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The radiation from oscillating kink in (1+1) dimensional relativistic \(\phi ^4\) model is considered. Both analytical and numerical approaches are presented and the comparison between these methods is discussed. Acceleration of the kink in external radiation is calculated and numerical results are also presented.

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We calculate the distribution of the \(k\)-th largest eigenvalue in the random matrix Lévi–Smirnov Ensemble (LSE), using the spectral dualism between LSE and chiral Gaussian Unitary Ensemble (GUE). Then we reconstruct universal spectral oscillations and we investigate an asymptotic behavior of the spectral distribution.

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A method of fundamental solutions has been used to study adiabatic transition amplitudes in two energy level systems for a class of Hamiltonians allowing some simplifications of Stokes graphs corresponding to such transitions. It has been shown that for simplest such cases the amplitudes take the Nikitin–Umanskii form but for more complicated ones they are formed by a sum of terms strictly related to a structure of Stokes graph corresponding to such cases. These results are in a full agreement with the ones of Joye, Mileti and Pfister [Phys. Rev. A44, 4280 (1991)] found by other method.

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We extend results of the recent paper by Kobayashi and Shimbori [Phys. Rev. A65, 042108 (2002)] to a large class of noncentral potentials. Namely, we have shown that zero-energy states of the central potentials considered by these Authors [\(V_{a}(\rho )=-a^{2}g_{a}\rho ^{2(a-1)}\) with \(\rho =\sqrt {x^{2}+y^{2}}\) and \(a\neq 0\)] and noncentral potentials discussed here, have both common set of solutions given by wave functions of the parabolic potential barrier (PPB). Moreover, it is observed that first few members of the infinite set of functions cancel the quantum correction to the classical Hamilton–Jacobi equation. The exact classical limit of quantum mechanics is thus precisely reached for them with no approximation involved.

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It is postulated in general relativity that the matter energy-momentum tensor vanishes if and only if all the matter fields vanish. In classical Lagrangian field theory the energy and momentum density are described by the variational (symmetric) energy-momentum tensor (named the stress tensor) and a priori it might occur that for some systems the tensor is identically to zero for all field configurations whereas evolution of the system is subject to deterministic Lagrange equations of motion. Such a system would not generate its own gravitational field. To check if these systems can exist in the framework of classical field theory we find a relationship between the stress tensor and the Euler operator (i.e.  the Lagrange field equations). We prove that if a system of interacting scalar fields (the number of fields cannot exceed the spacetime dimension \(d\)) or a single vector field (in spacetimes with \(d\) even) has the stress tensor such that its divergence is identically zero (i.e.  “on and off shell”), then the Lagrange equations of motion hold identically too. These systems have then no propagation equations at all and should be regarded as unphysical. Thus nontrivial field equations require the stress tensor be nontrivial too. This relationship between vanishing (of divergence) of the stress tensor and of the Euler operator breaks down if the number of fields is greater than \(d\). We show on concrete examples that a system of \(n\gt d\) interacting scalars or two interacting vector fields can have the stress tensor equal identically to zero while their propagation equations are nontrivial. This means that non-self-gravitating (and yet detectable) field systems are in principle admissible. Their equations of motion are, however, in some sense degenerate. We also show, that for a system of arbitrary number of interacting scalar fields or for a single vector field (in some specific spacetimes in the latter case), if the stress tensor is not identically zero, then it cannot vanish for all solutions. There do exist solutions with nonzero energy density and the system back-reacts on the spacetime.

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We investigate the interaction of the gravitational field with a quantum particle. We derive the wave equation in the curved Galilean space-time from the very broad Quantum Mechanical assumptions and from covariance under the Milne group. The inertial and gravitational masses are equal in that equation. So, we give the proof of the equality for the non-relativistic quantum particle, without applying the equivalence principle to the Schrödinger equation and without imposing any relation to the classical equations of motion. This result constitutes a substantial strengthening of the previous result obtained by Herdegen and the author.

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Recently we have described a mechanical system which exhibits spontaneous breaking of \(Z_2\) symmetry and related topological kinks called compactons. The corresponding field potential is not differentiable at its global minima. Therefore, standard derivation of dispersion relation \(\omega (k)\) for small perturbations around the ground state can not be applied. In the present paper we obtain the dispersion relation. It turns out that evolution equation remains nonlinear even for arbitrarily small perturbations. The shape of the resulting running wave is piecewise combined from \(\pm \cosh \) functions. We also analyze dynamics of the symmetry breaking transition. It turns out that the number of produced compacton–anticompacton pairs strongly depends on the form of initial perturbation of the unstable former ground state.

