abstract

We investigate dynamics of overlapping vortices in the nonlinear Schrö- dinger equation, the nonlinear heat equation and in the equation with an intermediate Schrödinger-diffusion dynamics. Because of formal similarity on a perturbative level we discuss also the nonlinear wave equation (Goldstone model). Special solutions are found like vortex helices, double-helices and braids, breather states and vortex mouths. A pair of vortices in the Goldstone model scatters by the right angle in the head-on collision. It is found that in a dissipative system there is a characteristic length scale above which vortices can be entangled but below which the entanglement is unstable.

abstract

Relation between the Dirac problem and the Weyl–Wigner–Moyal formalism is considered. The Moyal \(^*(g)\)-product and the generalized Moyal bracket are defined and analysed. It is shown that the first heavenly equation appears to be the \(\hbar \to 0\) limit of the SDYM equations for the Moyal algebra.

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The equation of motion of a point-like test body is derived from the field equations of Projective Unified Field Theory. We studied this equation of motion with respect to a potential violation of the equivalence principle. The Newtonian and the post-Newtonian approximations of the field equations and of the equation of motion of a test body are studied in detail. In analyzing some experimental data we performed some numeric estimates of the ratio of the inertial mass to the scalaric mass of matter.

abstract

Approximate regularized expectation values of the field fluctuation \(\langle \phi ^2 \rangle _{reg}\) and the stress-energy tensor \(\langle T^{\mu }_{\nu } \rangle _{reg}\) of the massless, conformally invariant, scalar field in the Boulware vacuum state in Schwarzschild spacetime are constructed by means of Hadamard regularization. It is shown that reconstruction of the characteristics of the vacuum polarization from its asymptotic behaviour leads to formulas that satisfactorily reproduce existing approximate expressions and closely follow exact numerical calculations.

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The diffusion of a particle in a linear array of \(N\) fluctuating barriers was investigated. The barriers are characterized by two parameters: \(\alpha _0\) - the probability to be closed, and \(\lambda \) - frequency of fluctuations between closed and open state. The rigorous analytical results for limit cases \(\lambda = 0\), \(\alpha _0 = 0\) and \(\lambda = 0\), \(\alpha _0 = 1\) were obtained. The phenomenon of stochastic resonance in the case of a particle moving with velocity \(\pm \upsilon \) and the process of switching between opposite velocities being a random telegraph process was investigated by numerical simulations.

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The continuous analogy to the spacing is introduced: the first derivative of energy with respect to its continuous labelling index and its distribution is calculated. As an example of application the Schrödinger particle with a random effective mass is investigated. The notion of quantum chaos and quantum integrability in continuous spectrum is widely discussed.

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The MST algorithm is applied to calculate generalized dimensions and singularity spectra of attractors of the Bloch magnetic domain wall a spatially extended nonlinear dynamical system. It is shown that the states of the Bloch wall are multifractal and that the time delay coordinate reconstruction enables access to the local multifractal properties of the system. Depending on the size of the system, for some states of the wall, the multifractal properties are uniform throughout the wall. For others, the multifractal properties are different at different points in the wall. In particular, the spatial distribution of the correlation dimension found earlier by means of the Grassberger–Proccacia algorithm is repeated in the spatial distribution of the generalised dimensions.

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Relativistic N-particle exactly integrable system with oscillator-like interactions in the two-dimensional space-time is considered within the framework of the front form of dynamics. Using the Weyl quantization rule we obtain eigenstates and eigenvalues of the mass-squared operator.

abstract

The well known domain wall type solutions are nowadays of great physical interest in classical field theory. These solutions can mostly be found only approximately. Recently the Hilbert–Chapman–Enskog method was successfully applied to obtain this type solutions in \(\phi ^4\) theory. The goal of the present paper is to verify these perturbative results by numerical computations.

abstract

The experimental detection of the sharp lines of the \((e^+e^-)\) Puzzle is viewed as a struggle against Doppler broadening. Gedanken experiments which are realistic in zeroth order of detail are analyzed to show that the ORANGE and EPOS/I geometries select narrower slices of a Doppler broadened line than spherically inclusive (APEX and EPOS/II-like) apparati. Roughly speaking, the latter require event-by-event Doppler reconstruction simply to regain an even footing with the former. This suggests that APEX’ or EPOS/II’s coincident pair distributions must be statistically superior to those of EPOS/I or ORANGE in order to support a comparable inference about sharp structure. Under such circumstances, independent alternative data is invaluable. Therefore, a corroboration of Sakai’s 330.1 keV (< 3 keV wide) electron line in few MeV \(e^+\) or \(e^-\) bombardments of U and Th targets could prove crucial.

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We show that the gauged SU(3) Wess–Zumino–Witten model can be classified into several classes by its target space metrics. This fact implies the appearance of target space transition and two target space dualities. We also consider the gauged SU(2,1) Wess–Zumino–Witten model as an analogy of SL(2,R) black hole. We show also that these Wess–Zumino–Witten models are connected continuously.

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We show how quantum dynamics can be introduced into the “texture” of fundamental-fermion mass matrices by means of annihilation and creation operators acting in the space of three families. Then, at least one texture zero appears in a natural way. A model of such a texture dynamics is described for charged leptons, predicting \(m_{\tau } = 1776.80\) MeV from experimental values of \(m_e\) and \(m_{\mu }\). The model is reasonably extended to quarks in a straightforward way.

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A nonlinear transformation in the momentum space is constructed which converts the deformed action of Lorentz and Weyl generators on momenta into the standard one.

