Quantum Equilibrium Distributions of Displacements and Momenta of Particles in Molecules and Solids

The quantum equilibrium distribution, ?Qm, of an arbitrary number, m, of momentum or displacement components is determined for atoms that are part of a polyatomic molecule or a solid. This is shown to be a multidimensional Gaussian distribution. Two cases are considered: (1) the motion of the system as a whole is given, (2) it is in itself determined by the statistical equilibrium conditions. In the first case we obtain distributions for the vibrational momenta and displacements and in the second for the total momenta, including the momenta of vibrational, translational and rotational motions. The distributions for momenta and displacements of one particle and for the maximum number of linearly independent components of momenta and displacements of all particles of the system are considered as particular cases. It is shown that the averaging of any function, F_m, depending on an arbitrary number, m, of components of displacements or momenta of particles, over the canonical ensemble is reduced to the integration of this function weighted by ?Qm over all its arguments between infinite limits.     

Theory of Weak Modified Electron Acoustic Double Layers and Solitary Waves in Presence of Negative Ions

We have studied the analytic solutions for modified electron acoustic double layers and solitary waves in a four component plasma system viz. two electrons and two ions, one positive and the other negative. It has been shown that DL solution does not exist when the temperatures of the free and the trapped particles are considered to be same for all the free species. On the other hand, DL solutions are found to exist when the effects of the reflected electrons (hot) are considered. The velocity and thickness of the DL have been valculated.     

Study of the high pressure effect on nanoparticles GdVO4: Eu3+ optical properties

This study considers the effects of hydrostatic pressure on the line position and fluorescence lifetime τ for ⁵D₀ → ⁷F₂ transitions in GdVO₄: Eu³⁺ nanocrystals. The results indicate that the pressure induced the red shift toward longer wavelengths for all the considered lines with different rate. The fluorescence lifetime τ nonlinearly decreases with pressure in the considered pressure range. High pressure induced the fluorescence lifetime τ that can be explained with a simple theoretical model. The measured line position and τ are in a satisfactory agreement with the theoretical calculations.     

Superspinors and Graded Lorentz Groups in Three,Four and Five Dimensions

Three superalgebras osp(1; 2; F) (F = R, C, H) and corresponding three supergroups are considered. The transformation laws of spinors with anticommuting components for 3-dimensional (O(2, 1) ≃ Sp(2; R)), 4-dimensional (O(3, 1) ≃ Sp(2, C)) and 5-dimensional (O(4, 1) ≃ Sp(2; H)) Lorentz group are extended in a supersymmetric way by introducing nonlinear realizations of the supergroups OSp(1, 2; F). The affine Grassmann spinors in all three cases are obtained by suitable “flat” limit of the nonlinear realization. Different gradings and different contractions of osp(1,2; F) (F = R, C, H) superalgebras are considered.     

On the theory of pseudocontact N.M.R. shifts due to lanthanide complexes

The pseudocontact N.M.R. shifts due to complexes of lanthanide ions are considered in a crystal field theoretical framework including all the states J, M of an L-S manifold and an arbitrary set of crystal field parameters. Deviations from Bleaney's earlier theory are shown to be of the order of 20 per cent when the higher crystal field parameters are added.     

Moment inequalities for the boltzmann equation and applications to spatially homogeneous problems

Some inequalities for the Boltzmann collision integral are proved. These inequalities can be considered as a generalization of the well-known Povzner inequality. The inequalities are used to obtain estimates of moments of the solution to the spatially homogeneous Boltzmann equation for a wide class of intermolecular forces. We obtain simple necessary and sufficient conditions (on the potential) for the uniform boundedness of all moments. For potentials with compact support the following statement is proved: if all moments of the initial distribution function are bounded by the corresponding moments of the MaxwellianA exp(−Bv ²), then all moments of the solution are bounded by the corresponding moments of the other MaxwellianA ₁ exp[−B ₁(t)v ²] for anyt > 0; moreoverB(t) = const for hard spheres. An estimate for a collision frequency is also obtained.     

