A method is developed to determine the eigenvalues and eigenfunction of two-boson 2 × 2 matrix Hamiltonians that include a wide class of quantum optical models. The quantum Hamiltonians are transformed in the form of the one variable differential equation and the conditions for their solvability are discussed. We present two different transformation procedures and we show our approach unify various approaches based on Lie algebraic technique. As an application, solutions of the modified Jaynes-Cummings and two-level Jahn-Teller Hamiltonians are studied.

We have investigated two conformally flat tilted Bianchi Type-V cosmological models in general relativity. To get a determinate solution, we have assumed a supplementary conditionA =Bⁿ between metric potentials wheren is a constant. The behaviour of the model forn = 2 is discussed in detail. Various physical and geometrical aspects of the models are also discussed.

We present an insightful ‘derivation’ of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton’s law of motion (mx = F) for the heavy particle reduces to a Langevin equation (valid on a coarser time-scale) with the assumption that the lighter gas particles follow a Boltzmann velocity distribution. Starting from the kinematics of the random collisions we show that (1) the average force 〈F〉 ∞ −x and (2) the correlation function of the fluctuating forceη = F — 〈F〉 is related to the strength of the average force.

We examine the effects of mixing induced light heavy charged lepton neutral currents on the partial wave amplitude for the process l⁺l⁻ →ZZ (withl = e,μ or τ). By imposing the constraints that the amplitude should not exceed the perturbative unitarity limit at high energy (√s = Λ), we obtain bounds on light heavy charged lepton mixing parameter sin²(2θ_L^a) where θ_L^a is the mixing angle of the ordinary charged lepton with its exotic partner. For Λ = 1 TeV, no bound is obtained on sin² (2θ_L^a) form_E < 0.69 TeV. However, sin² (2θ_L^a) ≤ 1.52×10⁻⁵ form_E = 5 TeV, sin² (2θ_L^a) ≤ 2.41 ×10⁻⁷ form_E = 10 TeV. Similarity for Λ = ∞ no bound is obtained on sin² (2θ_L^a) for m_E < 1.97 TeV and sin² (2θ_L^a) ≤ 0.15 form_E = 5 TeV and sin² (2θ_L^a) ≤ 3.88×10^-2 form_E = 10 TeV.

We calculate the cross-section of the inverse beta decay process,v_e+n → p+e, in a background magnetic field which is much smaller than m_p^2/e. Using exact solutions of the Dirac equation in a constant magnetic field, we find the cross-section for arbitrary polarization of the initial neutrons. The cross-section depends on the direction of the incident neutrino even when the initial neutron is assumed to be at rest and has no net polarization. Possible implications of the result are discussed.

Excitation functions for¹⁰³Rh (α,xn);x = 1–4 and¹⁰³Rh (α,αxn);x = 1–3 reactions were measured up to 50 MeV bombarding energy using stacked foil activation technique and high purity germanium (HPGe) γ-ray spectroscopy method. The experimental results were compared with calculations considering equilibrium as well as pre-equilibrium hybrid model of Blann (ALICE/90). It is found that the initial exciton configurationn₀ = 4(4p0h) gives fairly good agreements for (α,xn) reactions. There seems to be indication of direct inelastic scattering effects in (α,αxn)-type of reactions.

The triple differential cross-sections for ionization of hydrogen at incident energies in the range 17.6 eV to 13.7 eV are calculated in the distorted-wave Born approximation in the equal energy sharing andϑ_ab = 180° kinematics. It is found that a maximum in the cross-section, as was observed in the case of helium under similar conditions is also found here at excess energyE_ex ≤ 1.0 eV. This ‘maximum’ becomes more pronounced asE_ex decreases indicating dominance of short rangee-e correlations at these low energies. The angular distribution of the singlet and triplet partial waves and the asymmetry parameter have been analysed.

Experiments which have been undertaken over a number of years have shown that a rotating magnetic field can drive a significant non-linear Hall current in a plasma. Successful experiments of this concept have been made with a device called rotamak. In its original configuration this device was a field reversed configuration without a toroidal magnetic field but with a vertical field to establish the MHD equilibrium. However, modifications have shown that current can also be driven if a central current-carrying rod is used to provide an applied toroidal field. The new rotamak has then a spherical tokamak magnetic field structure.

Properties of steady state ion sheath formed in front of a negatively biased metal plate under the influence of negative ions have been investigated in collisionless argon/SF₆ plasma. This experiment is carried out at a fixed discharge voltage and fixed filament heating power. In this experiment, the decrement in plasma pre-sheath potential drop as well as positive ion drift velocity toward the plate is experimentally recorded in the presence of negative ions. It is also found that the plasma positive ion density and plasma electron temperature decrease in the presence of negative ions. These factors attribute to the decrease of ion current toward the plate. Hence the usual ion sheath expands.

Cotton fabric was treated with dichlorodimethylsilane (DCDMS) solution by two methods. In the first method, the fabrics were directly dipped into DCDMS solution for different time intervals and in the second method, the fabric was first subjected to radiofrequency (RF) plasma treatment for different durations and optimized exposure power condition and then immersed in DCDMS solution. The physical properties of cotton fabrics, treated with DCDMS in the presence/absence of air plasma have been compared with those of the control fabrics. Changes in the surface morphology structure and composition were observed through scanning electron microscopy and attenuated total reflectance-IR. The change in colour parameters of the fabric due to the treatment was assessed by Dataflash 100 colour measurement spectrophotometer with colourtools QC 1.3 colour quality software. The water repellent property of untreated and modified fabrics was studied using AATCC test method 39 (1971). The effectiveness of the water repellent property was checked by washing the treated fabrics up to ten cycles.

