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

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 .     

Electromagnetic structure of W± bosons in the e–e+ → W+W– reaction

A model-independent analysis of anomalous gauge coupling constants of W ^± bosons is presented and the corresponding restrictions on them and on the electromagnetic characteristics of W ^± bosons following from the experiments on measuring the e⁺ e^- ? W⁺ W^- ? ( e

Roy–Steiner equations for <Emphasis Type="Italic">γγ</Emphasis>→<Emphasis Type="Italic">ππ</Emphasis>

Starting from hyperbolic dispersion relations, we derive a system of Roy–Steiner equations for pion Compton scattering that respects analyticity, unitarity, gauge invariance, and crossing symmetry. It thus maintains all symmetries of the underlying quantum field theory. To suppress the dependence of observables on high-energy input, we also consider once- and twice-subtracted versions of the equations, and identify the subtraction constants with dipole and quadrupole pion polarizabilities. Based on the assumption of Mandelstam analyticity, we determine the kinematic range in which the equations are valid. As an application, we consider the resolution of the γγ→ππ partial waves by a Muskhelishvili–Omnès representation with finite matching point. We find a sum rule for the isospin-two S-wave, which, together with chiral constraints, produces an improved prediction for the charged-pion quadrupole polarizability (a₂-b₂)^p±=(15.3±3.7)×10^-4(\alpha_{2}-\beta_{2})^{\pi^{\pm}}=(15.3\pm3.7)\times 10^{-4} fm⁵. We investigate the prediction of our dispersion relations for the two-photon coupling of the σ-resonance Γ _σγγ . The twice-subtracted version predicts a correlation between this width and the isospin-zero pion polarizabilities, which is largely independent of the high-energy input used in the equations. Using this correlation, the chiral perturbation theory results for pion polarizabilities, and our new sum rule, we find Γ _σγγ =(1.7±0.4) keV.     

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.     

On parity-violating three-nucleon interactions and the predictive power of few-nucleon EFT at very low energies

We address the typical strengths of hadronic parity-violating three-nucleon interactions in “pion-less” Effective Field Theory (EFT) in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we conclude that no such interactions are needed at leading order, O(eQ^-1)\ensuremath {O}(\epsilon Q^{-1}) . The only two distinct parity-violating three-nucleon structures with one derivative mix ²S_\frac12\ensuremath ^2S_{\frac{1}{2}} and ²P_\frac12\ensuremath ^2P_{\frac{1}{2}} waves with iso-spin transitions D \Delta I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order, O(eQ⁰)\ensuremath {O}(\epsilon Q^0) . This observation is based on the approximate realisation of Wigner’s combined SU(4) spin-isospin symmetry in the two-nucleon system, even when effective-range corrections are included. Parity-violating three-nucleon interactions thus only appear beyond next-to-leading order. This guarantees renormalisability of the theory to that order without introducing new, unknown coupling constants and allows the direct extraction of parity-violating two-nucleon interactions from three-nucleon experiments.     

Relationship between capture coefficient and capture cross-section: Average velocity of a maxwellian distribution of carriers in a medium with an anisotropic effective mass tensor

The capture cross section of a trapping or recombination center for a charge carrier has been defined as the quotient of the capture coefficient and the average thermal velocity of the carrier distribution. For a Maxwellian distribution in a semiconductor band with an ellipsoidal effective mass tensor, this average velocity can be expressed as

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.     

D?→Dπ and D?→Dγ decays: axial coupling and magnetic moment of D? meson

The axial coupling and the magnetic moment of D ^∗-meson or, more specifically, the couplings g_D^*Dpg_{D^{\ast}D\pi} and g_D^*Dgg_{D^{\ast}D\gamma }, encode the non-perturbative QCD effects describing the decays D ^∗→Dπ and D ^∗→Dγ. We compute these quantities by means of lattice QCD with N _f=2 dynamical quarks, by employing the Wilson (“clover”) action. On our finer lattice (a≈0.065 fm) we obtain g_D^*Dp⁺=20±2g_{D^{\ast}D\pi^{+}}=20\pm2, and g_{D^*0 D⁰g}=2.0±0.6 GeV^-1g_{D^{\ast0} D^{0}\gamma}=2.0\pm 0.6~{\rm GeV}^{-1}. This is the first determination of g_{D^*0 D⁰g}g_{D^{\ast0} D^{0}\gamma} on the lattice. We also provide a short phenomenological discussion and the comparison of our result with experiment and with the results quoted in the literature.     

Dielectric spectroscopy study of the new compound [C<Subscript>12</Subscript>H<Subscript>17</Subscript>N<Subscript>2</Subscript>]<Subscript>2</Subscript>CdCl<Subscript>4</Subscript>

The temperature dependence of the electrical conductivity of the compound 2,4,4-trimethyl-4,5-dihydro-3H-benzo[b] [1,4] diazepin-1-ium tetrachlorocadmiate in the different phases follows the Arrhenius law. The imaginary part of the permittivity constant is analyzed with the Cole–Cole formalism. In the temperature range 348–394 K, the activation energy of conductivity obtained from complex permittivity in regions I and II are, respectively, 1.03 and 0.33 eV, and E _m (in regions I and II are, respectively, 0.97 and 0.36 eV) obtained from the modulus spectra is close, suggesting that the ion transport is probably due to a hopping mechanism. The Kohlrausch–Williams–Watts function, j(t) = exp( - ( \fractt_\textKWW )^b ) \varphi (t) = \exp \left( { - {{\left( {\frac{t}{{{\tau_{\text{KWW}}}}}} \right)}^\beta }} \right) , and the coupling model are utilized for analyzing electric modulus at various temperatures. The decreasing of β at 373 K is due to approaching the temperatures of change in the conduction mechanism of the sample.     

