Auxiliary “Massless” Spin-2 Field in De Sitter Universe

For the tensor field of rank-2 there are two unitary irreducible representation (UIR) in de Sitter (dS) space denoted by P^±_2,2\Pi^{\pm}_{2,2} and P^±_2,1\Pi^{\pm}_{2,1} (Dixmier in Bull Soc. Math. France 89:9, 1961). In the flat limit only the P^±_2,2\Pi^{\pm}_{2,2} coincides to the UIR of Poincaré group, the second one becomes important in the study of conformal gravity. In the previous work, Dirac’s six-cone formalism has been utilized to obtain conformally invariant (CI) field equation for the “massless” spin-2 field in dS space (Dehghani et al. in Phys. Rev. D 77:064028, 2008). This equation results in a field which transformed according to P^±_2,1\Pi^{\pm}_{2,1}, we name this field the auxiliary field. In this paper this auxiliary field is considered and also related two-point function is calculated as a product of a polarization tensor and “massless” conformally coupled scalar field. This two-point function is de Sitter invariant.     

Modeling Galactic Halos with Predominantly Quintessential Matter

This paper discusses a new model for galactic dark matter by combining an anisotropic pressure field corresponding to normal matter and a quintessence dark energy field having a characteristic parameter ω _q such that -1 < w_q < -\frac13-1<\omega_{q}< -\frac{1}{3}. Stable stellar orbits together with an attractive gravity exist only if ω _q is extremely close to -\frac13-\frac{1}{3}, a result consistent with the special case studied by Guzman et al. (Rev. Mex. Fis. 49:303, 2003). Less exceptional forms of quintessence dark energy do not yield the desired stable orbits and are therefore unsuitable for modeling dark matter.     

Temperature stable low loss PTFE/rutile composites using secondary polymer

Rutile filled PTFE composites have been fabricated through Sigma Mixing, Extrusion, Calendering and Hot pressing (SMECH) process. Dielectric constant (e_r￠\varepsilon_{r}') and loss tangent (tan δ) of filled composites at microwave frequency region were measured by waveguide cavity perturbation technique using a Vector Network Analyzer. The temperature coefficient of dielectric constant (t_er￠\tau_{\varepsilon_{r}'}) was measured in the 0–100°C temperature range. In order to tailor the temperature coefficient of dielectric constant of the composite, thermoplastic Poly (ether ether ketone) (PEEK) has been used as a secondary polymer. Flexible laminate having a dielectric constant, e_r￠ ~ 10.4\varepsilon_{r}'\sim10.4, loss tangent tan δ∼0.0045 and t_er￠ ~ -40 ppm/K\tau_{\varepsilon_{r}'}\sim-40\mbox{ ppm}/\mbox{K} was realized in Polytetrafluroethylene (PTFE)/rutile composites with the addition of 8 wt% PEEK. The reduction in t_er￠\tau_{\varepsilon_{r}'} is mainly attributed to the positive t_er￠\tau_{\varepsilon_{r}'} of PEEK and increased interface region in the composites as a result of the PEEK addition.     

Time-resolved photoelectron spectroscopy on small tungsten cluster anions

We have studied the dynamics of photoexcited tungsten cluster anions W_n^-\mathrm{W}_{n}^{-} (n=3,4,…,14) by means of time-resolved two-photon photodetachment spectroscopy. At an excitation energy of h ν _pump=1.56 eV the photoinduced dynamics is mainly dominated by fast electronic relaxation processes. For the smallest clusters, i.e., W₃^-\mathrm{W}_{3}^{-}, W₄^-\mathrm{W}_{4}^{-}, and W₅^-\mathrm{W}_{5}^{-}, individual relaxation channels have been identified and resolved on a timescale well below 100 fs. The time constants for the decay of nascent and secondary electrons have been deduced from a Bloch model. Complete thermalization takes place for all clusters on a timescale of ∼1 ps.     

