abstract

We argue that one has to distinguish between the Harari–Shupe model (HSM) and the Harari–Shupe observation (HSO). The former — in which quarks and leptons are viewed as composite objects built from confined fermionic subparticles (‘rishons’) — is known to be beset with many difficulties. The latter may be roughly defined as this part of the HSM that really works. We recall that the phase-space Clifford-algebra approach leads to the HSO without any of the HSM problems and discuss in some detail how this is achieved. The light which the phase-space-based view sheds on the HSO sets then a new direction along which the connection between space and particle properties could be studied and offers a glimpse into weird physics that probably lurks much deeper than the field-theoretical approach of the Standard Model.

abstract

In the framework of the Glauber model as implemented in GLISSANDO 2, we study the fluctuations of flow harmonics in Pb+Pb collisions at the LHC energy of \(\sqrt {s_{NN}}=2.76\) TeV. The model with wounded nucleons and the admixture of binary collisions leads to reasonable agreement for the ellipticity and triangularity fluctuations with the experimental data from the ATLAS, ALICE, and CMS collaborations, verifying the assumption that the initial eccentricity is approximately proportional to the harmonic flow of charged particles. While the agreement, in particular at the level of event-by-event distributions of eccentricities/flow coefficients in not perfect, it leads to a fair (at the level of a few percent for all centralities except the most peripheral collisions) description of the scaled standard deviation and the \(F\) measure which involves the four-particle cumulants. We also discuss the case of quadrangular flow. Computer scripts that generate our results from the GLISSANDO 2 simulations are provided.

abstract

In this paper, we investigate consequences of an assumption that the discrepancy of the predicted and observed \(W^+W^-\) production cross sections at the LHC is caused by the missing contribution of the double Drell–Yan process (DDYP). Using our simple model of DDYP [Acta Phys. Pol. B 45, 71 (2014)], we show that inclusion of this production mechanism leads to a satisfactory, parameter-free description of the two-lepton mass distribution for \(0\)-jet \(W^+W^-\) events and the four-lepton mass distribution for \(ZZ\) events. In such a scenario, the Higgs-boson contribution is no longer necessary to describe the data. An experimental programme to prove or falsify such an assumption is proposed.

abstract

In this study, we lay out a proposal of designing a short baseline reactor antineutrino experiment by reusing multiple detectors and commercial reactors in existing resources. A \(\chi ^{2}\) function is constructed to evaluate the experimental sensitivity in probing the existence of the sterile neutrino. Several sensitivities for different detector arrangements are studied. It is found that this setup is most sensitive to mass region of the \(10^{-2}\) eV\(^2\) \(\lesssim |\Delta m^2_{41}|\lesssim 1\) eV\(^2\) region. For the parameter space with \(\Delta {m^2_{41}}\gt 1\) eV\(^2\), the sensitivity is limited due to the intrinsic deficiency of the commercial reactor size. In order to probe \(\Delta {m^2_{41}} \sim 1\) eV\(^2\), the distance between the near antineutrino detector (AD) and the near reactor should be less than 30 m and the distance between ADs should be a small value of the order of meters. Sensitivity to \(\Delta {m^2_{41}} \sim \) several \(\times \,0.1\) eV\(^2\) is maximized by a symmetrical detector arrangement relative to the reactors.

abstract

Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the “Dirac comb” distribution and of its tensor products in higher dimensions lead to Poisson resummation, allowing for a useful approximation formula of a Fourier transform in terms of a limited number of terms. A connection with the Bochner theorem on positive definiteness of Fourier-positive functions is discussed. As a practical application, we find simple and rapid analytic algorithms for checking Fourier-positivity in 1- and (radial) 2-dimensions among a large variety of real positive functions. This may provide a step towards a classification of positive positive-definite functions.

abstract

It is shown that multi-waves are generated through direct or indirect nonlinear interactions of basic traveling waves. Direct and indirect nonlinear interactions are suggested via nonlinear combinations and bilinear transformations with nonlinear combinations of basic traveling wave solutions. Here, the used method is a generalization of the unified method presented by the first author in a recent work. Two- and three-soliton solutions have been obtained by the nonlocal Boussinesq equation through the simplified Hirota method very recently. Here, it is shown that they are particular cases of those found in this work. Multi-soliton waves are shown to be super-diffracted notably for higher speed of waves spreading. Further, a giant wave is formed in the region of interaction of the soliton waves.

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The eigenvalue statistics of real adjoints of \(N \times N\) Hermitian octonion random matrices are studied numerically. By allowing various matrix elements to be turned OFF or ON, we are able to observe eigenvalue statistics that are described by the three Gaussian ensembles of classical random matrix theory. In certain cases, we have also observed eigenvalues that appear to be a superposition of two independent spectra, each of which is described by statistics of the Gaussian symplectic ensemble.

abstract

Linear statistics, a random variable built out of the sum of the evaluation of functions at the eigenvalues of a \(N\times N\) random matrix, \(\sum _{j=1}^{N}f(x_{j})\) or \(\mathrm {tr} f(M)\), is an ubiquitous statistical characteristics in random matrix theory. Hermitian random matrix ensembles, under the eigenvalue–eigenvector decompositions give rise to the joint probability density functions of \(N\) random variables. We show that if \(f(\cdot )\) is a polynomial of degree \(K\), then the variance of \({\rm tr} f(M)\) is of the form of \(\sum _{n=1}^{K}n(d_{n})^{2}\) and \(d_{n}\) is related to the expansion coefficients \(c_{n}\) of the polynomial \(f(x)=\sum _{n=0}^{K}c_{n}\widehat {P}_{n}(x)\), where \(\widehat {P}_{n}(x)\) are polynomials of degree \(n\), orthogonal with respect to the weights \(\frac {1}{\sqrt {(b-x)(x-a)}}\), \(\sqrt {(b-x)(x-a)}\), \(\frac {\sqrt {(b-x)(x-a)}}{x},\; (0\lt a\lt x\lt b)\), \(\frac {\sqrt {(b-x)(x-a)}}{x(1-x)}, (0\lt a\lt x\lt b\lt 1)\), respectively.

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We analyze the impact of the Unruh effect on quantum Magic Square game. We find the values of acceleration parameter for which quantum strategy yields higher players’ winning probability than classical strategy.

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We derive a generalization of the virial theorem in terms of the canonically conjugate pair of variables. Then, we apply it to the Salpeter equation and to the reductions of the Salpeter equation. It is shown that the linear mass form and the quadratic mass form of the reductions of the Salpeter equation will be the same in the nonrelativistic limit but different in the ultrarelativistic limit. Therefore, different reductions are appropriate for different bound systems.

abstract

A well-defined spatial orientation of atomic basis functions is essential for the correct analysis of quantum-mechanical calculations in terms of chemical (bonding) concepts. Here, we present the implementation of a straightforward, convenient algorithm to rotate basis functions using real spherical harmonics within a linear combination of atomic orbitals (LCAO) framework. The highly efficient technique only relies on overlap integrals of the basis functions and Wigner’s rotation matrices. To do so, a previously known and simple way to calculate the latter (defined by a rotation axis and angle) for real spherical harmonics is modified to enable chemical-bonding interpretation. The method’s usefulness is illustrated by an application to carbon crystallizing in the diamond structure.