Letter: Anisotropic Born-Infeld Cosmologies

Anisotropic cosmological spacetimes are constructed from spherically symmetric solutions to Einstein's equations coupled to nonlinear electrodynamics and a positive cosmological constant. This is accomplished by finding solutions in which the roles of r and t are interchanged for all r > 0 (i.e. r becomes timelike and t becomes spacelike). Constant time hypersurfaces have topology R× S ² and in all the spacetimes considered the radius of the two sphere vanishes as t goes to zero. The scale factor of the other dimension diverges as t goes to zero in some solutions and vanishes (or goes to a constant) in other solutions. At late times local observers would see the universe to be homogeneous and isotropic.     

Accurate torsional potentials in conjugated systems: ab initio and density functional calculations on 1,3-butadiene and monohalogenated butadienes

Accurate calculations of the torsional potentials for rotation around the carbon–carbon single bond of all conceivable monohalogenated 1,3-butadienes C₄ H ₅X, (X?∈?[F, Cl, Br]), are presented. The parent compound, 1,3-butadiene, is also included as a benchmark and reference case. Large-scale ab initio calculations were performed at the second-order Møller–Plesset perturbation theory (MP2) and the coupled cluster, CCSD(T), levels. Additionally, density functional methods were applied. In all compounds considered, the anti- or s-trans-conformation is the most stable. For all three halogens, the 2-halo-1,3-butadiene is the most stable isomer, followed by the cis-1-halo-1,3-butadiene. Depending on the position and the type of halogen, the original 1,3-butadiene torsional potential is modified in a different manner. The modifications are particularly visible in the region of the syn- or s-cis and the gauche structures and in the barrier heights.     

Inhomogeneous Ballistic Aggregation

The one-dimensional ballistic aggregation process is considered when the initial mass density or the initial particle velocities vanish outside of a finite or semi-infinite interval. In all cases, we compute the mass distributions in closed analytical form and study their long time asymptotics. The relevant length scales are found different (of the order t, t ^2/3, t ^1/2) if, at the initial time, particles occupy a finite (or semi-infinite) interval and if a finite (or infinite) number of them are set into motion.     

On the Gravitational Collapse in Relativistic Theories of Gravitation

Following Einstein, we consider a simple model of a star, namely a spherically symmetric distribution of particles which are all moving along circular orbits around the center of the particle cluster. According to arguments given by Einstein, Laue, Treder and others, the existence of stationary circular motions for all values of r can be considered as a necessary condition for all collapse-free relativistic (classical) theory o gravitation. The discussion shows that, assuming the validity of the weak principle of equivalence and the principle of causality, one has to consider theories with a g₀₀-function different from the Einstein-Schwarzschild one. We discuss some g₀₀ types and show that our point of view leads in the direction of gravitational equations with a cut-off length.     

Photoionization of 3<Emphasis Type="Italic">d</Emphasis> electrons of Xe,Cs and Ba endohedral atoms: comparative analyses

We demonstrate rather interesting manifestations of co-existence of resonance features in characteristics of the photoionization of 3d-electrons in Xe, Cs and Ba endohedral atoms. It is shown that for all of the considered atoms the reflection by the fullerene shell of photoelectrons produced by the 3d subshell photoionization affects greatly partial photoionization cross-sections of 3d _5/2 and 3d _3/2 levels and respective angular anisotropy parameters, both dipole and non-dipole adding to all of them additional maximums and minimums. The results obtained demonstrate distinctive differences between the three atoms. The calculations are performed treating the 3/2 and 5/2 electrons as electrons of different kinds with their spins “up” and “down”. The effect of the C₆₀ shell is accounted for in the frame of the “orange” skin potential model. It is essential that in the considered photon frequency region the presented resonance features are not affected by the C₆₀polarization.      

