abstract

Recently the vector inflation has been proposed as the alternative to inflationary models based on scalar bosons and quintessence scalar fields. In the vector inflationary model, the vector field non-minimally couples to gravity. We should, however, inquire if there exists a relevant fundamental theory which supports the inflationary scenario. We investigate the possibility that Weyl’s gauge gravity theory could be such a fundamental theory. That is the reason why the Weyl’s gauge invariant vector and scalar fields are naturally introduced. After rescaling the Weyl’s gauge invariant Lagrangian to the Einstein frame, we find that in four dimensions the Lagrangian is equivalent to Einstein–Proca theory and does not have the vector field non-minimally coupled to gravity, but has the scalar boson with a polynomial potential which leads to the spontaneously symmetry breakdown.

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We propose a deterministic secure quantum communication protocol using genuine four-particle entangled states. With incomplete quantum teleportation, it reduces communication cost and needs no unitary operations to recover the original state.

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Half-life number sequences collected from nuclear data charts are found to obey the Newcomb–Benford law. Based on this fact, it has been suggested recently, that this law should be used to test the quality of nuclear decay models. In this paper we briefly recall how, when and why the Newcomb–Benford law can be observed in a set of numbers with a given probability distribution. We investigate the special case of nuclear half-lives, and show that the law provides no additional clue in understanding decay half-lives. Thus, it can play no significant role in testing nuclear decay theories.

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We apply a method of time-dependent Hurst exponent, proposed in the series of papers by Grech and Mazur [Physica A 336, 335 (2004)], Grech and Pamula [Physica A 387, 4299 (2008)] and Czarnecki, Grech and Pamula [Physica A 387, 6801 (2008)], on the stock market of the Czech Republic for a period between 1997 and 2009. Our results support the findings of the authors so that the time-dependent Hurst exponent can give some crucial information before a critical event happens on a market. We also discuss some potentially weak points of the method.

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Propagation of relativistic particles in the Schwarzschild gravitational field is studied. Particles emitted radially outward with speed at infinity exceeding \(c\) / \(\sqrt {2}\) are observed to be accelerated in the gravitational field by a distant observer. This is the Shapiro effect for relativistic particles. Slower particles are decelerated, as in Newtonian gravity. A speed-dependent potential for relativistic particles corresponding to the speed measured in terms of the coordinate time is derived to be \(V=GM\gamma \) \((\gamma ^2 -2)\) / \(r\) which is repulsive for \(v \gt c\) /\(\,\sqrt {2}\). The gravitational repulsion could be revealed in satellite experiments with beams of relativistic particles subject to very precise time measurements. Principles of laboratory measurements able to test kinetic energy changes of relativistic particles in the Earth gravitational field are discussed.

abstract

Three possible techniques to deal with a vector particle in the anti de Sitter cosmological model are viewed: the Duffin–Kemmer–Petiau matrix formalism based on the general tetrad recipe, the group theory 5-dimen- sional approach based on the symmetry group SO(3,2), and the tetrad form of Maxwell equations in complex Riemann–Silberstein–Majorana–Oppenheimer representation. In the first part, a spin-1 massive field is considered in static coordinates of the anti de Sitter space-time in tetrad-based approach. The complete set of spherical solutions with quantum numbers \((\varepsilon ,\,j,\,m,\,l)\) is constructed; angular dependence in wave functions is described in terms of Wigner \(D\)-functions. The energy quantization rule has been found. Transition to a massless case of electromagnetic field is specified, and electromagnetic solutions in Lorentz gauge have been constructed. In the second part, the problem of the particle with spin 1 is considered on the base of the 5-dimensional wave equation specified in the same static coordinates. In the third part, an approach, based on complex representation of the Maxwell field is applied in the anti de Sitter model.

abstract

In the model of hidden sector of the Universe, proposed and commented recently, a new nongauge mediating field transforming as an antisymmetric tensor (of dimension one) plays a crucial role. If it gets definite parity, say, \(-\), it can be split into two three-dimensional fields of spin 1 and parity \(-\) and +, respectively, much like the electromagnetic field (of dimension two) is split into its electric and magnetic parts. Then, the parity is preserved by a new weak interaction in the hidden sector. A priori, the parts of the nongauge mediating field may be either independent or dependent. We discuss a simple natural constraint that may relate them to each other in a relativistically covariant way, reducing their independent polarization degrees of freedom to three. In Appendix, we describe another option, where the mediating field (of dimension one) is gauged by a vector field (of dimension zero).

