Spin matrices for gravitons and the humblet decomposition of the angular momentum of gravitational radiation in the linearized theory

We develop spin matrices for a classical gravitational field in the linearized theory which satisfy angular-momentum commutation relations and are appropriate for a spin angular momentum of two. The same spin matrices come out of a decomposition of the angular momentum density of the linearized gravitational field into orbital and spin parts, similar to that carried out by Humblet for the electromagnetic field. To achieve this decomposition, we use the momentum density for the gravitational field obtained from the Landau-Lifshitz pseudo-tensor in the weak gravity limit. We note a formal connection between the spin angular momenta of gravitational and electromagnetic fields using the Kaluza-Klein idea.     

Shannon entropies of atomic structure factors,off-diagonal order and radial correlation

Shannon entropies of one- and two-electron atomic structure factors in the position and momentum representations are used to examine the behaviour of the off-diagonal elements of density matrices with respect to the uncertainty principle and to analyse the effects of radial correlation on off-diagonal order. We show that radial correlation induces off-diagonal order in position space which is characterized by larger entropic values. Radial correlation in momentum space is characterized by smaller entropic values as information is forced into regions closer to the diagonal. Related off-diagonal correlation functions are also discussed.     

Spin effects and factorization in the Drell-Yan process

We discuss the idea that the nontrivial vacuum structure in QCD may induce transverse momentum and spin correlations of the initial state partons in Drell-Yan type reactions, i.e. in hadron-hadron collisions with production of a vector bosonV=γ ^*,Z,W ^±. Transverse momentum correlations are found to have practically no effect on observable quantities, but spin correlations have drastic consequences for the polarization density matrices of theV-bosons. We therefore propose measurements of theV polarization as a good test for the basic factorization hypothesis which, so far, has been assumed to be valid in numerous applications of the naive and QCD-improved parton model. We compare our ansatz for a spin correlation violating factorization with data from the NA 10 collaboration onγ ^* production inπ ^? N scattering. We find that the data give an indication of spin correlations of the partons in the initial state to be present.     

Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles

We describe an apparatus that can measure the instantaneous angular displacement and torque applied to a quartz particle which is angularly trapped. Torque is measured by detecting the change in angular momentum of the transmitted trap beam. The rotational Brownian motion of the trapped particle and its power spectral density are used to determine the angular trap stiffness. The apparatus features a feedback control that clamps torque or other rotational quantities. The torque sensitivity demonstrated is ideal for the study of known biological molecular motors.     

Nonequilibrium molecular dynamics simulation of shear viscosity by a uniform momentum source-and-sink scheme

A uniform momentum source-and-sink scheme of nonequilibrium molecular dynamics (NEMD) is developed to calculate the shear viscosity of fluids in this paper. The uniform momentum source and sink are realized by momentum exchanges of individual atoms in the left and right half systems, like the reverse nonequilibrium molecular dynamics (RNEMD) method [20] [Müller-Plathe, Phys. Rev. E, 49 (359), 1999]. This method has all features of RNEMD. In addition, the present momentum swap strategy maximizes the perturbation relaxation and eliminates the boundary jumps, which often harm other NEMD methods greatly. With periodic boundary conditions quadratic velocity profiles can be constructed and from the mean velocities of the right and left half systems the shear viscosity can be easily extracted. The scheme is tested on Lennard-Jones fluids over a wide range of state points (temperature and density), momentum exchange intervals and system sizes. It is demonstrated that the present approach can give reliable results with fast convergence by properly selecting the simulation parameters, i.e. particle number and exchange interval.     

Electromagnetic angular momentum flux tensor in a medium

Electromagnetic angular momentum describes the ability of electromagnetic field to impose torque on matter. We show that for an electromagnetic field ?C such as an optical beam field ?C in a medium, the torque density is determined by two fundamental quantities: the angular momentum flux tensor and the angular momentum density of the field. It is remarkable that the tensor alone gives the full picture of the angular momentum transfer between the field and the medium in all stationary electromagnetic phenomena. We derive a general expression for this tensor and apply the theory to several important examples without resorting to the classical paraxial approximation.     

