Dielectric properties of KDP-type ferroelectric crystals in the presence of external electric field

Considering external electric field as well as third- and fourth-order phonon anharmonic interaction terms in the pseudospin-lattice coupled mode (PLCM) model Hamiltonian for KDP-type ferroelectrics, expressions for field-dependent shift, width, renormalized soft mode frequency, Curie temperature, dielectric constant and dielectric loss are evaluated. For the calculation, method of statistical double-time temperature-dependent Green’s function has been used. By fitting model values of physical quantities, temperature and electric field dependences of soft mode frequency, dielectric constant and loss have been calculated which compare well with experimental results of Baumgartner [8] and Choi and Lockwood [9]. Both dielectric constant and loss decrease with electric field.     

Computation of collective modes and acoustic investigations at different temperatures of vitrous silica

This paper is mainly concerned with elastic and acoustic properties of vitrous silica besides the computation of phonon frequencies. Thus the phonon frequencies of vitrous silica have been calculated assuming the electronic bulk modulus,K _e, as equal to zero. New equations have been derived to relate the pressure derivatives of second order elastic constants to the acoustic Gruneisen’s parameters using both Bhatia-Singh’s parameters and Schofield’s equations. The calculated longitudinal and transverse Gruneisen’s parameters and the predicted absorption band spectra from Nagendranath’s equation and Bhatia Singh’s parameters are in good agreement with experiment. The calculated mean acoustic mode Gruneisen’s parameter evaluated from the pressure derivative of Nagendranath’s equation is also in good agreement with experiment. An erratum to this article is available at .     

Saha’s ionization equation for highZ elements

Saha’s ionization equation has been solved for highZ elements with the aim of providing input for opacity calculations. Results are presented for two elements, tungsten and uranium. The ionization potentials have been evaluated using the simple Bohr’s formula with suitable effective charges for ions. The reliability of the free electron density, ion concentrations, etc., obtained from the Saha’s equation solutions has been checked by comparing theP _T andE _T computed from them with those given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperatures above 0.2 keV.     

Correlations for a new Bell’s inequality experiment

Proofs of Bell’s theorem and the data analysis used to show its violation have commonly assumed a spatially stationary underlying process. However, it has been shown recently that the appropriate Bell’s inequality holds identically for cross correlations of three or four lists of ±l’s, independently of statistical assumptions. When data consistent with its derivation are analyzed without imposition of the stationarity assumption, the resulting correlations satisfy the Bell inequality.     

Comparison between Weber’s electrodynamics and classical electrodynamics

We present the main aspects of Weber’s electrodynamics and of Maxwell’s equations. We discuss Maxwell’s point of view related to Weber’s electrodynamics. We compare Weber’s force with Lorentz’s force. We analyse the relation between Weber’s law and Maxwell’s equations. Finally, we discuss some experiments performed and proposed with which we can distinguish Weber’s force from Lorentz’s one.     

Properties of hard disc fluids by Baxter’s method

The radial distribution function and the equation of state for hard disc fluids have been calculated at various densities by solving Ornstein-Zernike equation using Baxter’s method.     

The effect of soft modes on solitons in a linear lattice

Solitons are simulated in an anharmonic linear lattice that is susceptible to a soft mode instability. The soft mode characteristic is introduced in the system by the addition of a term (−Au _n ² ) in the potential between the neighbouring atoms and the evolution of the system is studied as the soft mode parameterA varies from zero to the square of the limiting optical frequency. It is shown that the displacement pattern of the system shows three regions. First there is a region in which the relative displacements of the atoms show large amplitude oscillations. This is followed successively by a domain in which the relative displacements of the atoms are negligible and then by the soliton itself. In the soft mode region, the displacements of the atoms preceding the soliton decrease drastically in a linear fashion first, parabolically next and later become steady. It further exhibits a kind of devil’s stair cases.     

On the Material Invariant Formulation of Maxwell’s Displacement Current

Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere’s law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases. Maxwell’s original constitutive relations for both electrodynamics and fluid dynamics were not material invariant. In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative. Assuming that the electromagnetic field should follow the general requirements for a material field, we show that if the upper convected derivative is used in place of the partial time derivative in the displacement current term, Maxwell’s electrodynamics becomes material invariant. Note, that the material invariance of Faraday’s law is automatically established if the Lorentz force is admitted as an integral part of the model. The new formulation ensures that the equation for conservation of charge is also material invariant in vacuo. The viscoelastic medium whose apparent manifestation are the known phenomena of electrodynamics is called here the metacontinuum.     

Thermal conduction in a homogeneous two-phase system

Assuming a regular geometry of dispersed phase (λ ₂) an integrated theory for the effective thermal conductivityλ _e of all kind of two-phase materials (including loose materials) is developed. The flux modification is carried out by considering the effective neighbouring interactions in the solution of Poisson’s equation. A comparison of calculatedλ _e values with the reported experimental results over a wide range of two-phase materials shows a good agreement.     

Bell’s Theorem without Inequalities and without Unspeakable Information

A proof of Bell’s theorem without inequalities is presented in which distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups.     