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We clarify and study our previous observation that, under a compactification with boundaries or orbifolding, vacuum expectation value of a bulk scalar field can have different extra-dimensional wave-function profile from that of the lowest Kaluza–Klein mode of its quantum fluctuation, under presence of boundary-localized potentials which would be necessarily generated through renormalization group running. For concreteness, we analyze the Universal Extra Dimension model compactified on orbifold \(S^1\)/\(Z_2\), with brane-localized Higgs potentials at the orbifold fixed points. We compute the Kaluza–Klein expansion of the Higgs and gauge bosons in an \(R_{\,\xi }\)-like gauge by treating the brane-localized potential as a small perturbation. We also check that the \(\rho \) parameter is not altered by the brane localized potential.

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The recent PHENIX mid-rapidity measurements of multiplicity distributions for centrality bins are analyzed in the framework of superposition models. A simple superposition of \(pp\) events is shown to disagree with the heavy ion data for the scaled variance as a function of centrality. However, it is suggested that a model describing better the \(pp\) data and based on the “wounded quark” idea may be compatible with the multiplicity data for heavy ion collisions.

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The nuclear structure of some closed shell \(\pm 2\)-nucleons nuclei \(^{42}\)Ca and \(^{38}\)Ca is studied in the framework of the particle–particle and hole–hole Random Phase Approximation (\(pp\) RPA and \(hh\) RPA) with the space of wave functions being extended to include orbits up to the \(2d_{5/2}\). This model assumes that the low-lying states of \(^{42}\)Ca are correlated two-particle operators acting on a correlated \(^{40}\)Ca core, and those of \(^{38}\)Ca are correlated two-hole operators acting on the same correlated \(^{40}\)Ca ground state. The Hamiltonian is to be daigonalized in this extended space in the presence of the Modified Surface Delta Interaction (MSDI). The spectra of nuclear excitation energy levels for both \(^{42}\)Ca and \(^{38}\)Ca are compared with the experimental data. The \(pp\) RPA checked by using the resultant eigenvalues and eigenvectors to calculate the longitudinal form factors of the inelastic electron scattering, and then compared with the available experimental data. More correlations to the ground state are assumed by the inclusion of admixture from higher orbits, which leads to enhance the calculations of the longitudinal form factors. Effective charges are also used to account for the core polarization effect.

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In this paper we study the differential, integrated and total cross-sections for neutral-current neutrino scattering off \(^{82}\)Se\((\nu , \nu ') ^{82}\)Se\(^*\), using the Quasi-particle Random Phase Approximation (QRPA). As it is known this isotope plays a significant role in the NEMO double beta decay detector. Exploiting the obtained results, we investigate the response of this isotope as a supernova neutrino detector assuming a two parameter Fermi–Dirac distribution for the supernova neutrino energy spectra.

abstract

Dynamical properties of diffusion process on complex networks with arbitrary degree distribution are investigated. The rule of the diffusion process encompasses both the structural characteristics and the information processing dynamics. Considering the influence of a node on the global dynamical behavior, the dynamical generating function of the process, which is deeply reflecting the basic characteristic of the process and mutually decided with the dynamical process, is proposed. Based on the analysis of the dynamical generating function we introduce dynamical centrality for each node, which determines the relative importance of nodes and the capability of the given node to collect and communicate information with its neighbouring environment in the network via the diffusion process. Furthermore, a new parameter, dynamical entropy, is proposed to measure the interplay between dynamical centrality and diffusion dynamics. The experimental results on large-scale complex networks with Poisson distribution confirm our analytical prediction.

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We compare impulsively generated vertical oscillations in three-dimensional (3D) and two-dimensional (2D) solar coronal arcade loops. 3D and 2D magnetohydrodynamic equations are solved numerically in the limit of ideal plasma. Numerically obtained wave signatures are analyzed to reveal characteristic spatial and temporal scales. The numerical results show that in 2D case wave period is slightly longer than in 3D one. These results are reminiscent of the recent Hinode data.

abstract

A global disk model for spiral galaxies is modified by adding a spherical component to the galactic center to account for the presence of a central spherical bulge. It is verified whether such modification could be substantial for predictions of total mass and of its distribution in spiral galaxy M94.