Dynamical chaos in the highly excited states of a quantum Daffing oscillator in an external harmonic field

The energy spectrum of the highly excited states of a quantum Daffing oscillator is considered. It is shown that the energy levels satisfy E_n>E_n+1 and E_n -F²/8², when n , where F² and are the intensity and frequency of the external field. It is suggested that this property of the spectrum is the quantum manifestation of a stochastic attractor in the classical nonlinear limit. This property also takes place for large F².Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 90–94, March. 1993.     

On kaonic deuterium. Quantum field-theoretic and relativistic covariant approach

We study kaonic deuterium, the bound K^-d state A_{K d}. Within a quantum field-theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K^-d scattering for arbitrary relative momenta. Near threshold our formula reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering near threshold is defined by the resonances (1405), (1750) and a smooth elastic background, and the inelastic channels K^-d NY and K^-d NY, where Y = ^±,^{0} and ^{0}, where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K^-d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays A_Kd NY and experimental data on the rates of the NY pair production in the reactions K^-d NY. We obtain _{1s} = (630±100)eV. For the shift of the energy level of the ground state of kaonic deuterium we predict _{1s} = (325±60)eV.     

Studies on the microstructure of phase transitions in two kinds of liquid crystals by PAT and DSC

The positron lifetime and DSC measerments for EBBA and DOBAMBC have been made with heating and cooling clycles. The experimental results show that a shorter lifetime (₁) is essentially independent of temperature while the longer lifetime (₂) and the intensity (I ₂) change abruptly double or triple with temperature. Consequently, the EBBA has only nematic phases while the DOBAMBC has two liquid-crystalline phases (smectic C* and smectic A) with transition temperatures as follows: for EBBA, solid nematic (304.5 K), nematic isotropic (356.5 K), isotropic nematic (356.5 K), nematic solid (301 K); and for DOBAMBC, solid smectic C* (346 K), smectic C* smectic A (357.5 K), smectic A isotropic (389 K). These critical temperatures are in accordance with the transition temperatures measured by DSC. In addition, the difference in the solid-nematic transition temperature in the heating and cooling cycles was also observed. A discussion about the correlation of the observed changes in lifetime (₂) with the changes in molecular orientational order (S) and dielectric anisotropy () is presented.     

Radiative Decay of Vector Meson V → Pγ in the Spinor Strong Interaction Theory

The spinor strong interaction theory recentlydeveloped is applied to the radiative decay of atwo-quark vector meson into pseudoscalar meson V P. Expression of the decay rate isderived in this first-principle theory without assumptionand free parameter. The ratio (D^*0 D⁰)/(D^*+ D⁺) is correctly predicted. Theorders of magnitude of the radiative decay rates of B*,D*, K*, and estimated from this expression areconsistent with data. Very fast mesons have a smallersize then do mesons at rest, similar to Lorentzcontraction in laboratory space.     

Energy spectrum and angular distribution of muons from the decay of heavy leptons produced in colliding electron-positron beams

On the basis of an arbitrary (V, A) structure of the neutral weak ¯ee and LL currents (L=^–, M⁰) a study is made of the processes of production in colliding electron-positron beams of pairs of heavy leptons with subsequent decays in accordance with the schemes e⁺e^––(µ^–v_µv) + ⁺( anything) and e⁺e^–M⁰(µ^–e⁺v_e) + M⁰( anything). The energy spectrum and asymmetry of the distribution of the produced muons are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1981.     

Comparison of (π− d→nn withdσ(π+ d→pp) to test charge symmetry in the Δ-region

First results on ^– d are reported. The measurements were made using 8 specially designed neutron counters, which were carefully calibratedin situ. The differential cross sections atT =142, 180, 217, and 254 MeV were obtained at four angles between 0° and 90°, they are compared to ⁺ d pp data measured at the same energies and angles with the same setup. At every beam energy, the shape of the angular distributions of ^– d nn and ⁺ d pp is the same to ±2%. The absolute cross sections differ by 1 to 10%. The error in this comparison is ±4% implying a small violation of charge symmetry.Dedicated to Prof. I. laus on the occasion of his 60th birthdayDeceased     

Phase Transformations α → β → γ → δ → ε in Titanium Hydride TiH x with Increase in Hydrogen Concentration

Structural phase transformations of the hcp bcc fct fcc fct ( ) type in titanium hydrides TiH _x experimentally found to occur with increase in the hydrogen concentration x are studied theoretically. Free energy phases are statistically calculated, and their concentration dependence is determined. Phase transformation temperatures are found from intersection points of free energy curves and from points of common tangents to the curves. The energy parameters of the system are estimated. The calculation results are compared with the experimental data.     

