Kinetics of small perturbations in an isotropic world

Long-wavelength gravitational perturbations are studied in an isotropic expanding universe filled with an ultrarelativistic gas. A kinetic study in the collisionless approximation shows that scalar and vector perturbations which appear at a time ₀ 1/n, where N is the wave vector and is the time coordinate x⁴, grow if the perturbation of the macroscopic momentum density of the gas at time ₀ is nonvanishing. The growth continues until the time ₁=27₀, at which the perturbation of the macroscopic momentum density of the gas vanishes. A solution is also derived for tensor perturbations in the limit n 1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 37–45, April, 1978.     

Determination of the Order Parameter in Binary Fluid Mixtures

We propose a microscopic approach to the study of phase transitions in fluid mixtures. It is based on the collective variables method with a reference system. The problem of definition of the order parameter in a two-component fluid system is considered in detail. This system is described with two sets of collective variables: _k and _k. It is shown that the CV connected with the order parameter is _k=0 in the case of a gas–liquid critical point as well as in the case of a mixing–demixing phase transition. The relations between the microscopic parameters, temperature, density and concentration which determine the particular form of ₀ for each of these phenomena are obtained. Based on these results we will be able to construct an effective Ginsburg–Landau–Wilson Hamiltonian.     

TDPAC studies of internal AgIn alloy oxidation

The internal oxidation of dilute AgIn alloys in open air versus In concentration and oxidation temperature was investigated by the TDPAC technique. The¹¹¹In interaction described by the broad quadrupole frequencies distribution aroundv _Q = 115 MHz and =0.5–0.7 was observed and interpreted as due to nonstoichiometric In–O_X cluster formation. For higher temperatures and more concentrated alloys additionally quasiunique frequencyv _Q 157 MHz with 0.28 was evidenced and ascribed to¹¹¹In interaction inside In₂O₃ precipitates. The internal oxidation under reduced oxygen pressures was studied and the thermal stability of the complex formed was tested. The effect of surface preparation on internal oxidation was observed.     

Intensity measurement for Kβ η satellites in the radiative auger effect

Calculations have been performed on the integral shapes of the K lines, which are long-wave satellites of the K ₁ lines, for Cl, Ti, and Fe, where allowance has been made for interference between states in the 2p^–1 and 3p^–2p configurations. The calculations show that these satellites represent short-wave branches of the K lines strengthened by the 3p-1s transition with simultaneous M electron ejection. The strong interference between the amplitudes of these processes in the final state means that it is in principle quite impossible to speak of the intensities of the K satellites without stating how they are isolated from the measured spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 34–39, September, 1984.     

Translational and rotational diffusion in supercooled orthoterphenyl close to the glass transition

Self diffusion coefficients in supercooled orthoterphenyl (OTP) have been determined down toD _t =3·10^–14 m²s^–1 using a¹H-NMR technique applying static field gradients up to 53T m^–1 In a range of more than two decades theD _t values agree with those of photochromic tracer molecules of the same size determined by forced Rayleigh scattering down to the glass transition temperatureT _g . A change of mechanism is found for translational diffusion atT _c 1.2T _g whereD _t is proportional to the inverse shear viscosity ^–1 atT>T _c butD _t with =0.75 atT<T _c . Rotational correlation times determined by²H-NMR stimulated echo techniques in deuterated OTP remain proportinal to ^–1 down toT _g . Our results are discussed in relation with mode coupling theory and with models of cooperative motion at the glass transition.     

Investigations of the excitation energy transport mechanism in donor-acceptor systems

Measurements of fluorescence quantum yield _D/_oD of Na-fluorescein (donor; D) versus concentration of rhodamine B (acceptor; A) in viscous solutions have been carried out. The donor concentration in these solutions was as follows:C _D=2·10^–2 M (system I), 1.5·10^–2 M (II), 10^–2 M (III), 3·10^–3 M (IV), and 5·10^–5 M (V). The experimental results have been compared with current theories of nonradiative electronic energy transfer (NEET). In the case of very strong migration (systems I, II, and III), a significant influence of correlations (between configurations of D and A molecules in the surroundings of successively excited donors) on quantum yield _D/_oD has been determined. Experimental values have been found to be clearly higher in comparison with those predicted theoretically. The influence of possible factors on the decrease in the effectiveness of excitation energy transport to traps-acceptors in systems of very strong migration has been discussed.Dedicated to Professor A. Kawski on the occasion of his 65th birthday.     