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Presently the best terrestrial limit on light neutrino masses (\(m\!\lt \! 2.2\) eV) are given by the tritium beta decay experiments. Not maximal mixing of solar neutrinos following from the SNO and KamLAND together with neutrinoless double beta decay (\((\beta \beta )_{0\nu }\)) data open the chance for better determination of the lightest of Majorana neutrino mass. We combine all available fits for the solar neutrino parameters and collect all Nuclear Matrix Elements (NME) calculations for the \(^{76}\)Ge, nucleus for which presently the most stringent limit on the \((\beta \beta )_{0\nu }\) decay half-life time exist. We have shown that for some NME smaller bound on \((m_{\nu })_{\rm min}\) can be found. Unfortunately one order of magnitude discrepancies in NME calculations do not allow to give the final answer.

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We have compared polarized parton densities determined in the NLO QCD fits to polarized structure functions and spin asymmetries. We consider models of such distributions based on MRST 99 and MRST 2001 fits to non-polarized data. Simple power law corrections corresponding to higher twists are taken into account and their importance is analyzed. The role of positivity conditions for parton densities and their influence on the values of \(\chi ^2\) is discussed.

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The \(2\rightarrow n\) scattering with final particles at rest is discussed. The comparison with purely soft processes allows to identify symmetries responsible for vanishing of certain \(2\rightarrow n\) amplitudes. Some examples are given.

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An explicit mass formula for up and down quarks of three generations is proposed. Its structure contains an additional term in comparison to the efficient mass formula for charged leptons found out some time ago. The additional term is conjectured to be proportional to \((3B + Q^{(u,d)})^2 = 25/9\) or 4/9, where \(B = 1/3\) and \(Q^{(u,d)} = 2/3\) or \(-1/3\) are the baryon number and electric charge of quarks. It is interesting to observe that the analogical term for charged leptons proportional to \((L + Q^{(e)})^2\), where \(L = 1\) and \(Q^{(e)} = -1\), would vanish consistently (here, \(F = 3B+L\) is the fermion number). Under this conjecture, the mass formula predicts one quark mass, e.g. \(m_b\), in accordance with its experimental estimate, if the experimental estimations of five other quark masses are used as an input to determine five free parameters involved.

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It is shown that the method of eliminating the statistical fluctuations from event-by-event analysis proposed recently by Fu and Liu can be rewritten in a compact form involving the generalized factorial moments.

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We study the differential branching ratio, forward–backward asymmetry, CP violating asymmetry, CP violating asymmetry in the forward–backward asymmetry and polarization asymmetries of the final lepton in the \(B \to X_d l^+l^-\) decays in the context of a CP softly broken two Higgs doublet model. We analyze the dependencies of these observables on the model parameters by paying a special attention to the effects of neutral Higgs boson (NHB) exchanges and possible CP violating effects. We find that NHB effects are quite significant for the \(\tau \) mode. The above-mentioned observables seems to be promising as a testing ground for new physics beyond the SM, especially for the existence of the CP violating phase in the theory.

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The method of truncated Mellin moments in a solving QCD evolution equations of the nonsinglet structure functions \(F_2^{\rm NS}(x,Q^2)\) and \(g_1^{\rm NS}(x,Q^2)\) is presented. All calculations are performed within double logarithmic \(\ln ^2x\) approximation. An equation for truncated moments which incorporates \(\ln ^2x\) effects is formulated and solved for the unintegrated structure function \(f^{~\rm NS}(x,Q^2)\). The contribution to the Bjorken sum rule coming from the region of very small \(x\) is quantified. Further possible improvement of this approach is also discussed.

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Accuracy of a relativistic weak-coupling expansion procedure for solving the Hamiltonian bound-state eigenvalue problem in theories with asymptotic freedom is measured using a well-known matrix model. The model is exactly soluble and simple enough to study the method up to sixth order in the expansion. The procedure is found in this case to match the precision of the best available benchmark method of the altered Wegner flow equation, reaching the accuracy of a few percent.

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We present the exact and precise (\(\sim \)0.1%) numerical solution of the QCD evolution equations for the parton distributions in a wide range of \(Q\) and \(x\) using Monte Carlo (MC) method, which relies on the so-called Markovian algorithm. We point out certain advantages of such a method with respect to the existing non-MC methods. We also formulate a challenge of constructing non-Markovian MC algorithm for the evolution equations for the initial state QCD radiation with tagging the type and \(x\) of the exiting parton. This seems to be within the reach of the presently available computer CPUs and the sophistication of the MC techniques.

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In previous papers the relativistic corrections for the mass and potential energy to one-nucleon levels and the significant terms of the relativistic corrections for the mass of nucleons were obtained. In this paper the mathematical problems of semi-relativistic model are considered. The semi-relativistic single-particle equation is a differential equation of the fourth-order and it can be reduced to the integral–differential equations. The general solution of this equation must be expressed by the superposition of the four linearly independent solutions. Developing the modified method of Lagrange’s and the multiplicative perturbation theory we obtained the integral–differential equations for the wave functions with usual asymptotic at the origin \(r^{L+1}\) and unusual \(r^{L+3}\), \(r^{-L+2}\). The wave functions with asymptotic at the origin \(r^{L+3}\) must be used when the singular realistic nuclear potentials are included.

