On Zagier’s cusp form and the Ramanujan τ function

Zagier constructed a cusp form for each weightk of the full modular group. We use this construction to estimate Fourier coefficients of cusp forms. In particular, we get a non-trivial estimate, by elementary methods and indicate a relationship with the Lindelof hypothesis for classical Dirichlet L-functions. Dedicated to the memory of Professor K G Ramanathan     

Elastic constants of galena down to liquid helium temperatures

The elastic constants of single crystal galena have been determined from the measured ultrasonic velocities down to liquid helium temperature. A cryostat incorporating an arrangement to inject the liquid bonding material at low temperature is described. At 5 K, the values of elastic constants are C₁₁=14.9₀, C₁₂=3.5₁ and C₄₄=2.9₂×10¹⁰ N/m².     

Unrefined minimal K-types forp-adic groups

Oblatum 23-II-1993 & 18-V-1993     

Is there an antimatter-universe or antigalaxy?

Summary The very recent measurements on the ratio of cosmic antiproton to proton have contradicted seriously the previous measurements of the same for low-energy antiprotons. The controversial situation has been described and its implication for the validity of the postulate about the existence of antigalaxy has been examined. Although a very decisive conclusion cannot yet be made, a two-component behaviour of the ratio cannot, however, be excluded. Moreover, this two-component proposition seems to have better prospectsvis-a-vis the high-energy measurements of the ratio.     

Indirect strong coupling regime between a quantum emitter and a cavity mediated by a mechanical resonator

Achieving strong coupling between light and matter is usually a challenge in Cavity Quantum Electrodynamics (cQED), especially in solid state systems. For this reason is useful taking advantage of alternative approaches to reach this regime, and then, generate reliable quantum polaritons. In this work we study a system composed of a quantized single mode of a mechanical resonator interacting linearly with both a single mode cavity and a quantum two-level system. In particular, we focus on the behavior of the indirect light-matter interaction when the phonon mode interfaces both parts. By diagonalization of the Hamiltonian and computing the density matrix in a master equation approach, we evidence several features of strong coupling between photons and matter excitations. For large energy detuning between the cavity and the mechanical resonator it is obtained a phonon-dispersive effective Hamiltonian which is able to retrieve much of the physics of the conventional Jaynes–Cummings model (JCM). In order to characterize this mediated coupling, we make a quantitative comparison between both models and analyze light-matter entanglement and purity of the system leading to similar results in cQED.     

Biaxial bulge testing of polymeric sheets

The through thickness total strains of hydrostatically bulged domes of materials are usually determined indirectly. The in-plane circumferential strains are readily measured, and then constancy of volume is invoked to determine the “missing” or unknown strain. Some of our recent work with polymers has shown that volume constancy in large-scale deformation does not hold so that the usual computations of stress and strain during bulging of sheet may be in error. We describe an electrical device that reduces such errors by directly measuring the through thickness (and, thus, the thickness “strain”) for nonmetallic materials.     

High-Temperature superconductivity in the Y–Ba–Cu–O system

High-temperature superconductivity in the Y-Ba-Cu-O system has been discussed with special reference to the identification and characterization of the pure monophasic compound responsible for the superconductivity. The crucial role of oxygen has been examined in the light of the structure and thermogravimetric analysis.     

Monte Carlo calculation of electron spectra produced in water phantoms by 20 keV-1 GeV photons

Abstract

A Monte Carlo calculation for the energy spectra of electrons and positrons produced in infinite and semiinfinite water phantoms by photons ranging in energies from 20 keV to 1 GeV are presented. The dominant processes considered are the photoelectric effect, Auger effect, Compton effect, pair, and triplet production. Bremsstrahlung produced by electrons and positrons with energies greater than 1 MeV is also included. The effect of multiple Compton scattering, not considered in the earlier calculation, for the infinite phantom for photon energies higher than 2 MeV has been incorporated. For a semi-infinite phantom, multiple Compton scattering and backscattering through the top are considered. The results are compared with the earlier calculations for the first-collision spectrum. It is found that the inclusion of multiple Compton scattering significantly increases the average number of electrons/cm³ per photon/cm² at all energies considered whereas bremsstrahlung reduces the number of high energy electrons and produces more low energy electrons in the spectrum.