Gravity of Global U(1) Cosmic String

We show that a static one-dimensional U(1) global string is confined by its own gravitational field to a finite radius. The energy-momentum tensor of a global string decreases exponentially with the distance from its core. We call it self-localization. We show that the order parameter is a decreasing function of the symmetry breaking energy scale. We have found the maximum value of the energy scale _max, where the order parameter vanishes. Beyond the maximum value > _max the gravitational field of a global string gets so strong, that it restores the initial unbroken symmetry. In the close vicinity of the maximum value _max of the symmetry breaking scale we get a closed-form solution for the metric. It reduces to the Galileo metric on the axis and transforms into the Kasner-type solution near the boundary of a string.     

Electric quadrupole interaction at181Ta in RNi5 compounds

The time differential perturbed angular correlation measurements in PrNi₅, NdNi₅, GdNi₅, DyNi₅ and ErNi₅ rare-earth intermetallics with¹⁸¹Ta as probe nuclei have revealed that these impurity nuclei experience a non-axial electric quadrupole interaction. In all the cases, except in GdNi₅, the interaction frequency has a single value in the range 15–20 MHz with asymmetry parameter 0.98. In GdNi₅, however, there are two interaction frequencies (13.61 MHz and 26.89 MHz), the former being the dominant one (90%) with 0.35 and the latter (10%) with 0.98. It is concluded that in all cases the probe nuclei experiencing the highly asymmetric electric field gradient (efg) occupy the unique Ni(3g) site. Annealing studies have shown that in the case of GdNi₅ the interaction gets highly damped, while there is negligible effect in the other cases. The temperature variation of the efg in all cases seems to follow the empiricalT ^3/2 relation.     

Phase transitions in 2-dimensional systems of migrating orientable lattice defects

Phase transitions are studied in a system consisting of reorientating and migrating point defects in a two dimensional lattice. Due to the long range (r ^–2) nature of the dominant elastic interaction, surface effects are of central importance and have to be included. After diagonalizing the elastic interaction energy for defects characterized by arbitrary elastic dipole tensors the free energy of the system is minimized with respect to the tensor defect density (which describes the defect distribution in space and over a discrete number of orientations). Different types of phase transitions are obtained depending on the magnitude of the defect anisotropy. The phase below the paraelastic one is characterized for large by an anisotropic but homogeneous distribution, for small by an anisotropic and inhomogeneous distribution with a non linear space dependence. Similarities and differences with 3d results for=0 (or small) are discussed.     

On the possibilities to study the exotic state 1−+ in photoproduction of the πη, πη′ systems

We show that photoproduction experiments provide propitious conditions to study the exotic state 1^–+ in the and channels. For unpolarized photons contributions from natural and unnatural parity exchanges do not interfere with each other, a fact which permits to estimate the correctness of phase shift analyses. In photoproduction of the ⁺ system in the mass range ofa ₂(1320) a more stringent limit on the product (1^–+)Br(1^–+) can be obtained than in experiments on Primakoff production on nuclei. Particularly favourable is the study of the state 1^–+ in the coherent photoproduction of the ⁰ and ⁰ systems on nuclei, with significantly enlarged statistics and a simplified phase shift analysis.     

The influence of a surface on Ising and conjugate model spin correlations atT=T c

We calculate rigorously the two-point correlation function in the 2-d Ising model on a quasi-cylindrical lattice at the critical temperatureT _c .The scaling predictions for the surface critical exponents = 5/8, = 1 are confirmed and the change from surface to bulk behavior is studied. By a correspondence relation the results are mapped to the conjugate model, a subcase of the 8-vertex model. We find in this model = 5/4, = 2.     

Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities

The restricted eight-vertex solid-on-solid (SOS) model is an exactly solvable class of two-dimensional lattice models. To each sitei of the lattice there is associated an integer heightl _i restricted to the range 1l _i r–1. The Boltzmann weights of the model are expressed in terms of elliptic functions of period 2K, and involve a parameter. In an earlier paper we considered the case=K/r. Here we generalize those considerations to the case=sK/r, s an integer relatively prime tor. We are again led to generalizations of the Rogers-Ramanujan identities.     

Nuclear quadrupole interaction of199mHg-ferrocenethiol complexes

We determined the^199mHg nuclear quadrupole interaction (NQI) by time differential perturbed angular correlation in the following ferrocenethiol complexes with mercury: ferrocenethiol (v _Q =1253(4) MHz, =0); 1,1-ferrocenedithiol (47%v _Q =1555(8) MHz, =0.13(2); 25%v _Q =726(19) MHz, =0.81(2); rest unspecific); 2-ferrocenyl-ethanethiol (v _Q =1306(6) MHz, =0.17(1)); and a 1, 1-bis (2-mercapto-propylthio)ferrocene oligomer (v _Q =1411(5), =0). All NQIs are rather large with small asymmetry parameters, indicating essentially linear S-Hg-S bonds. The only exception is the minority fraction in 1,2-ferrocenedithiol which suggests the formation of a 1,3-dithia-2-mercura[3]ferrocenophane.     

