Equations governing the energy-momentum tensor of a system of charged particles

In this paper the equations governing the energy, momentum, and angular momentum of a system of charged particles in motion are obtained as a series in inverse powers of c. The mass motion and time-symmetric part of the retarded electromagnetic field are shown to contribute to these equations a total time derivative which is an even power series in c⁻¹. The radiation-reaction terms of O(c⁻⁵) are evaluated and discussed as a prototype for higher order, odd power terms in the asymptotic expansions of the equations.     

On the two-body problem in general relativity

We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third post-Newtonian order (∼1/c⁶ beyond the Newtonian acceleration). These equations are necessary when constructing the theoretical templates for searching and analyzing the gravitational-wave signals from inspiralling compact binaries in VIRGO and LISA type experiments.     

Pair production of pions with symmetric momenta in the range 0.5⩽pT⩽2.0 GeV/c In 70 GeV p-p collisions

The invariant cross-section slope of the pp→π⁺π^?+X process as a function of p_T is found to have a break near 1 GeV/c. Fitting the cross section by a sum of two exponents gives the values of powers (12.3±0.9)(GeV/c)^?1 and (8.7±0.6)(GeV/c)^?1. The experimental points at p_T?1 GeV/c are significantly higher than predictions based on hard scattering models such as QCD and CIM.     

The calculation of Dirac sea effects on finite solitons

The effects of polarization of the Dirac sea on finite solitons in a simple theory in which fermions interact with a single scalar field are studied. The mass shift for a given background scalar field is computed numerically and compared to approximations arising from expansions in inverse powers of the effective fermion mass and in powers of derivatives of the background scalar field. The conditions under which such approximations succeed are discussed. When such approximations work one can derive local equations of motion for the soliton fields which include the effects of polarizing the Dirac sea. These new equations are studied and energy minimization is used to explore the effects of the Dirac sea on the structure of the soliton. Calculations for a typical Friedberg-Lee soliton are presented, and it is shown that, while the approximations do not work well for fields employed to model the quark structure of nucleons, they do provide an upper bound for the mass of the soliton. A scalar field typical of those used to model ¹⁶O in quantum hadrodynamics is also studied, and it is shown that, when the effective potential is supplemented by the next term occurring in a derivative expansion, the renormalized shift in the energy of the Dirac sea is well approximated.     

On the definition of renormalized field products

We study the redefinition of the field products appearing in a Lagrangian and its equations of motion in a Normal Product framework. We propose a method of defining these products, which give the finite Green's functions, in such a way that the canonical derivation of the equations of motion is preserved. This involves the use of the Wilson Expansion in a Dimensionally Regularized form. As an example a ?⁴, ?³, field theory in four dimensions is fully redefined to the 1-loop level.     

The predissociation of the 2σ u −1 (c 4Σ u − , v states of the oxygen molecular ion

The dynamics of predissociation of the 2σ _u ^?1 (c ⁴Σ _u ^? ), v vibrational states of the O ₂ ⁺ ion was studied theoretically using the method of coupled differential equations. The main equations describing the vibrational motions of nuclei in the adiabatic and diabatic approximations are given. The applicability scope of approximate methods for solving these equations was studied. The predissociation widths for the v = 0 and 1 vibrational levels were found to be Γ₀ = 0.054 meV and Γ₁ = 9.71 meV. This substantiated the results of recent observations of neutral fragments formed after the dissociation of the O₂ molecule. About 99% of the O ₂ ⁺ ions in the 2σ _u ^?1 (c ⁴Σ _u ^? ), v states were found to decompose to the O(¹ D) + O⁺(⁴ S) dissociation products.     

Bound states of heavy quarks on the light plane

We investigate in detail the light plane formulation of bound state equations and of the interactions of bound states. This formalism is particularly well suited to discuss bound states of heavy quarks since these states can be well approximated as two particle states but yet there are significant relativistic corrections to the conventional nonrelativistic approach. Applications are made to electromagnetic decays of charmonium (ψ→e ⁺ e ^?, η _c →γγ, ψ′→η _c γ, etc.).     

