The structure of the new superspace

The new superspace of Wess and Zumino is generalized to the unconstrainedN-extendedD-dimensional case, it amounts actually to a reparametrization of the old superspace. Recurrence relations for the transformation law and for the covariant derivatives of the superfields defined in the new superspace are obtained. The definition of the component fields as local Lorentz covariant fields has the consequence that the gauge covariant expressions obtained for the vielbein and the connection of the new superspace don't contain the terms dropped out in the Wess-Zumino gauge of supergravity.     

TheB 2Σ-X 2Σ system of the CaF molecule

The spectrum of theB ²Σ-X ²Σ system of the CaF molecule has been photographed in the second order of a 10.6 m concave grating spectrograph with 0.33 Å/mm dispersion. The rotational structure of the (0, 0) and (1, 0) bands has been analysed and the precise molecular constants have been obtained. Using the constants so determined the band origins of a large number of bands with 0 <v′,v″ < 10 have been calculated and used to obtain the accurate vibrational constants forB andX states and these are presented.     

Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

Anomalous elastic behaviour of Bi-Pb-Ag composites

Bi-Pb and Bi-Pb-Ag superconducting composites have been prepared by the solid state reaction method. After the usual characterization, ultrasonic longitudinal velocity and attenuation studies have been undertaken over a temperature range 80–300 K by the pulse transmission technique. In contrast to normal solids, the ultrasonic velocities of both the samples in the temperature range 200-100 K are found to decrease with decreasing temperature (softening), followed by a velocity maximum. The samples are also found to exhibit longitudinal attenuation peaks at TEMPERATURES = 260, 160 and 120 K. An attempt has also been made to verify whether the Wachtman's equations can theoretically explain the low-temperature behaviour of the Young's modulus of these materials. A qualitative explanation for both the phenomena of softening of velocity as well as the occurrence of attenuation peaks is given.     

The dynamic analysis of circular plates and shallow spherical shells

In the investigation reported here an attempt has been made to study the influence of Berger's approximation on the non-linear transient response of circular plates and shallow spherical shells. The governing equations of motion obtained from Berger's approximation are solved by using the rapidly converging Chebyshev series spacewise and the Houbolt scheme for integration in the time domain. Results calculated when using Berger's approximation are compared with exact results. It is shown that Berger's method yields very accurate values for plates and shells under transient loading, in the case of immovable edge conditions.     

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     

Electronegativities in the calculation of diatomic molecular parameters (Hydrides of some transition elements)

The force constants for diatomic molecules and isolated bonds may be expressed by using equalized electro-negativities, bond orders, bond strengths and interatomicdistances. We have studied Mn¹H, Mn²H, Co²H, Ni¹H, Ni²H, Cu¹H, Cu²H, Ag¹H, and Ag²H and have determined the proportionality constant d, as well as the Lennard-Jones parameters a and b, for the potential energy functions used by Szöke and calculated the anharmonicity ω_eξ_e and the rotational-vibrational coupling constant α_e. The relation between electronegativity and ionization potential has been verified and the variations of molecular parameters with atomic number Z have been studied.     

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.