The expressions for the 2nd-order mixed partial derivatives of Slater-Koster matrix elements at spherical coordinate singularities

In a recent publication it has been shown how to generate derivatives with respect to atom coordinates of Slater-Koster matrix elements for the tight binding (TB) modelling of a system. For the special case of a mixed second partial derivative at coordinate singularities only the results were stated in that publication. In this work, the derivation of these results is given in detail. Though it may seem rather `technical' and only applicable to a very special case, atomic configurations where the connecting vector between the two atoms involved in a two-centre matrix element is aligned along the z-axis (in the usual approach) require results for precisely this case. The expressions derived in this work have been implemented in the DINAMO code.Comment: 9 pages, no figure

The Odd-Parity CMB Bispectrum

Measurement of the cosmic microwave background (CMB) bispectrum, or three-point correlation function, has now become one of the principle efforts in early-Universe cosmology. Here we show that there is a odd-parity component of the CMB bispectrum that has been hitherto unexplored. We argue that odd-parity temperature-polarization bispectra can arise, in principle, through weak lensing of the CMB by chiral gravitational waves or through cosmological birefringence, although the signals will be small even in the best-case scenarios. Measurement of these bispectra requires only modest modifications to the usual data-analysis algorithms. They may be useful as a consistency test in searches for the usual bispectrum and to search for surprises in the data.Comment: 5 pages, 1 figur

Testing cosmological variability of fundamental constants

One of the topical problems of contemporary physics is a possible variability of the fundamental constants. Here we consider possible variability of two dimensionless constants which are most important for calculation of atomic and molecular spectra (in particular, the X-ray ones): the fine-structure constant \alpha=e^2/\hbar c and the proton-to-electron mass ratio \mu=m_p/m_e. Values of the physical constants in the early epochs are estimated directly from observations of quasars - the most powerful sources of radiation, whose spectra were formed when the Universe was several times younger than now. A critical analysis of the available results leads to the conclusion that present-day data do not reveal any statistically significant evidence for variations of the fundamental constants under study. The most reliable upper limits to possible variation rates at the 95% confidence level, obtained in our work, read: |\dot\alpha/\alpha| < (1.4e-14)/yr, |\dot\mu/\mu| < (1.5e-14)/yr on the average over the last ten billion years.Comment: 9 pages, 2 figures, 2 tables, LaTeX using aipproc.sty (included). In: X-ray and Inner-Shell Processes, R.W. Dunford, D.S. Gemmel, E.P. Kanter, B. Kraessig, S.H. Southworth, L. Young (eds.), AIP Conf. Proc. (AIP, Melville, 2000) vol. 506, p. 50

Does the proton-to-electron mass ratio vary in the course of cosmological evolution?

The possible cosmological variation of the proton-to-electron mass ratio was estimated by measuring the H_2 wavelengths in the high-resolution spectrum of the quasar Q~0347-382. Our analysis yielded an estimate for the possible deviation of \mu value in the past, 10 Gyr ago: for the unweighted value $\Delta \mu / \mu = (3.0\pm2.4)\times10^{-5}$; for the weighted value $$\Delta \mu / \mu = (5.02\pm1.82)\times10^{-5}$$ Since the significance of the both results does not exceed 3$\sigma$, further observations are needed to increase the statistical significance. In any case, this result may be considered as the most stringent estimate on an upper limit of a possible variation of \mu (95% C.L.): $$|\Delta \mu / \mu| < 8\times 10^{-5}$$ This value serves as an effective tool for selection of models determining a relation between possible cosmological deviations of the fine-structure constant \alpha and the elementary particle masses (m$_p$, m$_e$, etc.).Comment: 6 pages, 1 figure. Talk presented at the JENAM 2002 Workshop on Varying Fundamental Constants, Porto, 4th September 2002. To be published in the Conference Proceeding

Asymmetric Beams and CMB Statistical Anisotropy

Beam asymmetries result in statistically-anisotropic cosmic microwave background (CMB) maps. Typically, they are studied for their effects on the CMB power spectrum, however they more closely mimic anisotropic effects such as gravitational lensing and primordial power asymmetry. We discuss tools for studying the effects of beam asymmetry on general quadratic estimators of anisotropy, analytically for full-sky observations as well as in the analysis of realistic data. We demonstrate this methodology in application to a recently-detected 9 sigma quadrupolar modulation effect in the WMAP data, showing that beams provide a complete and sufficient explanation for the anomaly.Comment: updated to match PRD version + typo correction in Eq. B

Dynamic equations for three different qudits in a magnetic field

A closed system of equations for the local Bloch vectors and spin correlation functions of three magnetic qudits, which are in an arbitrary, time-dependent, external magnetic field, is obtained using decomplexification of the Liouville-von Neumann equation. The algorithm of the derivation of the dynamic equations is presented. In the basis convenient for the important physical applications structure constants of algebra su(2S+1) are calculated.Comment: 11 page