Diffusive corrections to asymptotics of a strong-field quantum transport equation

The asymptotic analysis of a linear high-field Wigner-BGK equation is developed by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number ?, evolution equations are derived for the terms of zeroth and first order in ?. In particular, a quantum drift-diffusion equation for the position density of electrons, with an ?-order correction on the field terms, is obtained. Well-posedness and regularity of the approximate problems are established, and a rigorous proof that the difference between exact and asymptotic solutions is of order ?², uniformly in time and for arbitrary initial data is given.     

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U (n). As the result, one can create a theory of particle evolution that is gauge-invariant with regards to the group Uⁿ (1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U (1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping, and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory, the article considers a number of important particular examples, both known and new.     

The gravitational field in the wave zone I. The radiating terms of the metric tensor

We consider an asymptotically flat space-time generated by a perfect fluid source of compact spatial support. Using the de Donder gauge conditions, the Einstein equations are reduced to a new form of Poisson-type equations. A formal iterative scheme is set up to solve these equations by expanding the components of the metric tensor in powers ofc ^–1. The coefficient of each power ofc ^–1 depends on the asymptotically retarded timeu andx, y, z and satisfies a Poisson-type equation. Assuming asymptotic flatness the solution is carried out in the first orders. The results are explicit expressions of the metric up to orderc ^–4 in terms of the source functions. These expressions hold over all space-time. A further expansion in powers ofr ^–1 gives the first terms of the metric that contribute to gravitational radiation.     

Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent

The quantal system of Bose particles described by the non-linear Schrödinger equation i?φ/?t = -$\text{1}\text{2}$?²φ/?x² + cφ1φ², with c= cxf∞ and via the ground state with finite particle density, is the 1- dimensional gas of impenetrable bosons studied by M. Girardeau, T.D. Schultz, A. Lenard, H.G. Vaidya and C.A. Tracy. We show that the 2-point (resp. 2n-point) function, or the 1-particle (resp. n-particle) reduced density matrix, of this system satisfies a non-linear differential equation (resp. a system of non-linear partial differential equations) of Painlevé type. Derivation of these equations is based on the link between field operators in a Clifford group and monodromy preserving deformation theory, which was previously established and applied to the 2-dimensional Ising model and other problems. Several related topics are also discussed.     

Mössbauer study of aluminum-substituted hematites

A Mössbauer spectroscopic study is reported on a series of aluminum-substituted hematites, α(Fe_1-cAl_c)₂O₃, with c up to 0.32. These samples were prepared by heating aluminum-substituted goethites, αFeOOH, at 500°C. X-ray line broadening gives particle dimensions of ?200 Å to >1000 Å. Heating the samples to 900° improves crystallinity but reduces the maximum obtainable c to ?0.15. At 77 K for c?0.04 the magnetic structure is antiferromagnetic with the spins aligning close to the (111) axis. For c?0.08 and for all compositions at 298 K the spins are perpendicular to (111) and for this weakly ferromagnetic phase the supertransferred hyperfine field is (5±1) kOe per magnetic neighbor. Samples with 0.04?c<0.08 at 77 K have both magnetic phases present in varying proportions. The magnetic field at 298 K varies with aluminum content according to the 1/3-power law for the reduced sublattice magnetization. The asymmetric shape of the spectra for c?0.17 has been accounted for by a model based on the molecular field approximation with nearest neighbor superexchange interaction strength J_nn?15 K.     

Theory of the anisotropic magnetoresistance in copper

The motion of the guiding center of magnetic circulation generates a charge transport. The application of kinetic theory to the motion gives a modified Drude formula for the magnetoconductivity: σ=e²n_cτ/M^*, where M^? is the magnetotransport mass distinct from the cyclotron mass, n_c the density of the conduction electrons, and τ the relaxation time. The density n_c depends on the applied magnetic field direction relative to copper's face-centered-cubic lattice, when the Fermi surface of copper is nonspherical with necks. The anisotropic magnetoresistance of copper is calculated with the assumption of the necks representing by spheres of radius a centered at the eight singular points on the ideal Fermi surface. A good fit with experiments is obtained.     

