Solar system constraints on asymptotically flat IR modified Hořava gravity through light deflection

In this paper, we study the motion of photons around a Kehagias–Sfetsos (KS) black hole and obtain constraints on IR modified Ho?ava gravity without cosmological constant (~Λ _W ). An analytic formula for the light deflection angle is obtained. For a propagating photon, the deflection angle δφ increases with large values of the Ho?ava gravity parameter ω. Under the UV limit \({\omega \longrightarrow \infty}\), deflection angle reduces to the result of usual Schwarzschild case, 4GM/R. It is also found that with increasing scale of astronomical observation system the Ho?ava–Lifshitz gravity should satisfy |ω M ²| > 1.1725 × 10^?16 with 12% precision for Earth system, |ω M ²| > 8.27649 × 10^?17 with 17% precision for Jupiter system and |ω M ²| > 8.27650 × 10^?15 with 0.17% precision for solar system.     

Über die mathematische Struktur und eine Klasse strenger Lösungen der Jordanschen erweiterten Gravitationstheorie

Theβ-α. angular correlationW(Θ)=1+a cosΘ+cos² Θ of the decay of Li⁸ was measured for average electron energies ofE _β ≈5 MeV, 11 MeV and 12 MeV. The experiment yields an anisotropyA=(0·0036±0·0011)·E _β (MeV)^?1. This result is in good agreement with the results of the other groups. The measurements were performed in a counting chamber separated from the activation room simultaneously for two sealer positionsΘ=90° and 180°. The result is discussed in terms of the CVC-theory, taking into account the second forbidden Fermi-matrixelements (‖M1‖) and (‖E2‖).     

The signal photon flux,background photons and shot noise in electromagnetic response of high-frequency relic gravitational waves

On the basis of the electromagnetic response of high frequency relic gravitational waves (HFRGWs), we research on more accurate calculation of signal (i.e. transverse perturbative photon flux (PPF)) and background photons flux (BPF) in the sycro-resonance electromagnetic system, which consists of Gaussian beam (GB), a static magnetic field and fractal membranes. According to the relationship between frequency of gravitational waves and its dimensionless amplitude, we focus on the HFRGWs with ν _g  = 2.9 GHz, h ~ 10^?30 in the pre-big bang and quintessential inflationary models. The results show the peak value of the transverse BPF (~ 10²⁰ s^?1) is around |x| = 0.08 m, where |x| is the transverse distance to the longitudinal symmetrical surface of the GB, while the maximum transverse PPF always appears at x = 0 (\({N^{(1)}_{x} \sim 2.60\times10^{2}\,{\rm s}^{-1}}\) with the optimal phase difference between the GB and the resonant component of the HFRGWs δ = (n + 0.9)π, n = 0, 1, 2 . . .). However, the observable PPF should be ~ 1.19 × 10² s^?1 because of the stochastic nature of the HFRGWs’ phase. Since the decay speed of BPF is much quicker than PPF, it is hopeful to figure out the signal in some optimal regions. Moreover, we compare the decay speed of BPF and PPF in nature mode, and find the threshold value of x where PPF exceeds to BPF. It demonstrates that the limitation of our detection sensitivity comes from the strength of PPF rather than swamping by BPF. On the other hand, with the fractal membrane, the comparison between BPF and PPF provides the optimal detection area \({x\in[0.28,1]}\) m. In addition, through the calculation of shot noise and conservative estimation, we find that our sensitivity is h = 10^?26 in 4 months signal accumulate time.     

The Boundary Control Approach to the Titchmarsh-Weyl <Emphasis Type="Italic">m</Emphasis>–Function. I. The Response Operator and the <Emphasis Type="Italic">A</Emphasis>–Amplitude

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A?amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m?function associated with the Schrödinger operator H = ?? _x ²  + q(x) on L ₂(0, ∞) with Dirichlet boundary condition at x = 0.     

A modification of Einstein–Schrödinger theory that contains both general relativity and electrodynamics

We modify the Einstein–Schrödinger theory to include a cosmological constant Λ _z which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant Λ _z is assumed to be nearly cancelled by Schrödinger’s cosmological constant Λ _b which multiplies the nonsymmetric fundamental tensor, such that the total Λ =  Λ _z +  Λ _b matches measurement. The resulting theory becomes exactly Einstein–Maxwell theory in the limit as |Λ _z | → ∞. For |Λ _z | ~ 1/(Planck length)² the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10^?16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein–Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein–Infeld–Hoffmann (EIH) equations of motion match the equations of motion for Einstein–Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein–Schrödinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner–Nordström solution except for additional terms which are ~10^?66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein–Maxwell theory.     

Weyl’s Type Estimates on the Eigenvalues of Critical Schrödinger Operators

We consider on a bounded domain \(\Omega \subset {\mathbb{R}}^N\) , the Schrödinger operator ? Δ ? V supplemented with Dirichlet boundary solutions. The potential V is either the critical inverse square potential V(x) = (N ? 2)²/4|x|^?2 or the critical borderline potential V(x) =  (1/4)dist(x, ?Ω)^?2. We present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator in each case, based on recent results on improved Hardy–Sobolev type inequalities.     

