two disks in the right and left half plane, respectively, provided that the $L^1-norm$ of $V$ is bounded from above by the speed of light times the reduced Planck constant. An analogous result for the Schr\"odinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on $V$ implies the absence of nonreal eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials

Practice of using the magnetic treatment devices to intensify the processes of primary oil treating

During the primary treatment of oil, gas and water, complications arise associated with the presence of hard water-oil emulsions, which cause an increase in fluid pressure in the gathering systems, pipeline damage, as well as difficulties in gas separation and preliminary water discharge at the preliminary discharge unit (PRU). Additional problems arise during transportation of highly paraffinic oils associated with the crystallization of paraffin in the flow path of the oilfield equipment and on the inner surface of pipes, leading to a drop in the productivity of pipelines.  Article discusses the technology of magnetic-reagent treatment of water-oil media, which allows intensifying the processes of primary oil treatment at the facilities of its production. Bench and pilot tests have shown the ability of the magnetic field to accelerate oil demulsification processes, increasing the percentage of separated water during subsequent settling, and to reduce asphalt-resin-paraffin deposits (ARPD) on the inner surface of oil and gas field equipment. Mechanism of the magnetic field effect on water-oil media is described. Effect of treatment on the integrity of the armour shells of oil-water emulsions was studied. Various modes of magnetic treatment have been investigated with evaluation of its effectiveness. It is shown that the best effect is achieved with the combined use of reagents and a magnetic field. Synergistic effect is observed, which consists in increasing their effectiveness. This made it possible to conclude that this method can be applied to reduce the consumption of reagents used in oil production while maintaining the treatment efficiency

Lieb-Thirring inequalities for geometrically induced bound states

We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page