Group velocity difference effect on incoherent sum-frequency generation spectrum

The spectral distribution of optical sum-frequency generation (SFG) by incoherent non-linear mixing of two chaotic beams with identical spectral width is calculated theoretically in the first approximation of the iterative method including dispersion of the non-linear medium and the difference between the group velocity of the input beams. It is shown that for the same group velocities (=0) of the input beams in non-linear medium the resultant field has a spectral width narrower than , and if a phase mismatch is present the spectral maximum of the resultant field is shifted towards lower or higher frequencies according to the sign of the phase mismatch. If the input beams have different group velocities (0) in the non-linear medium, then the spectral distribution of SFG is strongly dependent on . For small the spectral distribution of SFG is the same irrespective of . For large the difference in group velocities broadens the spectrum of SFG and for very large differences in group velocity the SFG has a spectral width identical to that of the input beams.     

Metastates in Disordered Mean-Field Models II: The Superstates

We continue to investigate the size dependence of disordered mean-field models with finite local spin space in more detail, illustrating the concept of superstates as recently proposed by Bovier and Gayrard. We discuss various notions of convergence for the behavior of the paths (t_[tN]()) _{t(0, 1]} in the thermodynamic limit N. Here _n () is the Gibbs measure in the finite volume {1,..., n} and is the disorder variable. In particular we prove refined convergence statements in our concrete examples, the Hopfield model with finitely many patterns (having continuous paths) and the Curie–Weiss random-field Ising model (having singular paths).     

NMR enhancement and NMR relaxation in a <110> FeSi Néel-type single crystal

⁵⁷Fe NMR measurements with a Néel-type single crystal are described. The behaviour of the magnetic structure was calculated as function of the internal fieldH _i. A clear distinction between wall and domain signals could be made. The corresponding relative enhancement factors _w ^r (H _i) and _D ^r (H _i) have been calculated and are in agreement with the measurements. The relaxation in the 90° Bloch walls is pure exponential. Both ratesT ₁ ^–1 andT ₂ ^–1 are proportional to _w ² (H _i). The measurements make proof, that the 90° walls are folded inside the crystal.K.-H. König and H. Brömer, Verhandl. DPG(VI)22, I, AM-14.11 (1987)     

Mössbauer spectroscopy study of new examples of highly delocalized,fully averaged mixed valence di-iron and iron-ruthenium compounds, [trans-μ-(pentalenyl)bis(pentamethylcyclopentadienyl iron]+BF 4 − and the related μ-symmetric-indacene system

We report that the (FeII, FeIII) versions of the title compounds as well as what is formally [Cp*FeII -pentalenyl RuIII Cp*]⁺BF ₄ ^– (Cp* = ⁵-C₅Me₅) appear to be fully averaged mixed valence binuclear species on a Mössbauer spectroscopy time scale (100 ns) to as low as 1.5 K. This indicates essentially zero energy barrier to intramolecular electron transfer. At the other extreme, [Cp*FII -asymmetric-indacene FeIII Cp*]⁺BF ₄ ^– exhibits trapped (discrete) FeII and FeIII valence states at ambient temperature.     

Levinson's Theorem for the Schrödinger Equation in One Dimension

Levinson's theorem for the one-dimensional Schrödinger equation with asymmetric potential which decays at infinity faster thanx ^–2 is established by theSturm-Liouville theorem. The critical case where the Schrödinger equation hasa finite zero-energy solution is also analyzed. It is demonstrated that the numberof bound states with even (odd) parityn ₊(n _–) is related to the phase shift ₊ (0)[_– (0)] of the scattering states with the same parity at zero momentum as ₊ (0)+ /2 =n ₊ and _– (0) =n _– for the noncritical case, and ₊ (0) =n ₊ and_– (0) – /2 =n _– for the critical case.     

Distribution of nuclear quadrupole splittings in amorphous materials and the topology of the (Vzz, η)-parameter space

In structural investigations of amorphous materials by determination of nuclear quadrupole splittings, the connectivity of the region of non-zero probability density in the space of the splitting parameters V_zz and is important. The conventional presentation of the parameter plane conceals the continuous connection between regions of positive and negative V_zz via the common boundary defined by =1. A new conceptual view of the (V_zz, )-plane is proposed which clearly expresses its topological structure.     

Radiative E1 decay of the1P1 level of charmonium in the sum rules of quantum chromodynamics

An analysis of the radiative decay¹P₁ ¹S₀ + of charmonium is performed by using the sum rules of quantum chromodynamics (QCD). A sum rule that allows for luon power corrections is obtained, and the decay width _c + is computed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 80–84, November, 1991.Finally, the author express thanks to professor R. N. Faustov for valuable advice and useful discussion of the resulting work.