Particle polarizations in decays of5HeΛ and4HΛhypernuclei

Nucleon polarizations are examined in the hypernucleus decays⁵He, ⁴He + p + _–,⁴H, ³H + p + _–, and⁴H, ³He + n + _–. The effect of the strong interaction in the final state is taken into account. A significant role is predicted for the resonance interaction in the p-⁴He system in the formation of the proton polarization in the⁵He decay. It is also shown that in the⁴H, ³H + p + _– decay the proton-polarization components should attain significant magnitudes, while in the charge-exchange decay⁴H, ³He + n + _–, the neutron polarization is expected to be not too large.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 100–103, October, 1988.     

Resonance interaction of antineutrinos with electrons

Expressions are given for the cross sections of the processes v_ee v and v_ee v _e ^' e' from the viewpoint of the hypothesis of weak interactions via intermediary vector mesons taking separate account of the polarizations of the electron target and the muon (electron) emission. An analysis is given of the cross sections of processes which are admissible according to both the two- and four-component theories of the neutrino. The degree of longitudinal polarization of meson emission is also determined for the interaction of incident antineutrinos (neutrinos) with a polarized target in the processes ve v, ve⁺ v⁺.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 48–53, June, 1971.The author is grateful to B. K. Kerimov for his useful advice which stimulated the appearance of this work and also to Yu. M. Kasumov for his constant assistance with the work.     

QCD sum rule analysis of the coupling constant g ωσγ

We employ QCD sum rules to calculate the coupling constant g by studying the three point -correlation function. Our result complements the analysis of this coupling constant utilizing the experimental value of the ⁰⁰ decay rate studied within the framework of chiral perturbation theory including vector meson and meson intermediate states.     

The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

Rate equations in the hopping transport

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

Measurement of the reaction γp → K0Σat photon energies up to 2.6 GeV⋆

The reaction p K⁰⁺ was measured in the photon energy range from threshold up to 2.6 GeV with the SAPHIR detector at the electron stretcher facility, ELSA, in Bonn. Results are presented on the reaction cross-section and the polarization of the ⁺ as a function of the kaon production angle in the centre-of-mass system, cos^c.m._K, and the photon energy. The cross-section is lower and varies less with photon energy and kaon production angle than that of p K⁺⁰. The ⁺ is polarized predominantly at cos^c.m._K 0. The data presented here are more precise than previous ones obtained with SAPHIR and extend the photon energy range to higher values. They are compared to isobar model calculations.     

Phase diagram and scattering intensity of binary amphiphilic systems

A Ginzburg-Landau model with a scalar and a vector order parameter, which describe the concentration and orientation of the amphiphile, respectively, is used to study the phase diagram and the scattering intensity of binary amphiphilic systems. With increasing amphiphile concentration, the calculated phase diagram shows the typical sequence of ordered phases observed experimentally, that is micellar liquid cubic micellar hexagonal lamellar cubic bicontinuous invers hexagonal. The scattering intensity in the homogeneous phase is calculated in the oneloop approximation. In the vicinity of a phase transition to an ordered phase, the intensity is found to show a 1/q behavior for not too small wave vectorsq, followed by a small peak, and a 1/q ² decay for large wave vectors, in agreement with experimental observations in theL ₃-(or sponge-)phase.Dedicated to Prof. H. Wagner on the occasion of his 60th birthday     

Structural Transformations in a Bi2O3 Crystal and in Bi2O3‐Based Solid Solutions in the Temperature Interval 25–750°C

The Raman scattering spectra of isostructural Bi₂O₃ and Bi_1.8Tm_0.2O₃ in the course of heating have been investigated. It is shown that the sequences of structural changes with increase in temperature differ: and ^* , respectively. In the hightemperature region, the structure takes the form of a disordered cube irrespective of the previous history of specimens.     