A new perturbative approach to the classical anharmonic oscillator

The periodic motion of the classical anharmonic oscillator characterized by the potentialV(x)=1/2x ²+λ/2k x ^2k is considered. The period is first determined to all orders inλ in a perturbative series. Making use of this, the solution of the nonlinear equation of motion is then expressed in the form of a Fourier series. The Fourier coefficients are obtained by solving simple algebraic relations. Secular terms are inherently absent in this perturbative scheme. Explicit solution is presented for generalk up to the second order, from which the Duffing and the sextic oscillator results follow as special cases.     

On Schwarzschild black hole in large N matrix theory

D0-brane gas picture of Schwarzschild black hole (SBH) is considered in the large N regime of Matrix theory. An entropy formula, which reproduces the thermodynamics of SBH in the large 0N limit for all dimensions (D≥6), is proposed. The equations of states for supersymmetric Yang-Mills theory at low temperature are obtained. We also give a proof of the Newton gravitation law between two SBHs, whose masses are not equal.     

Charge overlap effects dependence on the nature of the interaction

The He-He, He-H(1s), H(1s)-H(1s) and H(1s)-H(2s) interactions are considered as model systems for studying how charge overlap effects in second-order dispersion energies vary as a function of the nature of the interacting species. The non-expanded second-order energy and the corresponding multipole R ^-1 expansions, through all powers of R ^-1, are obtained for each interaction using Unsöld's average energy approximation. The results are used to discuss the limitations of the usefulness of the R ^-1 expansions.     

The E687 cryptoexotic vector meson candidate

A new study of the dip observed at 1.9GeV by the Fermilab experiment E687 in diffractive photoproduction of 3π ⁺3π ^- is presented. The E687 and the BABAR data on the annihilation cross-section σ(e ⁺ e ^-→3π ⁺3π ^-), obtained with initial-state radiation, are fitted all together. The fit function is based on a simple mixing mechanism that explains the manifestation of a resonance as a dip. Possible interpretations in terms of hybrids and tetraquark states are considered.     

The fine structure levels and spin-singlet contributions to zero-field-splitting parameters of Cr2+ ion in CdGa2S4

A theoretical investigation is reported of the fine structure levels and the spin-singlet contributions to zero-field-splitting (ZFS) parameters for Cr²⁺ ion in CdGa₂S₄ crystals. Firstly, the complete energy matrix including all spin states for a 3d ⁴ ion in tetrahedral D _2d symmetry is constructed according the double-group chain in the strong-field scheme. Then, by diagonalizing the complete energy of electron–electron interactions, the crystal field and the spin–orbit coupling for the Cr²⁺ (3d ⁴) ion in CdGa₂S₄ crystal, the fine structure levels and the spin-singlet contributions to ZFS parameters a, D and F are calculated. The results show that the spin-singlet contribution to D is negligible, but the contributions to a and F are very important. So, to obtain more accurate ZFS parameters for 3d ⁴ ions in the tetrahedral crystals, all spin states should be considered.     

Lattice topological field theory in two dimensions

The lattice definition of a two-dimensional topological field theory (TFT) is given generically, and the exact solution is obtained explicitly. In particular, the set of all lattice topological field theories is shown to be in one-to-one correspondence with the set of all associative algebrasR, and the physical Hilbert space is identified with the centerZ(R) of the associative algebraR. Perturbations of TFT's are also considered in this approach, showing that the form of topological perturbations is automatically determined, and that all TFT's are obtained from one TFT by such perturbations. Several examples are presented, including twistedN=2 minimal topological matter and the case whereR is a group ring.     

Fundamental Units of Length and Time

Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime, at least in the non-quantum case. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.     

A search for excited fermions at HERA

A search for excited fermions f of the first generation in scattering at the collider HERA is presented using H1 data with an integrated luminosity of 37 pb. All electroweak decays of excited fermions, f f f W,f Z are considered and all possible final states resulting from the Z orW hadronic decays or decays into leptons of the first two generations are taken into account. No evidence for f production is found. Mass dependent exclusion limits on cross-sections and on the ratio of coupling constants to the compositeness scale are derived. Received: 19 July 2000 / Published online: 23 October 2000