A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein-Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.     

The Concept of Energy Densities and Stress Fields and its Applications in Quantum Mechanical Coulomb Systems within the Born-Oppenheimer Approximation

Recent papers and ideas concerning the global stress for crystals (obtained by a scaling of the total energy) as well as local stress and local energy (expressed by reduced density matrices or by Kohn-Sham orbitals) and related theorems and quantities like local momentum balances, forces, force sum rules, defect energies and defect stresses for perturbed crystals (surfaces, interfaces, point defects) are summarized. A new method for the calculation of relaxation or restoring forces is emphasized.     

Division of the energy and of the momentum of electromagnetic waves in linear media into electromagnetic and material parts

We defend a natural division of the energy density, energy flux and momentum density of electromagnetic waves in linear media in electromagnetic and material parts. In this division, the electromagnetic part of these quantities have the same form as in vacuum when written in terms of the macroscopic electric and magnetic fields, the material momentum is calculated directly from the Lorentz force that acts on the charges of the medium, the material energy is the sum of the kinetic and potential energies of the charges of the medium and the material energy flux results from the interaction of the electric field with the magnetized medium. We present reasonable models for linear dispersive non-absorptive dielectric and magnetic media that agree with this division. We also argue that the electromagnetic momentum of our division can be associated with the electromagnetic relativistic momentum, inspired on the recent work of Barnett [Phys. Rev. Lett. 104 (2010) 070401] that showed that the Abraham momentum is associated with the kinetic momentum and the Minkowski momentum is associated with the canonical momentum.     

Thirty years of gaseous positronics

The valence electronic structure of materials with crystalline order is described by the energy—momentum dispersion laws and densities of electron bands. These quantities are directly observed for the surfaces of thin (about 100 Å) solid films by electron momentum spectroscopy, based on kinematically complete observations of ionization events. The principles of the experiment and the imperfections of the probe are described and illustrated by examples. Comparison is made with other electron spectroscopies that measure subsets of the complete energy-momentum density information.     

Density and velocity statistics in variable density turbulent mixing

We experimentally study variable–density mixing of miscible gases in an open-circuit wind tunnel using simultaneous particle image velocimetry and planar laser-induced fluorescence. Experiments of a high Atwood number (0.6) and low Atwood number (0.1) are performed to compare non-Boussinesq cases with the Boussinesq limit. The higher density gas is injected into the wind tunnel co-flow using a round jet configuration, and near-field and far-field measurements are performed to examine mixing in both momentum and buoyancy-dominated regimes. The effects of buoyancy are measurable and important in both large-scale mixing features and in turbulence quantities. The low Atwood number PDFs (probability density functions) show fast and uniform mixing. The high Atwood number PDFs of density have skewness towards the larger densities, indicating less mixing of the heavy fluid due to its inertia. The skewness in the density gradient PDFs at high Atwood number displays strong density local variations that can enhance mixing at molecular scales. Turbulent kinetic energy decreases with streamwise distance from the jet for low Atwood number but increases for high Atwood number due to larger buoyancy and density-driven shear. Over 3000 experimental realisations are used to calculate statistical characteristics of the mixing, including valuable and rarely given data such as Favre-averaged turbulent quantities: mass flux velocity, Reynolds stress, turbulent kinetic energy, and density-specific volume correlation. Buoyancy effects are observed in these quantities and the trends are compared qualitatively with direct numerical simulations.     

States of non-zero density in the chiral invariant gross-neveu model

States describing a non-zero number density of massive particles are investigated in the SU(2) chiral-invariant Gross-Neveu model. It is found that for a fixed positive density, the lowest energy state is color ferromagnetic, with all color spins aligned. For asymptotically large densities, the total energy and density are calculated as functions of the Fermi momentum. These quantities tend toward their counterparts in a non-interacting theory, with logarithmic corrections typical of an asymptotically free system.     