Estimation of sound velocities from resonance measurements on tungsten carbide calibration spheres

Tungsten carbide spheres have been used as reference targets to calibrate echosounders. The target strength depends upon the longitudinal and transverse stress wave speeds, c₁ and c₂, in the sphere. These may be estimated from the resonance frequencies, which can be measured precisely given two or more resonances whose coupling characteristics are sufficiently different to provide well conditioned equations for these wave speeds. The resonance frequencies may be measured by sampling the echo amplitude or by spectrum analysis. The latter method is more accurate but requires more sophisticated equipment. The measurements have been corrected to remove the bias resulting from the finite bandwidth of the apparatus. Experimental results are given for 11 spheres 38·1 mm in diameter containing a nominal 6% of cobalt binder, procured in two batches from different production runs. Both stress wave speeds are significantly different between but not within the batches, and likewise the sphere density which indicates variation of the cobalt content. For a density of 14 900 kg m^?3 (6% cobalt) and at 11°C, c₁ and c₂ are estimated to be 6853 ± 19 and 4171 ± 7 m s^?1, respectively, within 95% confidence limits. Empirical equations are presented for the speeds as functions of density. The temperature coefficient of c₂ is estimated to be ?1·3 ± 0·6 m s^?1°C^?1. These results demonstrate the high accuracy of the resonance technique for estimating the stress wave speeds in spheres. The small differences observed between the spheres would have a negligible effect on the target strength at 38 kHz.     

Hole mobility in a homogeneous nucleotide chain

The conductivity of molecular DNA-based conductors has been calculated. Charge motion is described by quantum-mechanical equations, and macromolecular vibrations are described by classical equations of motion with dissipation and a source of temperature fluctuations. In a homogeneous sequence of G-C nucleotide pairs, the calculated hole mobility at T=300 K equals ≈2cm² V^?1 s^?1.     

The energy tensor of matter in the projectve theory of relativity

In the projective theory of relativity the 5-dimensional field equation \(_{\mu \nu } \) and the resulting equation of motion Tμυ_;μ = 0 are investigated. There Tμυ stands for the 5-dimensional tensor of macroscopic matter. The 4-dimensional field equations and equation of motion obtained by projection are a generalization of Einstein's theory of general relativity and Maxwell's electrodynamics, involving a scalar field φ.They contain a single constant φ₀.The weak field approximation is investigated for the case of an ideal fluid and leads to Newton's mechanics, including Newton's gravitational law, and to Maxwell's electrodynamics. For the constant φ₀ one obtains the approximate value φ₀c⁴/γ_N with Newton's gravitational constant γ_N.For homogeneous and isotropic cosmological models consisting of matter only the general solution for the radius K of curvature is given. This solution is independent of the equation of state of matter For a pure dust universe the general solution for the scalar field φ is given. For a closed universe a power law φ ?K^?1 is valid which leads to Mach's principle. The calculation of the age of a closed universe yields over 7×10⁹y,if one uses mean values of the present cosmological data.     

Manifestation of liquid-state and solid-state properties in electron relaxation of paramagnetic ions in solutions: Non-Markovian processes

The linewidth δH and the spin-spin relaxation time T ₂ for Gd³⁺, Mn²⁺, and Cr³⁺ ions in aqueous, water-glycerol, and water-poly(ethylene glycol) solutions at paramagnetic ion concentrations providing the dipole-dipole mechanism of spin relaxation are measured using two independent methods, namely, electron paramagnetic resonance (EPR) and nonresonance paramagnetic absorption in parallel fields. Analysis of the experimental results indicates a gradual crossover from pure liquid-state (diffusion) to quasi-solid-state (rigid lattice) spin relaxation. It is demonstrated that the limiting cases are adequately described by standard, universally accepted formulas for dipole-dipole interactions in the liquid-state (the correlation time of translational motion satisfies the condition τ _c ?τ₂) and solid-state (τ _c ?τ₂) approximations. A complete theoretical treatment of the experimental dependences (including the observed gradual crossover of spin relaxation) is performed in the framework of the non-Markovian theory of spin relaxation in disordered media, which is proposed by one of the authors. Within this approach, the collective memory effects for spin and molecular (lattice) variables are taken into account using the first-order and second-order memory functions for spin-spin and spin-lattice interactions. A correlation between the spin magnitude and the temperature-viscosity conditions corresponding to the crossover to non-Markovian relaxation is revealed, and the situations in which structural transformations occurring in the solutions favor the crossover to solid-state spin relaxation are analyzed.