Unusual sum rule for Clebsch–Gordan coefficients

Letters in Mathematical Physics - We present a new sum rule for Clebsch–Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is...     

The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch–Gordan Coefficients

We discuss the procedure of different partitions in the finite set of N integer numbers and construct generic formulas for a bijective map of real numbers s _y , where y = 1, 2,…, N, N = \( \underset{k=1}{\overset{n}{\varPi}}{X}_k, \) and X _k are positive integers, onto the set of numbers s(y(x ₁, x ₂,…, x _n )). We give the functions used to present the bijective map, namely, y(x ₁, x ₂, …, x _n ) and x _k (y) in an explicit form and call them the functions detecting the hidden correlations in the system. The idea to introduce and employ the notion of “hidden gates” for a single qudit is proposed. We obtain the entropic-information inequalities for an arbitrary finite set of real numbers and consider the inequalities for arbitrary Clebsch–Gordan coefficients as an example of the found relations for real numbers.     

Clebsch–Gordan and Racah–Wigner Coefficients for a Continuous Series of Representations of ?q (??(2, ℝ))

The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of U _q (sl(2,ℝ). It is described by an explicit integral transformation involving a distributional kernel that can be seen as an analogue of the Clebsch–Gordan coefficients. Moreover, we also study the relation between two canonical decompositions of triple tensor products into irreducibles. It can be represented by an integral transformation with a kernel that generalizes the Racah–Wigner coefficients. This kernel is explicitly calculated. Received: 9 August 2000 / Accepted: 2 July 2001     

Absurd Results from the Expression of Expectation Values of “Double—Wave Theory”

Two of the four fundamental hypotheses of the double-wave theory(DWT) are criticized.It is expounded that the hypothesis of two wavefunctions is unreasonable and the hypothesized expression of measured values or expectation values of mechanical quantities is incorrect and does not express the measured values or expectation values at all.This expression can lead to some absurd results.     

Formulation of Leggett–Garg Inequalities in Terms of q-Entropies

As is well known, the macroscopic realism and the noninvasive measurability together lead to Leggett–Garg inequalities violated by quantum mechanics. We consider tests of the Leggett–Garg type with use of the q-entropies.For all q≥1, quantum mechanics predicts violations of an entire family of q-entropic inequalities of the Leggett–Garg type. Violations are exemplified with a quantum spin-s system. In general, entropic Leggett–Garg inequalities give only necessary conditions that some probabilistic model is compatible with the macrorealism in the broader sense. The presented q-entropic inequalities allow to widen a class of situations, in which an incompatibility with the macrorealism can be tested. In the considered example, both the strength and range of violations are somehow improved by varying q.We also examine q-entropic inequalities of the Leggett–Garg type in the case of detection inefficiencies, when the no-click event may occur in each observation. With the use of the q-entropic inequalities, the required amount of efficiency may be reduced.     

Energy–Momentum Tensor in the Relativistic Theory of Gravity

It has been shown that the following modification of the symmetric (Gilbert) total energy–momentum tensor (EMT) density \({t^{\mu v}} \to {t^{\mu v}} - \frac{{{m^2}}}{{16\pi G}}{\tilde \varphi ^{\mu v}}\) leads to incorrect results in basic energetic calculations. It is pointed out that some attempts to prove the positive definiteness of the gravitational radiation flux in the RTG are based on the nonconservative energy–momentum tensor.     

Formulation of the Snell–Descartes Laws in Terms of Geometric Algebra

Russian Physics Journal - A formulation of the laws of reflection and refraction of optical rays by the interface of two isotropic media using the mathematical apparatus of geometric algebra is...     

Optical Coefficients of Nanoscale Copper Films in the Range of 9–11 GHz

Optics and Spectroscopy - The reflectance, transmittance, and absorption coefficient of ultrathin copper films on a quartz substrate have been measured in a waveguide at frequencies of 9–11...     

Landau–Khalatnikov Problem in Relativistic Fluid Dynamics

Journal of Experimental and Theoretical Physics - The results of experiments on the vacancy ordering in nanocrystalline nonstoichiometric titanium monoxide TiOy (space group Fm $$bar {3}$$ m),...     

