4D Equations of motion and fifth force in a 5D general Kaluza–Klein space

In this paper we present a new point of view on space–time–matter (STM) theory. First, some weak points from earlier research papers on STM theory are presented. Then, we obtain in a covariant form the fully general $4D$ 4 D equations of motion for STM theory. This enables us to classify the $5D$ 5 D motions and to give a new definition of the fifth force in $4D$ 4 D physics.     

Fine and hyperfine structures of heavy quarkonia and perturbative quantum chromodynamics

Spectroscopies of the heavy quarkonia, \(c\bar c\) , \(b\bar b\) and \(t\bar t\) , are analysed with a potential model. Relativistic effects are taken into account and spin dependent interactions are investigated in detail. We propose a flavor independent potential which has a Lorentz vector term determined by the perturbative QCD at short distances and a Lorentz scalar term confining quarks at large distances. It is stressed that the short range attenuation of the vector Coulomb potential has significant effects on the fine and hyperfine structures of the \(c\bar c\) and \(b\bar b\) systems, and also on the \(t\bar t\) level structure. We study the decay property of the \(t\bar t\) system using the calculated wave functions.     

Entanglement of Bipartite Quantum Systems Driven by Repeated Interactions

We consider a non-interacting bipartite quantum system $\mathcal H_S^A\otimes \mathcal H_S^B$ undergoing repeated quantum interactions with an environment modeled by a chain of independent quantum systems interacting one after the other with the bipartite system. The interactions are made so that the pieces of environment interact first with $\mathcal H_S^A$ and then with $\mathcal H_S^B$ . Even though the bipartite systems are not interacting, the interactions with the environment create an entanglement. We show that, in the limit of short interaction times, the environment creates an effective interaction Hamiltonian between the two systems. This interaction Hamiltonian is explicitly computed and we show that it keeps track of the order of the successive interactions with $\mathcal H_S^A$ and $\mathcal H_S^B$ . Particular physical models are studied, where the evolution of the entanglement can be explicitly computed. We also show the property of return of equilibrium and thermalization for a family of examples.     

On the Nature of Fermi Golden Rule for Open Quantum Systems

We consider a general class of models consisting of a small quantum system $S$ interacting with a reservoir $R$ . We compare three applications of 2nd order perturbation theory (the Fermi Golden Rule) to the study of such models: (1) the van Hove (weak coupling) limit for the dynamics reduced to $S$ ; (2) the Fermi Golden Rule applied to the Liouvillean—an argument that was used in recent papers on the return to equilibrium; (3) the Fermi Golden Rule applied to the so-called C-Liouvillean. These three applications lead to three Level Shift Operators. As our main result, we prove that if the reservoir $R$ is thermal (if it satisfies the KMS condition), then the Level Shift Operator obtained in (1) (often called the Davies generator) and the Level Shift Operator constructed in (2) are connected by a similarity transformation. We also show that the Davies generator coincides with the Level Shift Operator obtained in (3) for a general $R$ .     

Simulation and optimization of reflection optical module design for single LED

Illuminance uniformity and illuminating efficiency are always the key problems of light emitting diode (LED) lighting system design. Based on the new design of the reflection optical module, illuminance uniformity and illuminating efficiency are investigated simultaneously in this paper. At the first stage, a reflector with various profile designs is installed to improve the uniformity and efficiency of irradiances collected through the receiver. Using the macro commands, an effective process is presented through the optimal design of the reflector geometries, and the merit function is used as the optical quality objective to find the optimal design value of $K2$ K 2 and $R2$ R 2 parameters of the reflector. At the second stage, based on the optimal design result, the displacement between LED source and reflector is further adjusted automatically by the macro commands too. The results from the ray tracing simulation indicate that the optimal design can be achieved through the compromise of Illuminance uniformity and illuminating efficiency. Finally, we obtain the merit function value of $1.81$ 1.81 with $K2=-1.09, R2=1.11\,\hbox {mm}$ K 2 = - 1.09 , R 2 = 1.11 mm , and the source position $Z1= 1.68\,\hbox {mm}$ Z 1 = 1.68 mm . The results shown in this paper could be beneficial for machine vision systems which are heavily demanded in the light source applications for the uniform and efficient illuminance.     