Inertial-Range Behavior of a Passive Scalar Field in a Random Shear Flow: Renormalization Group Analysis of a Simple Model

Infrared asymptotic behavior of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with correlation function of the form μ d(t-t￠) / k_^^d-1+x\propto\delta(t-t') / k_{\bot}^{d-1+\xi}, where k _⊥=|k _⊥| and k _⊥ is the component of the wave vector, perpendicular to the distinguished direction (‘direction of the flow’)—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (Commun. Math. Phys. 131:381, 1990). The structure functions of the scalar field in the infrared range exhibit scaling behavior with exactly known critical dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular to the flow are essentially different. In contrast to the isotropic Kraichnan’s rapid-change model, the structure functions show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity. On the contrary, the dependence of the internal scale (or diffusivity coefficient) persists in the infrared range. Generalization to the velocity field with a finite correlation time is also obtained. Depending on the relation between the exponents in the energy spectrum E μ k_^^1-e\mathcal{E} \propto k_{\bot}^{1-\varepsilon} and in the dispersion law w μ k_^^2-h\omega\propto k_{\bot}^{2-\eta}, the infrared behavior of the model is given by the limits of vanishing or infinite correlation time, with the crossover at the ray η=0, ε>0 in the ε–η plane. The physical (Kolmogorov) point ε=8/3, η=4/3 lies inside the domain of stability of the rapid-change regime; there is no crossover line going through this point.     

Genesis of Dark Energy: Dark Energy as Consequence of Release and Two-Stage Tracking of Cosmological Nuclear Energy

Recent observations on Type-Ia supernovae and low density (Ω _m =0.3) measurement of matter including dark matter suggest that the present-day universe consists mainly of repulsive-gravity type ‘exotic matter’ with negative-pressure often said ‘dark energy’ (Ω _x =0.7). But the nature of dark energy is mysterious and its puzzling questions, such as why, how, where and when about the dark energy, are intriguing. In the present paper the authors attempt to answer these questions while making an effort to reveal the genesis of dark energy and suggest that ‘the cosmological nuclear binding energy liberated during primordial nucleo-synthesis remains trapped for a long time and then is released free which manifests itself as dark energy in the universe’. It is also explained why for dark energy the parameter w=-\frac23w=-\frac{2}{3} . Noting that w=1 for stiff matter and w=\frac13w=\frac{1}{3} for radiation; w=-\frac23w=-\frac{2}{3} is for dark energy because “−1” is due to ‘deficiency of stiff-nuclear-matter’ and that this binding energy is ultimately released as ‘radiation’ contributing “ +\frac13+\frac{1}{3} ”, making w=-1+\frac13=-\frac23w=-1+\frac{1}{3}=-\frac{2}{3} . When dark energy is released free at Z=80, w=-\frac23w=-\frac{2}{3} . But as on present day at Z=0 when the radiation-strength-fraction (δ), has diminished to δ→0, the w=-1+d\frac13=-1w=-1+\delta\frac{1}{3}=-1 . This, almost solves the dark-energy mystery of negative pressure and repulsive-gravity. The proposed theory makes several estimates/predictions which agree reasonably well with the astrophysical constraints and observations. Though there are many candidate-theories, the proposed model of this paper presents an entirely new approach (cosmological nuclear energy) as a possible candidate for dark energy.     

Space-like hypersurfaces with positive constant r-mean curvature in Lorentzian product spaces

In this paper we obtain a height estimate concerning compact space-like hypersurfaces Σ ⁿ immersed with some positive constant r-mean curvature into an (n + 1)-dimensional Lorentzian product space , and whose boundary is contained into a slice {t} × M ⁿ . By considering the hyperbolic caps of the Lorentz–Minkowski space , we show that our estimate is sharp. Furthermore, we apply this estimate to study the complete space-like hypersurfaces immersed with some positive constant r-mean curvature into a Lorentzian product space. For instance, when the ambient space–time is spatially closed, we show that such hypersurfaces must satisfy the topological property of having more than one end which constitutes a necessary condition for their existence.     

