Moments of a single entry of circular orthogonal ensembles and Weingarten calculus

Consider a symmetric unitary random matrix $V=(v_{ij})_{1 \le i,j \le N}$ from a circular orthogonal ensemble. In this paper, we study moments of a single entry $v_{ij}$. For a diagonal entry $v_{ii}$ we give the explicit values of the moments, and for an off-diagonal entry $v_{ij}$ we give leading and subleading terms in the asymptotic expansion with respect to a large matrix size $N$. Our technique is to apply the Weingarten calculus for a Haar-distributed unitary matrix.Comment: 17 page

Improvement of magnetic hardness at finite temperatures: ab initio disordered local moment approach for YCo5_5

Temperature dependence of the magnetocrystalline anisotropy energy and magnetization of the prototypical rare-earth magnet YCo$_5$ is calculated from first principles, utilizing the relativistic disordered local moment approach. We discuss a strategy to enhance the finite-temperature anisotropy field by hole doping, paving the way for an improvement of the coercivity near room temperature or higher.Comment: 12 pages, 13 figures, some corrections made and a reference update

Role of shocked accretion flows in regulating the QPO of galactic black hole candidates

Using a generalized non-spherical, multi-transonic accretion flow model, we analytically calculate the normalized QPO frequency ${\bar {\bf {\nu}}}_{qpo}$ of galactic black hole candidates in terms of dynamical flow variables and self-consistently study the dependence of ${\bar {\bf {\nu}}}_{qpo}$ on such variables. Our results are in fairly close agreement with the observed QPO frequencies of GRS 1915+105. We find that ${\bar {\bf {\nu}}}_{qpo}$ is quite sensitive to various parameters describing the black hole accretion flow containing dissipative and non-dissipative shock waves. Thus the QPO phenomena is, {\it indeed}, regulated by `shocked' black hole accretion, and, for the first time, we establish a definitive connection between the QPO frequency and the properties of advective BH accretion flows. This information may provide the explanation of some important observations of galactic micro quasars.Comment: Final version accepted for publication in the Astrophysical Journal Letters (ApJL). A considerable part of the paper is almost completely re-written, though the results and the final conclussions are the same. One can now ignore the previous version. 8 pages with four black and white figures. For high resolution Fig. 3, please mail the author <[email protected]

Airborne tracking sunphotometer apparatus and system

An airborne tracking Sun photometer apparatus has a rotatable dome. An azimuth drive motor is connected to rotate the dome. The dome has an equatorial slot. A cylindrical housing is pivotally mounted inside the dome at the equatorial slot. A photometer is mounted in the housing to move in the equatorial slot as the housing pivots. The photometer has an end facing from the slot with an optical flat transparent window. An elevation drive motor is connected to pivot the cylindrical housing. The rotatable dome is mounted in the bulkhead of an aircraft to extend from the interior of the aircraft. A Sun sensor causes the photometer to track the Sun automatically. Alternatively, the photometer may be oriented manually or by computer

Accretion flows: the Role of the Outer Boundary Condition

We investigate the influences of the outer boundary conditions(OBCs) on the structure of an optically thin accretion flow. We find that OBC plays an important role in determining the topological structure and the profiles of the surface density and temperature of the solution, therefore it should be regarded as a new parameter in the accretion disk model.Comment: 9 pages, 2 figures, to appear in ApJ Letters, Vol. 521, L5

New Kinetic Equation for Pair-annihilating Particles: Generalization of the Boltzmann Equation

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic abundance is possible using this new equilibrium abundance in the sudden freeze-out approximation.Comment: 19 pages, LATEX file with 2 PS figure

Properties of Accretion Shocks in Viscous Flows with Cooling Effects

Low angular momentum accretion flows can have standing and oscillating shock waves. We study the region of the parameter space in which multiple sonic points occur in viscous flows in presence of various cooling effects such as bremsstrahlung and Comptonization. We also quantify the parameter space in which shocks are steady or oscillating. We find that cooling induces effects opposite to heating by viscosity even in modifying the topology of the solutions, though one can never be exactly balanced by the other due to their dissimilar dependence on dynamic and thermodynamic parameters. We show that beyond a critical value of cooling, the flow ceases to contain a shock wave.Comment: 18 pages, 12 figures, Accepted for Publication in Int. J. Mod. Phys.

Temperature Power Law of Equilibrium Heavy Particle Density

A standard calculation of the energy density of heavy stable particles that may pair-annihilate into light particles making up thermal medium is performed to second order of coupling, using the technique of thermal field theory. At very low temperatures a power law of temperature is derived for the energy density of the heavy particle. This is in sharp contrast to the exponentially suppressed contribution estimated from the ideal gas distribution function. The result supports a previous dynamical calculation based on the Hartree approximation, and implies that the relic abundance of dark matter particles is enhanced compared to that based on the Boltzmann equation.Comment: 12 pages, LATEX file with 6 PS figure

Boltzmann Suppression of Interacting Heavy Particles

Matsumoto and Yoshimura have recently argued that the number density of heavy particles in a thermal bath is not necessarily Boltzmann-suppressed for T << M, as power law corrections may emerge at higher orders in perturbation theory. This fact might have important implications on the determination of WIMP relic densities. On the other hand, the definition of number densities in a interacting theory is not a straightforward procedure. It usually requires renormalization of composite operators and operator mixing, which obscure the physical interpretation of the computed thermal average. We propose a new definition for the thermal average of a composite operator, which does not require any new renormalization counterterm and is thus free from such ambiguities. Applying this definition to the model of Matsumoto and Yoshimura we find that it gives number densities which are Boltzmann-suppressed at any order in perturbation theory. We discuss also heavy particles which are unstable already at T=0, showing that power law corrections do in general emerge in this case.Comment: 7 pages, 5 figures. New section added, with the discussion of the case of an unstable heavy particle. Version to appear on Phys. Rev.