Spin Effects in the Interaction of Antiprotons with the Deuteron at Low and Intermediate Energies

Antiproton-deuteron scattering is analyzed within the Glauber theory, accounting for the full spin dependence of the underlying \({\bar{N}N}\) amplitudes. The latter are taken from the Jülich \({\bar{N}N}\) models and from a recently published new partial-wave analysis of \({\bar{p}p}\) scattering data. Predictions for differential cross sections and the spin observables \({A_y^d}\) , \({A_y^{\bar{p}}}\) , A _xx , A _yy are presented for antiproton beam energies up to about 300 MeV. The efficiency of the polarization buildup for antiprotons in a storage ring is investigated.     

Resonance studies at STAR

Preliminary results from measurements of resonances (K ^*0(892), $\overline {K*^0 } (892)$ , Φ(1020), and ρ(770)) and weakly decaying particles (Λ(1116), $\bar \Lambda (1116)$ , and K _S ⁰ (498)) are presented. The measurements are performed at mid-rapidity by the STAR detector in $\sqrt {s_{NN} } = 130$ GeV Au?Au collisions at RHIC. The ratios K ^*0/h?, $\overline {K*^0 } /K$ , and $\bar \Lambda /\Lambda $ are compared to measurements at different energies and colliding systems. Estimates of thermal parameters, such as temperature and baryon chemical potential, are also presented.     

The Microscopic Foundations of Vlasov Theory for Jellium-Like Newtonian N-Body Systems

The kinetic equations of Vlasov theory, in the weak formulation, are rigorously shown to govern the $N\rightarrow \infty $ limit of the Newtonian dynamics of $D\ge 2$ -dimensional $N$ -body systems with attractive harmonic pair interactions and locally integrable repulsive inverse power law pair interactions, provided a mild higher moment hypothesis on the forces (which is shown to propagate globally in time for each $N$ ) will hold uniformly in $N$ at later times if it holds uniformly in $N$ initially (the uniformity in $N$ of this moment condition is demonstrated to hold for an open set of initial data). Logarithmic interactions are included as a limiting case. The proof is based on the Liouville equation, more precisely the first member of the pertinent BBGKY hierarchy, and does not invoke the Hewitt–Savage theorem, nor any regularization of the interactions. In addition, a rigorous proof of the virial theorem and of some of its interesting ramifications is given.     

Spectroscopic properties of Ho 3 + -doped K–Sr–Al phosphate glasses

Trivalent holmium-doped K–Sr–Al phosphate glasses ( $\mathrm{P}_{2}\mathrm{O}_{5}$ – $\mathrm{K}_{2}\mathrm{O}$ –SrO– $\mathrm{Al}_{2}\mathrm{O}_{3}$ – $\mathrm{Ho}_{2}\mathrm{O}_{3}$ ) were prepared, and their spectroscopic properties have been evaluated using absorption, emission, and excitation measurements. The Judd–Ofelt theory has been used to derive spectral intensities of various absorption bands from measured absorption spectrum of 1.0 mol% $\mathrm{Ho}_{2}\mathrm{O}_{3}$ -doped K–Sr–Al phosphate glass. The Judd–Ofelt intensity parameters ( $\varOmega_{\lambda}$ , $\times10^{-20}~\mathrm{cm}^{2}$ ) have been determined of the order of $\varOmega_{2} = 11.39$ , $\varOmega_{4} = 3.59$ , and $\varOmega_{6} = 2.92$ , which in turn used to derive radiative properties such as radiative transition probability, radiative lifetime, branching ratios, etc. for excited states of $\mathrm{Ho}^{3+}$ ions. The radiative lifetimes for the ${}^{5}F_{4}$ , ${}^{5}S_{2}$ , and ${}^{5}F_{5}$ levels of $\mathrm{Ho}^{3+}$ ions are found to be 169, 296, and 317 μs, respectively. The stimulated emission cross-section for 2.05-μm emission was calculated by the McCumber theory and found to be $9.3\times10^{-2 1}~\mathrm{cm}^{2}$ . The wavelength-dependent gain coefficient with population inversion rate has been evaluated. The results obtained in the titled glasses are discussed systematically and compared with other $\mathrm{Ho}^{3+}$ -doped systems to assess the possibility for visible and infrared device applications.     