Measurements of the electronic conductivities of In-doped CaZrO<Subscript>3</Subscript> by a DC polarization technique

The following hydrogen and oxygen concentration cells using the oxide protonic conductors, \textCaZ\textr_0.98\textI\textn_0.02\textO_{3 - d} {\text{CaZ}}{{\text{r}}_{0.98}}{\text{I}}{{\text{n}}_{0.02}}{{\text{O}}_{3 - \delta }} and \textCaZ\textr_0.9\textI\textn_0.1\textO_{3 - d} {\text{CaZ}}{{\text{r}}_{0.{9}}}{\text{I}}{{\text{n}}_{0.{1}}}{{\text{O}}_{{3} - \delta }} , as the solid electrolyte were constructed, and their polarization behavior was studied,

Critical Hardy–Lieb–Thirring Inequalities for Fourth-Order Operators in Low Dimensions

This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality

Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε ⁻²|log ε|⁻¹ where Ω is the rotational velocity and the coupling parameter is written as ε ⁻² with ε≪1. Three critical speeds can be identified. At \varOmega = \varOmega_c1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for |loge| << \varOmega < \varOmega_c2 ~ e^-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For \varOmega 3 \varOmega _c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε ⁻²|log ε|⁻¹ vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at \varOmega = \varOmega_c3 ~ e^-2|loge|^-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.     

Spacelike Hypersurfaces with Free Boundary in the Minkowski Space under the Effect of a Timelike Potential

In this paper we consider a variational problem for spacelike hypersurfaces in the (n + 1)-dimensional Lorentz-Minkowski space , whose critical points are hypersurfaces supported in a spacelike hyperplane Π determined by two facts: the mean curvature is a linear function of the distance to Π and the hypersurface makes a constant angle with Π along its boundary. We prove that the hypersurface is rotational symmetric with respect to a straight-line orthogonal to Π and that each (non-empty) intersection with a parallel hyperplane to Π is a round (n − 1)-sphere. A similar result is proved for hypersurfaces trapped between two parallel hyperplanes.     

A fresh look at hadronic light-by-light scattering in the muon g - 2 with the Dyson-Schwinger approach

Using the Dyson-Schwinger and Bethe-Salpeter equations, we calculate the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon a_m\ensuremath a_\mu , using a phenomenological model for the gluon and quark-gluon interaction. We find a_m=(84 ±13)×10^-11\ensuremath a_\mu=(84 \pm 13)\times 10^{-11} for meson exchange, and a_m = (107 ±2 ±46)×10^-11\ensuremath a_\mu = (107 \pm 2 \pm 46)\times 10^{-11} for the quark loop. The former is commensurate with past calculations; the latter much larger due to dressing effects. This leads to a revised estimate of a_m=116 591 865.0(96.6)×10^-11\ensuremath a_\mu=116 591 865.0(96.6)\times 10^{-11} , reducing the difference between theory and experiment to ≃ 1.9s \sigma .     

Phase diagram for the Grover algorithm with static imperfections

We study effects of static inter-qubit interactions on the stability of the Grover quantum search algorithm. Our numerical and analytical results show existence of regular and chaotic phases depending on the imperfection strength e\varepsilon . The critical border e_c\varepsilon_c between two phases drops polynomially with the number of qubits n _q as e_c ~ n_q^-3/2\varepsilon_c \sim n_q^{-3/2} . In the regular phase (e < e_c)(\varepsilon < \varepsilon_c) the algorithm remains robust against imperfections showing the efficiency gain e_c / e\varepsilon_c / \varepsilon for e >~2^-n_q/2\varepsilon \gtrsim 2^{-n_q/2} . In the chaotic phase $(\varepsilon > \varepsilon_c)$(\varepsilon > \varepsilon_c) the algorithm is completely destroyed.     