A Generalization of Powers–Størmer Inequality

In this note, we prove the following inequality: \({2\Vert\Delta_{\eta\varphi}^{\frac s2}\xi_{\varphi}\Vert ^2 \ge \varphi(1)+\eta(1)- \vert\varphi-\eta\vert(1)}\) , where \({\varphi}\) and η are positive normal linear functionals over a von Neumann algebra. This is a generalization of the famous Powers–Størmer inequality (Powers and Størmer proved the inequality for \({L({\mathcal H})}\) in Commun Math Phys 16:1–33, 1970; Takesaki in Theory of Operator Algebras II, 2001). For matrices, this inequality was proven by Audenaert et al. (Phys Rev Lett 98:160501, 2007). We extend their result to general von Neumann algebras.     

Relativistic spin-zero bosons in a Som–Raychaudhuri space–time

We investigate the Duffin–Kemmer–Petiau equation for spin-zero bosons in a (\(3+1\))-dimensional Som–Raychaudhuri space–time. We establish the covariant Duffin–Kemmer–Petiau equation in this curved space–time for the so-called oscillator and we include interaction with a scalar potential. We determine eigenfunctions and the corresponding eigenvalues for the oscillator with the Cornell potential. We investigate the effect of the space–time’s parameters, oscillator’s frequency and the Cornell potential’s parameters on the wave functions.     

Collective Oscillation of Relativistic Electrons in Hot Plasma

The interactions between relativistic electrons in a hot plasma are analysed theoretically. By splitting the electron density fluctuations into the individual part and the collective part, we are concerned with the collective oscillation of the relativistic electrons resulting from the Coulomb interactions. Consequently, we derive the frequency of the hot plasma and the “Debye length“ with relativistic modification.     

The Existence of Non-Topological Multivortex Solutions in the Relativistic Self-Dual Chern–Simons Theory

We construct a general type of multivortex solutions of the self-duality equations (the Bogomol'nyi equations) of (2+1) dimensional relativistic Chern–Simons model with the non-topological boundary condition near infinity. For such construction we use a perturbation argument around the explicit solutions of the Liouville equation. Received: 6 July 1999 / Accepted: 14 June 2000     

Phase Transition of FeS in Terms of In-Situ Resistance Measurement

Electrical properties of stoichiometric iron sulfide （FeS） are investigated under high pressure with a designed diamond anvil cell. The process of phase transition is reflected by changing the electrical conductivity under high pressure, and the conductivity of FeS with the NiAs structure is found to be much smaller than other phases. Two new phase transitions without structural change are observed at 34.7 GPa and 61.3 GPa. The temperature dependence of the conductivity is found to be similar to that of a semiconductor when the pressure is higher than 35 GPa     

Measurement of Angular Coefficients in the Drell–Yan Process in the CMS Experiment at the LHC

Physics of Atomic Nuclei - A review is given of measurements of the first five polarization coefficients $${{A}_{0}}$$ – $${{A}_{4}}$$ of angular distributions of muons resulting from the Z0...     

Hamilton–Jacobi Formulation for Systems in Terms of?Riesz’s Fractional Derivatives

The paper presents fractional Hamilton–Jacobi formulations for systems containing Riesz fractional derivatives (RFD’s). The Hamilton–Jacobi equations of motion are obtained. An illustrative example for simple harmonic oscillator (SHO) has been discussed. It was observed that the classical results are recovered for integer order derivatives.     

Chaotic Motion of a Nucleon in Mean Field Potential With Octupole Deformation (Ⅱ) Characteristics of Expectation Values and Uncertainty Measures of Canonical Variables in Space-Temporal Variation of Initial Coherent States

Coherent states of two dimensional asymmetrical harmonic oscillator, which prop- agate in additional octupole deformation potentials, are used to investigate the characteristics of expectation values and uncertainty measures of canonical variables in space-temporal varia- tions.The quantum chaotic system shows varying behaviors as the corresponding classical chaotic system does. Thus the characteristics of quantum chaos are associated with the geom- atric symmetry of the potential surface, specifically, the existence of the negative curvature and the magnitude of the curvature in the potential surface.     

Scattering of Relativistic Spinless Particles by the Woods–Saxon Potential

The Klein–Gordon equation with vector and scalar Woods–Saxon potentials is solved in terms of hypergeometric functions. The transmission and reflection coefficients as well as the bound state solutions are reported.