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The contributions of multistep direct reactions with different sequences of the leading continuum nucleons are presented for neutron scattering by niobium at incident energy of 26 MeV. The multistep cross sections are calculated within the framework of the Feshbach, Kerman and Koonin theory using non-DWBA matrix elements. The one-step cross sections include excitations of both incoherent particle–hole pairs and coherent collective vibrations. The results show that the dominant sequences involve only neutrons in the continuum, while sequences involving protons can be neglected.

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The single-freeze-out model of hadron production is used to describe the particle ratios and the transverse-momentum spectra from RHIC. The emphasis is put on the new measurements done at the highest beam energy of \(\sqrt {s_{NN}}=200\) GeV. An overall very good agreement is found between the data and the model predictions. The data for different centrality windows are analyzed separately. A simple scaling of the two expansion parameters of the model with the centrality is found. Interestingly, this scaling turns out to be equivalent to the scaling of hadron production with the number of wounded nucleons.

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It is shown that an oscillatory character of the solutions of the collisionless kinetic equations describing production of the quark–gluon plasma in strong color fields leads to the exponential (thermal-like) transverse-momentum spectra of partons produced in the soft region (\(100 \mathrm {\,MeV} \lt p_\perp \lt 1 \mathrm {\,GeV}\)). In addition, the production of partons in the very soft region (\(p_\perp \lt 100 \mathrm {\,MeV}\)) is clearly enhanced above the thermal-like background.

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Fluctuations of the spatial pattern are investigated by analyzing \(14.5\,A\) GeV/\(c\) \(^{28}\)Si-nucleus interactions on event-by-event basis. For this the nearest neighbor rapidity spacings are analyzed. The two entropy like quantities, \(S_q\) and \({\mit \Sigma }_q\), estimated from the two moments of the rapidity gap distributions \(G_q\) and \(H_q\), are observed to deviate significantly from 1. This would indicate the presence of erratic nature of event-by-event fluctuations in rapidity gap distributions. The variations of \(\ln S_q\) and \(\ln {\mit \Sigma }_q\) with \(q\) and their dependence on multiplicity of relativistic charged particles are investigated. A similar analysis is carried out for a Monte Carlo generated event sample using the event generator, Hijing 1.33. The results obtained for the simulated data are observed to compare well with the corresponding experimental values.

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We argue that recent data on fluctuations observed in heavy ion collisions show non-monotonic behaviour as function of number of participants (or “wounded nucleons”) \(N_{\rm W}\). When interpreted in thermodynamical approach this result can be associated with a possible structure occurring in the corresponding equation of state (EoS). This in turn could be further interpreted as due to the occurrence of some characteristic points (like softest point or critical point) of EoS discussed in the literature and therefore be regarded as a possible signal of the QGP formation in such collisions. We show, however, that the actual situation is still far from being clear and calls for more investigations of fluctuation phenomena in multiparticle production processes to be performed.

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In a previous paper, the convergence of a new effective field theory and density functional theory (EFT/DFT) approach to the description of the nuclear many-body system was studied. The most sophisticated parameter set (here G1) determined by Furnstahl, Serot and Tang from a fit along the valley of stability was found to provide quantitative predictions for total binding energies and single-particle and single-hole binding energies, spins, and parities for selected doubly-magic nuclei far from stability. Binding energies of all the even Sn isotopes (\(Z=50\)) were also well described. Here the calculations are extended to all isotones with magic numbers \(N=28\), 50, 82, 126, and isotopes with \(Z=28\), 50, 82 with similar predictive results.

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The collision integral cross sections in two-photon Compton scattering are measured experimentally for 0.662 MeV incident gamma photons. Two simultaneously emitted gamma quanta are investigated using a slow-fast coincidence technique of 25 ns resolving time. The coincidence spectra for different energy windows of one of the two final photons are recorded using HPGe detector. The experimental data do not suffer from inherent energy resolution of gamma detector and provide more faithful reproduction of the distribution under the full energy peak of recorded coincidence spectra. The present results of collision integral cross sections are in agreement with the currently acceptable theory of this higher order process.

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Nature is full of random networks of complex topology describing such apparently disparate systems as biological, economical or informatical ones. Their most characteristic feature is the apparent scale-free character of interconnections between nodes. Using an information theory approach, we show that maximalization of information entropy leads to a wide spectrum of possible types of distributions including, in the case of nonextensive information entropy, the power-like scale-free distributions characteristic of complex systems.

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Gamma-ray bursts are enigmatic flashes of gamma-rays at cosmological distances, so bright that the implied energetics is astounding: energies of order of about solar rest-energy are liberated in a time scale of the order of seconds in space regions only a few kilometres in size. Central engines capable to produce such enormous explosions, leading to a highly relativistic expending fireballs, remain a mystery. Here we propose a new candidate for the gamma-ray bursts central engine.