Analytic Structure of Many-Body Coulombic Wave Functions

We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic many-particle systems. We prove the following: Let ψ(x) with \({{\bf x} = (x_{1},\dots, x_{N})\in \mathbb {R}^{3N}}\) denote an N-electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a coalescence point, for which x ₁ = 0 and the other electron coordinates do not coincide, and differ from 0, ψ can be represented locally as ψ(x) = ψ ⁽¹⁾(x) + |x ₁|ψ ⁽²⁾(x) with ψ ⁽¹⁾, ψ ⁽²⁾ real analytic. A similar representation holds near two-electron coalescence points. The Kustaanheimo-Stiefel transform and analytic hypoellipticity play an essential role in the proof.     

Messungen der Winkelverteilung der 440 keV-γ-Strahlung aus der Reaktion23Na (p,p′ γ)23Na in den ResonanzenE p =1281 keV undE p =1456 keV

The angular distribution of the 440 keV-γ-radiation following the reaction²³Na(p, p′)²³Na has been measured. The experimental results areW(Θ)=1-(0,147±0,05)P ₂(cosΘ) in the resonanceE _p =1281 keV andW(Θ)=1-(0,099 ± 0,06)P ₂(cosΘ) in the resonanceE _p =1456 keV.     

Angular correlation measurements in the Be9(d,p, γ)Be10 reaction

Thep-γ angular correlations in the Be⁹(d, p, γ)Be¹⁰ reaction have been measured in the reaction plane atE _d =1.3, 1.5, 1.9, 2.3 and 2.45 MeV for proton anglesθ _p =35°, 80° and 120°. The anisotropy of the angular correlations measured forθ _p =35° is independent of deuteron energy. A systematic shift of the symmetry axis from the recoil direction has been observed. The shift is 20.5° at E_d=2.45 MeV. The anisotropy decreases with increasing proton angle and vanishes atθ _p =120°.     

Multiplicative Lévy noise in bistable systems

Stochastic motion in a bistable, periodically modulated potential is discussed. Thesystem is stimulated by a white noise increments of which have a symmetric stable Lévydistribution. The noise is multiplicative: its intensity depends on the process variablelike |x|^?θ . The Stratonovich and Itôinterpretations of the stochastic integral are taken into account. The mean first passagetime is calculated as a function of θ for different values of thestability index α and size of the barrier. Dependence of the outputamplitude on the noise intensity reveals a pattern typical for the stochastic resonance.Properties of the resonance as a function of α, θ andsize of the barrier are discussed. Both height and position of the peak strongly dependson θ and on a specific interpretation of the stochastic integral.     

On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

Typical Gibbs Configurations for the 1d Random Field Ising Model with Long Range Interaction

We study one–dimensional Ising spin systems with ferromagnetic, long–range interaction decaying as n ^?2+α , \({\alpha \in [0,\frac 12]}\), in the presence of external random fields. We assume that the random fields are given by a collection of symmetric, independent, identically distributed real random variables, which are gaussian or subgaussian with variance θ. We show that when the temperature and the variance of the randomness are sufficiently small, with overwhelming probability with respect to the random fields, the typical configurations, within intervals centered at the origin whose length grow faster than any power of θ ^?1, are intervals of + spins followed by intervals of ? spins whose typical length is \({ \simeq\,\theta^{-\frac{2}{(1-2\alpha)}}}\) for 0 ≤ α < 1/2 and between \({ e^{\frac{1}{\theta}}}\) and \({e^{\frac 1 {\theta^{2}}}}\) for α = 1/2.     

Ion dynamics in methylcellulose–LiBOB solid polymer electrolytes

A polymer electrolyte system comprising methylcellulose (MC) as the host polymer and lithium bis(oxalato) borate (LiBOB) as the lithium ion source has been prepared via the solution cast technique. The electrolyte with the highest conductivity of 2.79 μS cm^?1 has a composition of 75 wt% MC–25 wt% LiBOB. The mobile ion concentration (n) in this sample was estimated to be 5.70?×?10²⁰ cm^?3. A good correlation between ionic conductivity, dielectric constant, and free ion concentration has been observed. The ratio of mobile ion number density (n) at a particular temperature to the concentration n ₀ of free ions at T?=?∞ (n/n ₀) and the power law exponents (s) exhibit opposite trends when varied with salt concentration.     

On the Negative Spectrum of the Two-Dimensional Schrödinger Operator with Radial Potential

For a two-dimensional Schrödinger operator H _{α V}  = ?Δ ?αV with the radial potential V(x) = F(|x|), F(r) ≥ 0, we study the behavior of the number N _?(H _{α V} ) of its negative eigenvalues, as the coupling parameter α tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth N _?(H _{α V} ) = O(α) and for the validity of the Weyl asymptotic law.     

