Density of states for Bose-Einstein condensation in harmonic oscillator potentials

We discuss how it is possible to obtain a reliable approximation for the density of states for a system of particles in an anisotropic harmonic oscillator potential. A direct application of the result to study Bose-Einstein condensation of atomic gases in a potential trap can be given. In contrast to a previous study, our method involves only analytic calculations.Comment: 7 pages, LaTeX2e, no figure

Singularities of Green functions of the products of the Laplace type operators

The structure of diagonal singularities of Green functions of partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian man ifold is studied. A special class of operators formed by the products of second-order operators of Laplace type defined with the help of a unique Riemannian metric and a unique bundle connection but with different potential terms is investigated. Explicit simple formulas for singularities of Green functions of such operators in terms of the usual heat kernel coefficients are obtained.Comment: 12 Pages, LaTeX, 30 KB, No Figures, submitted to Physics Letters B, Discussion of the Huygence principle is remove

Relation between chiral symmetry breaking and confinement in YM-theories

Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop are thoroughly investigated. The approach by Gattringer is generalized to mode sums which reconstruct the Polyakov loop locally. This opens the possibility to study the mode sum approximation to the Polyakov loop correlator. The approach is re-derived for the ab initio continuum formulation of Yang-Mills theories, and the convergence of the mode sum is studied in detail. The mode sums are then explicitly calculated for the Schwinger model and SU(2) gauge theory in a homogeneous background field. Using SU(2) lattice gauge theory, the IR dominated mode sums are considered and the mode sum approximation to the static quark anti-quark potential is obtained numerically. We find a good agreement between the mode sum approximation and the static potential at large distances for the confinement and the high temperature plasma phase.Comment: 17 pages, 10 figures, typos corrected, references added, final version to appear in PR

A Local Effective Action for Photon-Gravity Interactions

Quantum phenomena such as vacuum polarisation in curved spacetime induce interactions between photons and gravity with quite striking consequences, including the violation of the strong equivalence principle and the apparent prediction of `superluminal' photon propagation. These quantum interactions can be encoded in an effective action. In this paper, we extend previous results on the effective action for QED in curved spacetime due to Barvinsky, Vilkovisky and others and present a new, local effective action valid to all orders in a derivative expansion, as required for a full analysis of the quantum theory of high-frequency photon propagation in gravitational fields.Comment: 22 pages, 9 figures, harvmac Te

Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$

Practical guidance on insulin injection practice in diabetes self-management in the Indian setting: an expert consensus statement

This consensus statement aimed to provide a simple and easily implementable practical educational guide- line for healthcare professionals (HCPs) and patients regarding insulin injection practice in diabetes self- management in the Indian setting. A group of experts analysed published data from guidelines, clinical trials and real world evidence to reach consensus recommendations on optimal insulin injection practices in terms of a) the injection sites (preparation of site of injection, choosing the injec- tion site, site rotation), b) choice of device and storage of insulins, and c) safety precautions, sharp disposal practice and complications. Findings from Global and Indian arm of 2014-2015 ITQ Study were considered to emphasize a need for improved practice by HCPs covering all the vital topics essential to proper injection habits. The consensus statement provides a simple and easily implementable practical educational guideline for HCPs and patients to optimize insulin injection practices in accordance with recent advances in device manufac- turing, newer research findings, and updated interna- tional guidelines as well as widespread concerns about neglected safety precautions such as single-patient use of pens and appropriate sharp disposal practices.This consensus statement aimed to provide a simple and easily implementable practical educational guide- line for healthcare professionals (HCPs) and patients regarding insulin injection practice in diabetes self- management in the Indian setting. A group of experts analysed published data from guidelines, clinical trials and real world evidence to reach consensus recommendations on optimal insulin injection practices in terms of a) the injection sites (preparation of site of injection, choosing the injec- tion site, site rotation), b) choice of device and storage of insulins, and c) safety precautions, sharp disposal practice and complications. Findings from Global and Indian arm of 2014-2015 ITQ Study were considered to emphasize a need for improved practice by HCPs covering all the vital topics essential to proper injection habits. The consensus statement provides a simple and easily implementable practical educational guideline for HCPs and patients to optimize insulin injection practices in accordance with recent advances in device manufac- turing, newer research findings, and updated interna- tional guidelines as well as widespread concerns about neglected safety precautions such as single-patient use of pens and appropriate sharp disposal practices