Magnetocaloric properties of as-quenched Ni50.4Mn34.9In14.7 ferromagnetic shape memory alloy ribbons

The temperature dependences of magnetic entropy change and refrigerant capacity have been calculated for a maximum field change of Δ H=30 kOe in as-quenched ribbons of the ferromagnetic shape memory alloy Ni_50.4Mn_34.9In_14.7 around the structural reverse martensitic transformation and magnetic transition of austenite. The ribbons crystallize into a single-phase austenite with the L2₁-type crystal structure and Curie point of 284 K. At 262 K austenite starts its transformation into a 10-layered structurally modulated monoclinic martensite. The first- and second-order character of the structural and magnetic transitions was confirmed by the Arrott plot method. Despite the superior absolute value of the maximum magnetic entropy change obtained in the temperature interval where the reverse martensitic transformation occurs (|\varDelta S_M^max|=7.2 J kg^-1 K^-1)(|\varDelta S_{\mathrm{M}}^{\max}|=7.2\mbox{ J}\,\mbox{kg}^{-1}\,\mbox{K}^{-1}) with respect to that obtained around the ferromagnetic transition of austenite (|\varDelta S_M^max|=2.6 J kg^-1 K^-1)(|\varDelta S_{\mathrm{M}}^{\max}|=2.6\mbox{ J}\,\mbox{kg}^{-1}\,\mbox{K}^{-1}), the large average hysteretic losses due to the effect of the magnetic field on the phase transformation as well as the narrow thermal dependence of the magnetic entropy change make the temperature interval around the ferromagnetic transition of austenite of a higher effective refrigerant capacity (RC^magn_eff=95J kg^-1\mathrm{RC}^{\mathrm{magn}}_{\mathrm{eff}}=95\mbox{J}\,\mbox{kg}^{-1} versus RC^struct_eff=60J kg^-1)\mathrm{RC}^{\mathrm{struct}}_{\mathrm{eff}}=60\mbox{J}\,\mbox{kg}^{-1}).     

General Dynamical Equations for Dingle’s Space-Times Filled with a Charged Non-perfect Fluid

In this paper we have assumed charged non-perfect fluid as the material content of the space-time. The expression for the “mass function-M(r,y,z,t)” is obtained for the general situation and the contributions from the Ricci tensor in the form of material energy density ρ, pressure anisotropy [\fracp₂+p₃2-p₁][\frac{p_{2}+p_{3}}{2}-p_{1}] , electromagnetic field energy ℰ and the conformal Weyl tensor, viz. energy density of the free gravitational field ε (=\frac-3Y₂4p)(=\frac{-3\Psi_{2}}{4\pi}) are made explicit. This work is an extension of the work obtained earlier by Rao and Hasmani (Math. Today XIIA:71, 1993; New Directions in Relativity and Cosmology, Hadronic Press, Nonantum, 1997) for deriving general dynamical equations for Dingle’s space-times described by this most general orthogonal metric,

Stochastic Porous Media Equations and Self-Organized Criticality: Convergence to the Critical State in all Dimensions

If X = X(t, ξ) is the solution to the stochastic porous media equation in O ì R^d, 1 ￡ d ￡ 3,{\mathcal{O}\subset \mathbf{R}^d, 1\le d\le 3,} modelling the self-organized criticality (Barbu et al. in Commun Math Phys 285:901–923, 2009) and X _c is the critical state, then it is proved that ò^￥₀m(O\O^t₀)dt < ￥,\mathbbP-a.s.{\int^{\infty}_0m(\mathcal{O}{\setminus}\mathcal{O}^t_0)dt<{\infty},\mathbb{P}\hbox{-a.s.}} and lim_t?￥ ò_O|X(t)-X_c|dx = l < ￥, \mathbbP-a.s.{\lim_{t\to{\infty}} \int_\mathcal{O}|X(t)-X_c|d\xi=\ell<{\infty},\ \mathbb{P}\hbox{-a.s.}} Here, m is the Lebesgue measure and O^t_c{\mathcal{O}^t_c} is the critical region {x ? O; X(t,x)=X_c(x)}{\{\xi\in\mathcal{O}; X(t,\xi)=X_c(\xi)\}} and X _c (ξ) ≤ X(0, ξ) a.e. x ? O{\xi\in\mathcal{O}}. If the stochastic Gaussian perturbation has only finitely many modes (but is still function-valued), lim_{t ? ￥} ò_K|X(t)-X_c|dx = 0{\lim_{t \to {\infty}} \int_K|X(t)-X_c|d\xi=0} exponentially fast for all compact K ì O{K\subset\mathcal{O}} with probability one, if the noise is sufficiently strong. We also recover that in the deterministic case ℓ = 0.     

