Thermodynamic Geometry of the Born-Infeld-anti-de Sitter black holes

Thermodynamic geometry is applied to the Born-Infeld-anti-de Sitter black hole (BIAdS) in the four dimensions, which is a nonlinear generalization of the Reissner-Norstr\"Aom-AdS black hole (RNAdS). We compute the Weinhold as well as the Ruppeiner scalar curvature and find that the singular points are not the same with the ones obtained using the heat capacity. Legendre-invariant metric proposed by Quevedo and the metric obtained by using the free energy as the thermodynamic potential are obtained and the corresponding scalar curvatures diverge at the Davies points.Comment: Latex,19 pages,14 figure

On the Thermodynamic Geometry of Hot QCD

We study the nature of the covariant thermodynamic geometry arising from the free energy of hot QCD. We systematically analyze the underlying equilibrium thermodynamic configurations of the free energy of 2- and 3-flavor hot QCD with or without including thermal fluctuations in the neighborhood of the QCD transition temperature. We show that there exists a well-defined thermodynamic geometric notion for QCD thermodynamics. The geometry thus obtained has no singularity as an intrinsic Riemannian manifold. We further show that there is a close connection of this geometric approach with the existing studies of correlations and quark number susceptibilities in hot QCD.Comment: 15 pages, 12 figures, Keywords: Thermodynamic Geometry, Hot QCD, Quasi-particles, PACS: 12.38.-t; 05.70.Fh; 02.40.Ky; 12.40.E

Thermal photon to dilepton ratio in ultra-relativistic heavy ion collisions

The ratio of transverse momentum distribution of thermal photons to dilepton has been evaluated. It is observed that this ratio reaches a plateau beyond a certain value of transverse momentum. We argue that this ratio can be used to estimate the initial temperature of the system by selecting the transverse momentum and invariance mass windows judiciously. It is demonstrated that if the radial flow is large then the plateau disappear and hence a deviation from the plateau can be used as an indicator of large radial flow. The sensitivity of the results on various input parameters has been studied.Comment: 9 pages with 11 eps figure

Commutant lifting, interpolation, and perturbations on the polydisc

The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting problem to the contractivity of certain linear functionals. The second one transforms it into nonnegative real numbers. We also solve the Nevanlinna-Pick interpolation problem for bounded analytic functions on the polydisc. Along the way, we solve a perturbation problem for bounded analytic functions. Commutant lifting and interpolation on the polydisc solve two well-known problems in Hilbert function space theory.Comment: 56 pages. Thoroughly revised, new results, sections, and example

A new study of muons in air showers by NBU air shower array

The North Bengal University (NBU) air shower array has been in operation in conjunction with two muon magnetic spectrographs. The array incorporates 21 particle density sampling detectors around the magnetic spectrographs covering an area of 900 sq m. The layout of the array is based on the arrangement of detectors in a square symmetry. The array set up on the ground level is around a 10 m high magnetic spectrograph housing. This magnetic spectrograph housing limits the zenith angular acceptance of the incident showers to a few degrees. Three hundred muons in the fitted showers of size range 10 to the 4th power to 10 to the 5th power particles have so far been scanned and the momenta determined in the momentum range 2 - 440 GeV/c. More than 1500 recorded showers are now in the process of scanning and fitting. A lateral distribution of muons of energy greater than 300 MeV in the shower size range 10 to the 5th power to 7 x 10 to the 5th power has been obtained