PV Cohomology of the Pinwheel Tilings, their Integer Group of Coinvariants and Gap-Labeling

In this paper, we first remind how we can see the “hull” of the pinwheel tiling as an inverse limit of simplicial complexes (Anderson and Putnam in Ergod Th Dynam Sys 18:509–537, 1998) and we then adapt the PV cohomology introduced in Savinien and Bellissard (Ergod Th Dynam Sys 29:997–1031, 2009) to define it for pinwheel tilings. We then prove that this cohomology is isomorphic to the integer Čech cohomology of the quotient of the hull by S ¹ which let us prove that the top integer Čech cohomology of the hull is in fact the integer group of coinvariants of the canonical transversal Ξ of the hull. The gap-labeling for pinwheel tilings is then proved and we end this article by an explicit computation of this gap-labeling, showing that m^t ( C(X,\mathbb Z) ) = \frac1264\mathbb Z [ \frac15]{\mu^t \left( C(\Xi,\mathbb {Z}) \right) = \frac{1}{264}\mathbb {Z} \left [ \frac{1}{5}\right ]}.     

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.     

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier–Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e^|k|/k_d{{{\rm e}^{|k|/k_{\rm d}}}} at high wavenumbers |k|. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e^{-C(k/k_d) ln(|k|/k_d)}{{{\rm e}^{-C(k/k_{\rm d})\,{\rm ln}(|k|/k_{\rm d})}}} for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C _* = 1/ ln 2. The same behavior with a universal constant C _* is conjectured for the Navier–Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier–Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.     

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.     

Kraus Operator-Sum Representation and Time Evolution of Distribution Functions in Phase-Sensitive Reservoirs

Using the thermal entangled state representation 〈η|, we examine the master equation (ME) describing phase-sensitive reservoirs. We present the analytical expression of solution to the ME, i.e., the Kraus operator-sum representation of density operator ρ is given, and its normalization is also proved by using the IWOP technique. Further, by converting the characteristic function χ(λ) into an overlap between two “pure states” in enlarged Fock space, i.e., χ(λ)=〈η _=−λ |ρ|η ₌₀〉, we consider time evolution of distribution functions, such as Wigner, Q- and P-function. As applications, the photon-count distribution and the evolution of Wigner function of photon-added coherent state are examined in phase-sensitive reservoirs. It is shown that the Wigner function has a negative value when kt\leqslant\frac 12ln( 1+m_￥) \kappa t\leqslant\frac {1}{2}\ln ( 1+\mu_{\infty}) is satisfied, where μ _∞ depends on the squeezing parameter |M|² of environment, and increases as the increase of |M|.     

Striped Periodic Minimizers of a Two-Dimensional Model for Martensitic Phase Transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Müller (Philos Mag A 66(5):697–715, 1992), is defined by the following functional:

The model-independent analysis indications for spectroscopy of scalar mesons. Proof for the K0* (900)

In a model-independent approach the data on ππ → ππ, K $ \bar K $ \bar K , ηη, ηη′ in the I ^G J ^PC = 0⁺0⁺⁺ channel and on the Kπ scattering in the $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) channel are analyzed jointly for studying the status and QCD nature of the f ₀- and the K*₀-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q $ \bar q $ \bar q ). In the Kπ-scattering data analysis, the proof for the K*₀(900) is given.     

Dielectric relaxation and ionic conductivity studies of Ag<Subscript>2</Subscript>ZnP<Subscript>2</Subscript>O<Subscript>7</Subscript>

The complex impedance of the Ag₂ZnP₂O₇ compound has been investigated in the temperature range 419–557 K and in the frequency range 200 Hz–5 MHz. The Z′ and Z′ versus frequency plots are well fitted to an equivalent circuit model. Dielectric data were analyzed using complex electrical modulus M* for the sample at various temperatures. The modulus plot can be characterized by full width at half-height or in terms of a non-exponential decay function f( \textt ) = exp( - \textt/t )^b \phi \left( {\text{t}} \right) = \exp {\left( { - {\text{t}}/\tau } \right)^\beta } . The frequency dependence of the conductivity is interpreted in terms of Jonscher’s law: s( w) = s_\textdc + \textAwⁿ \sigma \left( \omega \right) = {\sigma_{\text{dc}}} + {\text{A}}{\omega^n} . The conductivity σ _dc follows the Arrhenius relation. The near value of activation energies obtained from the analysis of M″, conductivity data, and equivalent circuit confirms that the transport is through ion hopping mechanism dominated by the motion of the Ag⁺ ions in the structure of the investigated material.     

An ab initio molecular dynamics study of ionic conductivity in hexagonal lithium lanthanum titanate oxide La0.5Li0.5TiO3

To date, the fastest lithium ion-conducting solid electrolytes known are the perovskite-type ABO₃ oxide, with A = Li, La and B = Ti, lithium lanthanum titanate (LLTO) Li_3x La_{( 2 \mathord}