Cylindrically symmetric relativistic fluids: a study based on structure scalars

Applying the 1 + 3 formalism we write down the full set of equations governing the structure and the evolution of self-gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, in terms of scalar quantities obtained from the orthogonal splitting of the Riemann tensor (structure scalars), in the context of general relativity. These scalars which have been shown previously (in the spherically symmetric case) to be related to fundamental properties of the fluid distribution, such as: energy density, energy density inhomogeneity, local anisotropy of pressure, dissipative flux, active gravitational mass etc, are shown here to play also a very important role in the dynamics of cylindrically symmetric fluids. It is also shown that in the static case, all possible solutions to Einstein equations may be expressed explicitly through three of these scalars.     

Die experimentelle Bestimmung der Neutronenstreulänge für das Wismutatom mit Hilfe der Totalreflexion an einem flüssigen Wismutspiegel

We construct generalized HF- and HB-equations fitted for building the symmetry properties of the Hamiltonian into. Therefore we use the method of Green's functions for condensed systems. The structure of HF- and HB-equations is conserved, only the density and pairing matrices change. Physical quantities may easily be calculated.     

Influence of electron diffraction on measured energy-resolved momentum densities in single-crystalline silicon

Electron momentum spectroscopy is used to determine the spectral function of silicon single crystals. In these experiments 50 keV electrons impinge on a self-supporting thin silicon film and scattered and ejected electrons emerging from this sample with energies near 25 keV are detected in coincidence. Diffraction effects are present that give rise to additional structures in the measured spectral momentum densities. Spectra for a specific momentum value can be obtained at different orientations of the crystal relative to the analysers. By comparing these spectra for which the measured momentum density is the same, but the diffraction conditions of the incoming and outgoing electron trajectories differ, one can distinguish between features due to diffraction of the incoming and/or outgoing electrons, and those due to the electronic structure of the target itself.     

Modified one-body memory function for classical fluids

A microscopic theory applicable to simple classical fluids, particularly in the hydrodynamic regime, is presented. A simple isomorphic transformation of the space of one-body additive phase-space functions is considered whose distinguishing feature is that the total energy density is contained in the new space. A projection operator formalism for this subspace has certain desirable properties for the study of the hydrodynamic regime. It is shown that, for a broad class of approximations, one obtains a prediction for the VanHove structure factorS(k, ω) that has the correct hydrodynamic structure and in which the only quantities that are approximated are the dissipative transport coefficients; all thermodynamic quantities appearing in the expression are rendered exactly. In particular, a weak coupling approximation is made on the memory function, and results are compared with the analogous theory of Forster and Martin. Agreement is found for the dissipative transport coefficients to lowest nontrivial order in the coupling. On the other hand, thermodynamic quantities are accurately predicted only to second order by Forster and Martin, whereas in the present theory they are exact.     

Vector parameterization of the Lorentz group transformations and polar decomposition of Mueller matrices

It is shown that the representation of the coherence matrix (the polarization density matrix) of beams of electromagnetic waves as a biquaternion corresponding to the four-vector of a pseudo-Euclidean space whose components are the intensity and the Stokes parameters provides a possibility of introducing the group transformations of these quantities isomorphic to SO(3.1) group. These transformations are a subset of the set of Mueller polarization matrices which, generally speaking, form a semigroup. The reduction of the semigroup of Mueller matrices to the group of transformations opens the possibility to use the vector parameterization of SO(3.1) group for interpretation of the polar decomposition of Mueller matrices. In particular, in this approach, the elements of the Mueller matrices corresponding to phase elements and polarizers turn out to be most simply and naturally related to their eigenpolarizations.     

Momentum, radiation pressure, and other second-order quantities in ideal gas (liquid) in some boundary-value problems

Problems related to such properties of sound waves as momentum, radiation pressure, and sound energy density and flux are investigated on the basis of the solutions of particular problems in the first-and second-order approximations using the Eulerian representation. Specifically, it is shown that a disturbance propagating in a continuous medium may have a nonzero momentum when the average density of the medium in the volume occupied by the wave coincides with the density of the undisturbed medium. In this case, the momentum and the related mass transfer and radiation pressure are caused by variations in the wave profile (envelope). Andreev’s expression for the energy density that differs from the commonly used one is verified, and some other paradoxical consequences of the theory of sound are considered. The correctness of using the quantities averaged over time and space is discussed.