Appearance of P-odd nuclear forces in photoproduction of pions on6Li

P-odd effects in the photoproduction of pions on⁶Li nuclei, +⁶Li ⁺ +⁶He, are studied. Collisions of linearly and circularly polarized photons with a polarized nuclear target are studied, and in addition both vectorial and tensorial polarization are taken into account. It is shown that in the general case P-odd effects in +⁶Li ⁺ +⁶He are characterized by 18 real structure functions, which determine different P-odd asymmetries in the angular distribution of the pions. The structure functions in their turn depend on different products of three p-even and three p-odd amplitudes of the process +⁶Li ⁺ +⁶He. The P-odd effects at the threshold of the reaction +⁶Li ⁺+⁶He are analyzed. Using available experimental data on the behavior of the cross section of the reaction +⁶Li ⁺ +⁶He at threshold, the ⁶Li⁶He strong-interaction constant is evaluated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 78–82 July 1985.     

A derivation of the Broadwell equation

We consider a stochastic system of particles in a two dimensional lattice and prove that, under a suitable limit (i.e.N, 0,N²const, whereN is the number of particles and is the mesh of the lattice) the one-particle distribution function converges to a solution of the two-dimensional Broadwell equation for all times for which the solution (of this equation) exists. Propagation of chaos is also proven.Research partially supported by CNR-PS-MMAIT     

Study of the πn → π<Superscript>{-}</Superscript>π<Superscript>{-}</Superscript>p reaction at 430 MeV energy

The total cross-section for the ^{-}n ^{-}{-}p reaction has been measured at a pion kinetic energy of 430MeV in a deuterium bubble chamber. The cross-section value was found to be 0.197±0.016mb that is much smaller than the predictions of the chiral perturbation theory. The differential spectra are compared with calculations made in the framework of the model of Bolokhov et al. 13.60.LeMeson production [:AND:]13.85.LgTotal cross-sections     

π0 → γγ in the Spinor Strong Interaction Theory

An expression for the decay rate (⁰ ) has been derived in the frameworkof the spinor strong interaction theory, a first-principles strong interaction theoryproposed some years ago as an alternative to low-energy QCD. The startingpoint is the SO(3) gauge-invariant action for two quark mesons which has beensuccessful in accounting for confinement, ^{+ +} , e⁺, and ⁰ e⁺, nonexistenceof the Higgs boson, and other low-energy mesonic phenomena. The quasi-four-quarkmeson equations developed for the decay of a vector meson into twopseudoscalar mesons V PP has been taken over here to apply to P(⁰) VV(^{+ –}) (plus ⁺ and ^– which annihilate each other). This mechanismin principle agrees with that of the assumption of vector meson dominance inthe literature. It, together with the effect of form factors, arises naturally in theformalism and need not be assumed. Equations for the perturbed vector mesonwave functions cannot be simply solved and an assumption has been made toobtain an estimate of their magnitude. Together with a constant associated withthe strong coupling obtained earlier from V() PP(K⁺K^–), the estimated decayrate is 19.2 eV, in order-of-magnitude agreement with data (7.74 eV).     

The Micro-Canonical Point Vortex Ensemble: Beyond Equivalence

The fluid limit N is constructed for a sequence of ensembles of N classical point vortices in a finite domain ² whose ensemble densities (w.r.t. Liouville measure) are Gaussian approximations to (E-H). Letting the variance 0 after N has been taken, one recovers the special class of nonlinear stationary Euler flows that is expected from the micro-canonical ensemble. The construction improves over previous ones which either had to regularize the logarithmic singularities of the point vortex Hamiltonian or had to assume equivalence of ensembles. In particular, nonequivalence between micro-canonical and canonical ensemble prevails for certain geometries where conditionally stable configurations with negative 'global vortex pair-specific heat' can and do exist in the micro-canonical but not in the canonical ensemble.