Results of an experimental study of short and longp-Ge(Au) samples are presented and compared qualitatively with data furnished by the one-dimensional theoretical model describing the evolution of domain instability in a two-parametric space ‘voltageV-emission coefficient β’. According to the theory, single-, double-, and multi-subdomain states and order-disorder-order transitions via intermittency have been observed in the system with increasing voltage. Three operation regimes of the system are found, depending on the region of the parametric space: ohmic, quenched (pulsing) and transit-time. In short samples, a second portion with S-switching is revealed in the current-voltage characteristic.

It is found that the nucleation of domains can take place in Ba₅Ti₂O₇Cl₄ under the influence of temperature unlike in many other ferroelectrics. The nucleated domain can also be removed from the structure under the randomizing effect of temperature. These observations have been explained on the basis of a nucleation model of Ingle and coworkers suggested for KNbO₃. Similarity of physical situation in KNbO₃ and Ba₅Ti₂O₇Cl₄ regarding the existence of ordered point defects inducing nucleation of domains around them has been highlighted. This surprising similarity is suggested to be due to the physical processes occurring at the phase transition rather than due to any structural resemblance. The nature of nucleation occurring under the influence of temperature is shown to be identical with the nature of nucleation occurring under the influence of externally applied stress, and/or DC electric field. A new technique of identifying point defects responsible for nucleation of domains is reported.

Dielectric constants of the binary mixtures of acetophenone,p-chloroaceto-phenone,p-methylacetophenone ando-hydroxyacetophenone in dilute solutions of benzene and 1,4-dioxane were measured at 303 K and at frequency 100 kHz. The low frequency molecular dynamics of acetophenone and its derivatives have been studied by evaluating the Kirkwood correlation factorg, molar polarizationP₂, excess correlation factor δg and excess free energy ΔG. The dipolar contribution to excess free energy of mixing arising from long-range electrostatic interaction and short-range interaction between identical molecules has been assessed separately. The presence of α- and β-multimers in the above systems was identified. The results have been used to interpret the fluid structure in such mixtures.

Molar extinction coefficients of aqueous solutions of some organic compounds, viz. formamide (CH₃NO),N-methylformamide (C₂H₅NO),NN-dimethylformamide (C₃H₇NO),NN-dimethylacetamide (C₄H₉NO), 1,4-dioxane (C₄H₈O₂₄), succinimide (C₄H₅NO₂) and solutions of acetamide (C₂H₅NO) and benzoic acid (C₇H₆O₂) in 1,4-dioxane (C₄H₈O₂) have been determined by narrow beam γ-ray transmission method at 81, 356, 511, 662, 1173 and 1332 keV. The experimental values of mass attenuation coefficients of these compounds have been used to calculate effective atomic numbers and electron densities. The additivity rule earlier used for aqueous solution has been extended to non-aqueous (1,4-dioxane) solutions.

The measurements of ultrasonic velocity and density were made for the ternary mixtures of l-naphthol/2-naphthol with 2-propanone in benzene at 20, 30 and 40°C in the mole fraction range of 0.00 to 0.05. Adiabatic compressibility and intermolecular free length have been evaluated using ultrasonic velocity data. The non-linear variation of ultrasonic velocity and allied parameters with mole fraction indicates solute-solute interactions through hydrogen bonding between unlike molecules. Results of ultrasonic velocity and density measurements are further supported by FT-IR spectra. The change in transmittance as well as the shift in the frequency of the representative peak of the OH stretching in FT-IR spectra give inferences about the complex formation.

In this communication we present theoretical demonstration of electron dichroism in the relativistic (e, 2e) process for K-shell ionization of atoms in non-coplanar asymmetric geometry. The theoretical formalism has been developed in plane wave Born approximation and in this approximation the triple differential cross-section (TDCS) has been expressed as a product of kinematical factors and atomic structure functions. The longitudinal spin asymmetry in the relativistic (e, 2e) process on K-shell of atoms has been shown to depend on the interference between the transition charge and component of the transition current in the direction perpendicular to the scattering plane. Further, the longitudinal spin asymmetry has been shown to depend on incident electron energy, atomic number of the target, azimuthal angle of the ejected electron and scattered electron angle.

The effect of a spatially dependent effective mass on the energy levels in a rectangular quantum wire with finite barrier potential is considered. The heterojunction is modelled by an error function rather than a step function to more accurately model the material transition region at the interface between the two materials. The carrier ground state is calculated using the envelope function approximation for Ga_0.47In_0.53As/InP and GaAs/Ga_0.63Al_0.37As systems. The results are lower than those reported before, and are in better agreement with the experimental points.

Polycrystalline Mg_xAl_2xLi_0.5(1−x)Fe_2.5(1−x) O₄ (x = 0.0, 0.2, 0.5, 0.6 and 0.7) ferrites were prepared by standard ceramic method, and characterized by X-ray diffraction and infrared absorption spectroscopy. The spectra show two significant absorption bands in the wave number range of 400–1000 cm⁻¹ arising from interatomic vibrations in the tetrahedral and octahedral coordination compounds. The decrease in intensity and increase in broadness of bands with concentration (x) are explained on the basis of cation distribution. The force constants and bulk modulus are found to decrease with Mg-Al content (x) which suggested weakening of interatomic bonding. An alternate method for the determination of bulk modulus, longitudinal and transverse velocities is suggested. The magnetic and electrical properties of these compounds are explained in the light of structural and optical properties.