Identical Quantum Particles and Weak Discernibility

Saunders has recently claimed that “identical quantum particles” with an anti-symmetric state (fermions) are weakly discernible objects, just like irreflexively related ordinary objects in situations with perfect symmetry (Black’s spheres, for example). Weakly discernible objects have all their qualitative properties in common but nevertheless differ from each other by virtue of (a generalized version of) Leibniz’s principle, since they stand in relations an entity cannot have to itself. This notion of weak discernibility has been criticized as question begging, but we defend and accept it for classical cases likes Black’s spheres. We argue, however, that the quantum mechanical case is different. Here the application of the notion of weak discernibility indeed is question begging and in conflict with standard interpretational ideas. We conclude that the introduction of the conceptual resource of weak discernibility does not change the interpretational status quo in quantum mechanics.     

Extended Hydrodynamics from Enskog’s Equation for a Two-Dimensional System General Formalism

Balance equations are derived from Enskog’s kinetic equation for a two-dimensional system of hard disks using Grad’s moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional fluids. The set of independent hydrodynamic fields in the present formulations are: density, velocity, temperature and also—following Grad’s original idea—the symmetric and traceless pressure tensor p _ij and the heat flux vector q ^k . An approximation scheme similar in spirit to one made by Grad in his original work is made. Once the hydrodynamics is derived it is used to discuss the nature of a simple one-dimensional heat conduction problem. It is shown that, not too far from equilibrium, the nonequilibrium pressure in this case only depends on the density, temperature and heat flux vector. PACS: 51.10.+y, 05.20.Jj, 44.10.+i, 05.70.Ln     

Adiabatic anholonomy and canonical transformations

Biswas and Soni [4] have surmised a semiclassical formula for Berry’s phase in terms of a generating function. We derive this formula apart from showing that it is not true in general and investigate its domain of validity. We also derive transformation formulae for Berry’s phase (Hannay’s angle) under general canonical transformations. A simpler proof for total angle invariance than hitherto available, is given.     

Bethe-Salpeter equation with the sine-Gordon interaction

An attempt is made to study the interaction Hamiltonian,H _int =Gψ ²(x)U(φ(x)) in the Bethe-Salpeter framework for the confined states of theψ particles interactingvia the exchange of theU field, whereU(φ) = cos (gφ). An approximate solution of the eigenvalue problem is obtained in the instantaneous approximation by projecting the Wick-rotated Bethe-Salpeter equation onto the surface of a four-dimensional sphere and employing Hecke’s theorem in the weak-binding limit. We find that the spectrum of energies for the confined states,E =2m+B (B is the binding energy), is characterized byE ∼n ⁶, wheren is the principal quantum number.     

Focusing of an electromagnetic plane wave into a uniaxial crystal by a Wood lens

High frequency fields, refracted by a geometry containing a Wood lens placed at a certain distance from a planar uniaxial interface, are derived by using Maslov’s method. The geometrical optics approximation generally valid for high frequency fields fails in the vicinity of a caustic. Maslov’s method is a systematic procedure for predicting the field in the caustic region, combining the simplicity of the ray and the generality of the transform method. Numerical computations are made for the field pattern around the caustic by using Maslov’s method. The results are found to be in good agreement with those obtained using Kirchhoff’s approximation.      

Green’s functions for spin half field theory in Rindler space

The solutions of Dirac equation in different regions of the complete extension of Rindler space are obtained near the event horizons and in the asymptotic limits. Continuity of these solutions across the event horizons is established. The Green’s functions are written down in the two causally disconnected regions, continued in the future (F) and past (P) regions using the techniques a la Boulware and a consistent scheme of Green’s functions in all regions is exhibited.     

Method of Green’s function of nonlinear vibration of corrugated shallow shells

Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated. The nonlinear partial differential equations of shallow shell were reduced to the nonlinear integral-differential equations by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s function as a series of characteristic function. Therefore, the integral-differential equations became nonlinear ordinary differential equations with regard to time. The amplitude-frequency relation, with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration. As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions are available for reference to the design of corrugated shells.     

Isoscalar and isovector nuclear matter properties and neutron skin thickness

Isoscalar and isovector nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and the isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. We also discovered that the correlations between the isovector properties and the incompressibility K show a singularity at the critical incompressibility K_c=306 MeV. It is shown that the neutron skin thickness gives crucial information about not only for the neutron EOS but also about the isovector nuclear matter properties and about the parameterization of Skyrme interaction. Charge exchange spin-dipole (SD) excitations are proposed to determine the neutron skin thickness model independently.     

Interplay of superconductivity and antiferromagnetism in SmRh4B4

A microscopic theory of interplay of superconductivity and antiferromagnetism in rare earth ternary systems is developed from first principles for less than half filledf atomic shells. Self consistent equations for the superconducting order parameter Δ and magnetic order parameter Γ, are derived using a Green’s function technique and equation of motion method. The theory is applied to explain the experimental results in the antiferromagnetic superconductor SmRh₄B₄. The present model explains true coexistence of superconductivity and antiferromagnetism and the suppression of superconductivity by antiferromagnetism. The behaviour of superconducting order parameter (Δ), magnetic order parameter (Γ), the specific heat, the density of states, free energy and critical field (H _c) is also studied for the system SmRh₄B₄.     

Elastic constants of lead-bismuth alloys

A study of ultrasonic velocities and internal friction has been carried out in Pb-Bi alloys in the concentration range of 0 to 49.5 atomic % Bi using the composite oscillator technique. From the velocity and density data a set of elastic constants namely, Young’s modulus, rigidity modulus, bulk modulus and Poisson’s ratio are estimated. The results are interpreted in terms of the phase changes occurring in the alloy system. Internal friction is found to be more sensitive than the elastic constants to the phase changes.