Factorization of Combinatorial R Matrices and Associated Cellular Automata

Solvable vertex models in statistical mechanics give rise to soliton cellular automata at q=0 in a ferromagnetic regime. By means of the crystal base theory we study a class of such automata associated with non-exceptional quantum affine algebras U′ $_q$ ( $\widehat {\mathfrak{g}}$ $_n$ ). Let B $_l$ be the crystal of the U′ $_q$ ( $\widehat {\mathfrak{g}}$ $_n$ )-module corresponding to the l-fold symmetric fusion of the vector representation. For any crystal of the form B = $B_{l_1 }$ ? ...? $B_{l_N }$ , we prove that the combinatorial R matrix B $_M$ ?B $\widetilde \to$ B?B $_M$ is factorized into a product of Weyl group operators in a certain domain if M is sufficiently large. It implies the factorization of certain transfer matrix at q=0, hence the time evolution in the associated cellular automata. The result generalizes the ball-moving algorithm in the box-ball systems.     

Heavy quarkonium effective theory

We formulate a QCD-based effective theory approach to heavy quarkonia-like systems as $\bar cc$ and $\bar bb$ resonances andB _c states. We apply the method to inclusive decays, working out a few examples in detail.     

Free Field Construction for the ABF Models in Regime II

The Wakimoto construction for the quantum affine algebra U $_q$ ( $(\widehat{\mathfrak{s}\mathfrak{l}_2 })$ ) admits a reduction to the q-deformed parafermion algebras. We interpret the latter theory as a free field realization of the Andrews–Baxter–Forrester models in regime II. We give multi-particle form factors of some local operators on the lattice and compute their scaling limit, where the models are described by a massive field theory with $\mathbb{Z}$ $_k$ symmetric minimal scattering matrices.     

Fluctuation–Dissipation Relation for Systems with Spatially Varying Friction

When a particle diffuses in a medium with spatially dependent friction coefficient \(\alpha (r)\) at constant temperature \(T\) , it drifts toward the low friction end of the system even in the absence of any real physical force \(f\) . This phenomenon, which has been previously studied in the context of non-inertial Brownian dynamics, is termed “spurious drift”, although the drift is real and stems from an inertial effect taking place at the short temporal scales. Here, we study the diffusion of particles in inhomogeneous media within the framework of the inertial Langevin equation. We demonstrate that the quantity which characterizes the dynamics with non-uniform \(\alpha (r)\) is not the displacement of the particle \(\Delta r=r-r^0\) (where \(r^0\) is the initial position), but rather \(\Delta A(r)=A(r)-A(r^0)\) , where \(A(r)\) is the primitive function of \(\alpha (r)\) . We derive expressions relating the mean and variance of \(\Delta A\) to \(f\) , \(T\) , and the duration of the dynamics \(\Delta t\) . For a constant friction coefficient \(\alpha (r)=\alpha \) , these expressions reduce to the well known forms of the force-drift and fluctuation–dissipation relations. We introduce a very accurate method for Langevin dynamics simulations in systems with spatially varying \(\alpha (r)\) , and use the method to validate the newly derived expressions.     

4D Einstein equations in a 5D general Kaluza–Klein space

Based on the new point of view on space–time–matter theory developed in our paper (Bejancu, Gen Rel Grav, 2013), we obtain the $4D$ 4 D Einstein equations in a general $5D$ 5 D Kaluza–Klein space with electromagnetic potentials. In particular, we recover the $4D$ 4 D Einstein equations obtained by Wesson and Ponce de Leon (J Math Phys 33:3883, 1992) in case the electromagnetic potentials vanish identically on $\bar{M}$ M ¯ . The Riemannian horizontal connection and the $4D$ 4 D tensor calculus on $\bar{M}$ M ¯ , are the main tools in the study.     

The Kaon-Few-Nucleon Levels and Lifetimes Calculated by a Variational Method

The search for nuclear states of ${\overline{\rm K}}$ mesons is presented and the main uncertainties: off-shell extrapolation of meson-nucleon scattering amplitudes, behavior of hadronic resonances in nuclei and extrapolation to high density nuclear regions are discussed. A two step method to perform variational calculations in the ${\overline{\rm K}}$ -few-nucleon systems is suggested.     