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The bicovariant differential calculus on three-dimensional \(\kappa \)-Poincaré group and the corresponding Lie algebra structure are described. The equivalence of this Lie algebra structure and the three-dimensional \(\kappa \)-Poincaré algebra is proved.

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We measure the masses of \({\mit \Lambda }^0\) and \(\overline {{\mit \Lambda }^0}\) hyperons using a very clean sample of 30844 hyperons produced in 230 GeV/\(c\) \(\pi ^-\)-Cu interactions and decaying in a silicon vertex detector. Systematic errors were estimated by using \(K^0_s\) decays registered in the same vertex detector. For the average \({\mit \Lambda }^0/\overline {{\mit \Lambda }^0}\) mass we obtain \((1115.766 \pm 0.006 \pm 0.042)\) MeV/\(c^2\). The mass difference \(M_{\mit \Lambda }\)–\(M_{\overline {\mit \Lambda }} = (0.015 \pm 0.013)\) MeV/\(c^2\) averaged with the E766 result of \((-0.012 \pm 0.010)\) MeV/\(c^2\) yields \((-0.002 \pm 0.008)\) MeV/\(c^2\). This confirms the CPT invariance within the accuracy of \(7 \times 10^{-6}\).

abstract

A discussion is continued on the author’s recent conjecture that the overall particle number, when it changes in a localized physical process, induces in its proximity a tiny deformation of the time run. In some cases, the corresponding weak time-deformation field can be emitted and also detected by matter sources. Sometimes, it can propagate freely through the spacetime as ultraluminal waves. Though these hypothetic waves cannot transport energy between matter sources, they can do it with a new thermodynamic-type quantity called here the energy width. This causes the quantum time evolution of matter sources to deviate slightly from the conventional unitary evolution.

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The infinitesimal action of \(\kappa \)-Poincaré group on \(\kappa \)-Minkowski space is computed both for generators of \(\kappa \)-Poincaré algebra and those of Woronowicz generalized Lie algebra. The notion of invariant operators is introduced and generalized Klein–Gordon equation is written out.

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The multiparton density matrices of the QCD gluon cascade are investigated. The generating functional and master equation for momentum space multiparton density in the double logarithmic approximation (DLA) are proposed.

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We have calculated the relativistic corrections for the mass and potential energy to one-nucleon levels. We have found new depths of Woods–Saxon potentials for the nuclei in the region \(15 \leq A \leq 209\). The semirelativistic equation has been reduced to the integral-differential equation with the kernel, which is proportional to the Green’s function. It can be expressed by unperturbed wave functions and nonphysical solutions of the Schrödinger equation. It has been shown that for an average field of the nuclei this approach is sufficiently exact. The corrections for mass are comparable with the energies of excited states and they are increasing the binding energies. The corrections to potential are positive and small, except for some light nuclei, where they can compensate the negative corrections for mass.

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Differential cross section of the double charge exchange (DCX) reaction \(^{56}\)Fe\((\pi ^+,\pi ^-)^{56}\)Ni at the pion energies 10 and 60 MeV is calculated in the proton–neutron quasiparticle random phase approximation using a realistic nucleon–nucleon interaction. A detailed structure of the transition amplitude through intermediate states is discussed in some extent. It is shown that the observed resonance-like behaviour can be explained at least semi-quantitatively in terms of an ordinary NN process due to all over increase of the transition amplitudes with pion energy for each \(J^{\pi }\)-multipolarity. The pn-QRPA seems to be a good framework for a description of structure of nuclei involved in double charge exchange processes.

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In the present work, we test the validity of replacing the nondiagonal densities \(\rho \vec r,\vec r^{\,\prime }\) appearing in the exchange part of the nucleus–nucleus optical potential by an approximation based on the density matrix expansion (DME) used frequently in nuclear structure calculations. This procedure has been used recently by many authors in driving the real nucleus–nucleus potential. We have found that for M3Y-Paris nucleon–nucleon interaction the use of DME may produce a maximum error of 12% in the nucleus–nucleus potential.

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The permanent magnetization of the proton crystal immersed in the neutron background inside the neutron star core is studied. The magnetization is produced by the ferromagnetic ordering of spins of protons localized at the lattice sites. We calculate the magnetization of the crystal in a simple model based on the Skyrme forces in which we use variational wave functions for localized protons and Bloch neutrons in the Hartree–Fock approximation. The induced spin excess of the neutron Fermi sea is found and its contribution to the magnetization is included.

abstract

Two models were applied to reproduce the experimentally obtained charge distribution for \(^{40}\)Ar \(+ ^{159}\)Tb system at 9.5 MeV/nucleon. They are based on either random walk phenomena or on one body dissipative processes. The charge numbers of measured outgoing fragments were in the range of \(Z = 7\)–20. The model taking into account the differences in the density of final states of the heavier and lighter ions appeared to be suitable for the description of peripheral collisions. The drift of the mass and charge is expected towards asymmetric division, producing in the exit channel the projectile-like fragments lighter than the projectile. In order to compare the model calculations with experimental data the statistical deexcitation of the primary hot fragments has been taken into account. The successful description of the data by the proposed model supplemented by statistical evaporation illustrates the great importance of the phase space factors for directing the mass and charge flow in peripheral and damped heavy ion collisions.

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Using the backpropagation algorithm, we have trained the feed forward neural network to pronounce Polish language, more precisely to translate Polish text into its phonematic counterpart. Depending on the input coding and network architecture, 88%–95% translation efficiency was achieved.

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Results of teaching procedures for neural network for two different algorithms are presented. The first one is based on the well known backpropagation technique, the second is an adopted version of the Monte Carlo global minimum seeking method. Combination of these two, different in nature, approaches provides promising results.