The value of the cosmological constant

We make the cosmological constant, Λ, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and is the requirement that the cosmological wave function possess a classical limit. When applied to the Friedmann metric it requires that the cosmological constant measured today, t _U , be L ~ t_U^-2 ~ 10^-122{\Lambda \sim t_{U}^{-2} \sim 10^{-122}} , as observed. This is the classical value of Λ that dominates the wave function of the universe. Our new field equation determines Λ in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature parameter of the universe is W_k0 o -k/a₀²H²=-0.0055{\Omega _{\mathrm{k0}} \equiv -k/a_{0}^{2}H^{2}=-0.0055} , which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological history.     

Exact Solution for a Class of Random Walk on the Hypercube

A class of families of Markov chains defined on the vertices of the n-dimensional hypercube, Ω _n ={0,1} ⁿ , is studied. The single-step transition probabilities P _n,ij , with i,j∈Ω _n , are given by P_n,ij=\frac(1-a)^d_ij(2-a)ⁿP_{n,ij}=\frac{(1-{\alpha})^{d_{ij}}}{(2-{\alpha})^{n}}, where α∈(0,1) and d _ij is the Hamming distance between i and j. This corresponds to flip independently each component of the vertex with probability \frac1-a2-a\frac{1-{\alpha}}{2-{\alpha}}. The m-step transition matrix P_n,ij^mP_{n,ij}^{m} is explicitly computed in a close form. The class is proved to exhibit cutoff. A model-independent result about the vanishing of the first m terms of the expansion in α of P_n,ij^mP_{n,ij}^{m} is also proved.     

The Transformations from the New Intermediate Entangled State

The new intermediate entangled state |η;θ〉 is proposed by virtue of IWOP technique, which is the common eigenvector of [([^(x)]₁ - [^(x)]₂)cosq-([^(p)]₁ - [^(p)]₂)sinq][(\hat{x}_{1} - \hat{x}_{2})\cos\theta -(\hat{p}_{1} - \hat{p}_{2})\sin\theta ] and [([^(x)]₁ +[^(x)]₂)sinq+ ([^(p)]₁ + [^(p)]₂)cosq][(\hat{x}_{1} +\hat{x}_{2})\sin\theta + (\hat{p}_{1} + \hat{p}_{2})\cos\theta ]. The squeezing transformation operator, Hadamard transformation operator, Fresnel transformation operator and Radon transform operator are constructed by |η;θ〉.     

Photo-Degradation Study of CdTe Nanocrystals by Fluorescence Measurement

The photo-degradation of green-, yellow-, orange- and red-emitting CdTe nanocrystals (NCs) in sol–gel SiO₂ films was investigated quantitatively by measuring the PL efficiency as a function of the irradiation intensity. The degradation behaviors of the NCs depended strongly on the particle size and the surface state. Green- and yellow-emitting CdTe NCs exhibited a red-shifted PL peak wavelength and decreased PL efficiency after irradiation. In contrast, the PL peak wavelength of red-emitting CdTe NCs remained unchange and their PL efficiency increased. Furthermore, the degraded degree of green-emitting NCs depended linearly on the irradiation intensity ( \textrate \textconstant k₁ = ( 1.10±0.04 ) ×10 ^{- 6} \textphoton ) \left( {{\text{rate}}\,{\text{constant}}\,{k_{{1}}} = \left( {{1}.{1}0\pm 0.0{4}} \right) \times {1}{0^{{ - {6}}}}\,{\text{photon}}} \right) , whereas hat of red-emitting NCs showed a quadratic dependence ( \textrate \textconstant k₂ = ( 2.26±0.1 ) ×10 ^{- 26}( \textc\textm² \texts )/\textphoton ) \left( {{\text{rate}}\,{\text{constant}}\,{k_{{2}}} = \left( {{2}.{26}\pm 0.{1}} \right) \times {1}{0^{{ - {26}}}}\left( {{\text{c}}{{\text{m}}^{{2}}}\,{\text{s}}} \right)/{\text{photon}}} \right) at room temperature. This is ascribed to the different surface state of green- and red-emitting CdTe NCs.