The Baker–Akhiezer Function and Factorization of the Chebotarev–Khrapkov Matrix

A new technique is proposed for the solution of the Riemann–Hilbert problem with the Chebotarev–Khrapkov matrix coefficient \({G(t) = \alpha_{1}(t)I + \alpha_{2}(t)Q(t)}\) , \({\alpha_{1}(t), \alpha_{2}(t) \in H(L)}\) , I = diag{1, 1}, Q(t) is a \({2\times2}\) zero-trace polynomial matrix. This problem has numerous applications in elasticity and diffraction theory. The main feature of the method is the removal of essential singularities of the solution to the associated homogeneous scalar Riemann–Hilbert problem on the hyperelliptic surface of an algebraic function by means of the Baker–Akhiezer function. The consequent application of this function for the derivation of the general solution to the vector Riemann–Hilbert problem requires the finding of the \({\rho}\) zeros of the Baker–Akhiezer function ( \({\rho}\) is the genus of the surface). These zeros are recovered through the solution to the associated Jacobi problem of inversion of abelian integrals or, equivalently, the determination of the zeros of the associated degree- \({\rho}\) polynomial and solution of a certain linear algebraic system of \({\rho}\) equations.     

Quantum Measures on Finite Effect Algebras with the Riesz Decomposition Properties

One kind of generalized measures called quantum measures on finite effect algebras, which fulfil the grade-2 additive sum rule, is considered. One basis of vector space of quantum measures on a finite effect algebra with the Riesz decomposition property (RDP for short) is given. It is proved that any diagonally positive symmetric signed measure \(\lambda \) on the tensor product \(E\otimes E\) can determine a quantum measure \(\mu \) on a finite effect algebra \(E\) with the RDP such that \(\mu (x)=\lambda (x\otimes x)\) for any \(x\in E\) . Furthermore, some conditions for a grade-2 additive measure \(\mu \) on a finite effect algebra \(E\) are provided to guarantee that there exists a unique diagonally positive symmetric signed measure \(\lambda \) on \(E\otimes E\) such that \(\mu (x)=\lambda (x\otimes x)\) for any \(x\in E\) . At last, it is showed that any grade- \(t\) quantum measure on a finite effect algebra \(E\) with the RDP is essentially established by the values on a subset of \(E\) .     

{\Xi} Hypernucler States Predicted by the New Interaction Model ESC08c

The features of the new interaction model ESC08c in ${\Lambda N}$ , ${\Sigma N}$ and ${\Xi N}$ channels are demonstrated single hyperon potentials ${U_Y(Y=\Lambda, \Sigma, \Xi)}$ in nuclear matter on the basis of the G-matrix theory. (K ^?, K ⁺) productions of ${\Xi}$ hypernuclei are studied with ${\Xi}$ -nucleus folding potentials.     

Non-Equilibrium Statistical Mechanics of Turbulence

The macroscopic study of hydrodynamic turbulence is equivalent, at an abstract level, to the microscopic study of a heat flow for a suitable mechanical system (Ruelle, PNAS 109:20344–20346, 2012). Turbulent fluctuations (intermittency) then correspond to thermal fluctuations, and this allows to estimate the exponents \(\tau _p\) and \(\zeta _p\) associated with moments of dissipation fluctuations and velocity fluctuations. This approach, initiated in an earlier note (Ruelle, 2012), is pursued here more carefully. In particular we derive probability distributions at finite Reynolds number for the dissipation and velocity fluctuations, and the latter permit an interpretation of numerical experiments (Schumacher, Preprint, 2014). Specifically, if \(p(z)dz\) is the probability distribution of the radial velocity gradient we can explain why, when the Reynolds number \(\mathcal{R}\) increases, \(\ln p(z)\) passes from a concave to a linear then to a convex profile for large \(z\) as observed in (Schumacher, 2014). We show that the central limit theorem applies to the dissipation and velocity distribution functions, so that a logical relation with the lognormal theory of Kolmogorov (J. Fluid Mech. 13:82–85, 1962) and Obukhov is established. We find however that the lognormal behavior of the distribution functions fails at large value of the argument, so that a lognormal theory cannot correctly predict the exponents \(\tau _p\) and \(\zeta _p\) .