Photoinduced semiconductor-metal phase transition in a peierls system

The dynamical equation for the order parameter of the metal-semiconductor phase transition, as well as the kinetic equation for the density of nonequilibrium electron-hole pairs of a Peierls system in a light field, has been derived. An expression for the time τ of the nonthermal photoinduced semiconductor-metal phase transition has been obtained from these equations for the case of an ultrashort light pulse. It has been shown that, to initiate the phase transition, the energy density W of the light pulse must be higher than the critical value W _c. The W _c, τ, and optical absorption coefficient γ₀ that are calculated in the framework of the proposed model are in agreement with the experimental data (W _c ≈ 12 mJ/cm², τ ≈ 75 fs, and γ₀ ≈ 10⁵ cm^?1) on the irradiation of a vanadium dioxide film by a laser pulse with a duration of τ_p ≈ 15 fs, a photon energy of ?θ₀ = 1.6 eV, and an energy density of W = 50 mJ/cm².     

High-energy sub-nanosecond optical pulse generation with a semiconductor laser diode for pulsed TOF laser ranging utilizing the single photon detection approach

Bulk and quantum well laser diodes with a large equivalent spot size of d _a /Γ _a  ≈ 3 µm and stripe width/cavity length of 30 µm/3 mm were realized and tested. They achieved a pulse energy and pulse length of the order of ~1 nJ and ~100 ps, respectively, with a peak pulse current of 6–8 A and a current pulse width of 1 ns. The 2D characteristics of the optical output power versus wavelength and time were also analyzed with a monochromator/streak camera set-up. The far-field characteristics were studied with respect to the time-homogeneity and energy distribution. The feasibility of a laser diode with a large equivalent spot size in single photon detection based laser ranging was demonstrated to a non-cooperative target at a distance of a few tens of meters.     

Potential dependent EIS investigation of FeF<Subscript>3</Subscript> · 0.33H<Subscript>2</Subscript>O/C nano-composite synthesized by one-step solid-state method

To further study the lithium ion transportation behavior of cathode material FeF₃?·?0.33H₂O/C synthesized by a simple one-step chemico-mechanical method, the Electrochemical impedance spectrum (EIS) measured at series of open-circuit voltages were investigated in detail. The results showed that the EIS profiles of FeF₃?·?0.33H₂O/C materials were strongly potential dependent. The equivalent circuit parameters obtained by fitting the experimental data as a function of open-circuit voltage (OCV) level were depicted. The ohmic resistance R0, solid electrolyte inter-phase resistance R _SEI, electronic conduction resistance R _E, charge transfer resistance R _R, and Q parameter of CPE circuit characteristic of Li⁺ diffusion Q _diff all showed a sudden change at the OCV level 2.5 V. Ohmic resistance R0 had a relatively lower resistance of ca. 10 Ω above OCV level 2.5 V and a higher resistance of about 40 Ω below 2.5 V. Similar situation was also observed for R _SEI, which was around 20 Ω above 2.5 V and soared up quickly when the equilibrium potential fell below 2.5 V. Similar variations were also observed for R _E and R _R. A high resistance of ca. 410 and 520 Ω was obtained at OCV level 2.05 V, respectively. Q _diff showed a convex profile, which matched the variation of Li⁺ diffusion coefficient well.     

Diffraction enhancement effect and new possibilities of measuring the electric charge of the neutron and its inertial-to-gravitational mass ratio

Diffraction enhancement of small effects affecting a neutron undergoing Laue diffraction at Bragg angles θ _B close to 90° is predicted and experimentally observed. The enhancement is due to the delay of the neutron inside the crystal during diffraction and is proportional to tan² θ _B. As a result, the diffraction enhancement factor may be as large as ～10⁸–10⁹. On this basis, a new method is proposed for searching for the electric charge of the neutron and for measuring the ratio of its inertial mass m _i to the gravitational mass m _G . It is shown that the accuracy of the neutron charge measurement can be improved by more than two orders of magnitude in relation to the present-day accuracy and that the ratio m _i /m _G can be measured to an precision of σ(m _i /m _G ) ～ 10^?6.     

Double Chooz project: Status of a reactor experiment aimed at searches for neutrino oscillations

Double Chooz is an experiment that is devoted to searches for reactor-antineutrino oscillations at the CHOOZ nuclear power plant. This project is aimed at measuring the unknown mixing angle θ ₁₃. It is assumed that the value of θ ₁₃ will be extracted from an analysis of the distortion of the antineutrino spectra obtained in relative measurements at two distances from the nuclear reactors by means of two identical detectors. The method makes it possible to minimize systematic errors of the experiment and to improve the sensitivity to the sought parameter. To date, the most stringent constraint on the parameter θ ₁₃ was obtained from the CHOOZ experiment in 1995–1997 [sin²(2θ ₁₃) < 0.19, with the difference of the squares of the neutrino masses being Δm ₁₃ ² = 2.5 × 10^?3 eV²].