<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity constraints from gravitational waves

The recent LIGO observation sparked interest in the field of gravitational wave signals. Besides the gravitational wave observation the LIGO collaboration used the inspiraling black hole pair to constrain the graviton mass. Unlike general relativity, f(R) theories have a characteristic non-zero mass graviton. We apply this constraint on the graviton mass to viable f(R) models in order to find the effects on model parameters. We find it possible to constrain the parameter space with these gravity wave based observations. We consider the popular Hu–Sawicki model as a case study and find an appropriate parameter bracket. The result generalizes to other f(R) theories and can be used to constrain the parameter space.     

Low-temperature contribution to the resonant tunneling conductance of a disordered N–I–N junction

A formula for the contribution ΔG ^res(T) to the resonant tunneling conductance of the N–I–N junction (where N is a normal metal and I is an insulator) with a weak (low impurity concentrations) structural disorder in the I layer from the low-temperature “smearing” electron Fermi surfaces in its N shores is obtained. It is shown that the temperature dependence ΔG ^res(T) in such a “dirty” junction qualitatively differs from the corresponding dependence ΔG ₀(T) in a “pure” (without resonant impurities in the I layer) junction: ΔG ^res(T) < 0, d(ΔG ^res)/dT < 0; ΔG ₀(T) > 0, d(ΔG ₀)/dT > 0, which can serve as an experimental test of the presence of impurity tunneling resonances in the disordered I layer.     

Das Kernquadrupolmoment des Mn55

With a recording photoelectric Fabry-Perot spectrometer and an atomic-beam light source the hyperfine structure of the Mn I-resonance linesλ=4031 Å,λ=4033 Å,λ=4034 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁶ P _7/2,5/2,3/2 ⁰)and of the inter-combination linesλ=5395 Å andλ=5433 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁸ P _7/2,5/2 ⁰) was measured. Furthermore the resonance lines have been measured with a pulsed atomic-beam in absorption. In this case the quotient (I ₀(ν)?I(ν))/I ₀(ν) was recorded, whereI(ν)=I ₀(ν) exp(?α(ν)d) is the observed intensity with absorption andI ₀(ν) the intensity of the light source. From the hyperfine structure splitting the value of the electric quadrupole moment of Mn⁵⁵ was derived to be:Q(Mn⁵⁵)=+(0.35±0.05)·10^?24 cm².     

<Emphasis Type="Italic">O</Emphasis>(1) eV sterile neutrino in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We refer [1] to the role of an additional O(1) eV sterile neutrino in modified gravity models. We find parameter constraints in particular f(R) gravity model using following up-to-dated cosmological data: measurements of the cosmic microwave background (CMB) anisotropy, the CMB lensing potential, the baryon acoustic oscillations (BAO), the cluster mass function and the Hubble constant. It was obtained for the sterile neutrino mass 0.47 eV < m _ν,sterile < 1 eV (2σ) assuming that the sterile neutrinos are thermalized and the active neutrinos are massless, not significantly larger than in the standard cosmology model within the same data set: 0.45 eV < m _ν,sterile < 0.92 eV (2σ). But, if the mass of sterile neutrino is fixed and equals ≈ 1.5 eV according to various anomalies in neutrino oscillation experiments, f(R) gravity is much more consistent with observation data than the CDM model.     

Probing the sign-changeable interaction between dark energy and dark matter with current observations

We consider the models of vacuum energy interacting with cold dark matter in this study, in which the coupling can change sigh during the cosmological evolution. We parameterize the running coupling b by the form b(a) = b_0 a + b_e(1-a), where at the earlytime the coupling is given by a constant b_e and today the coupling is described by another constant b_0. We explore six specific models with(i) Q = b(a)H_0ρ_0,(ii) Q = b(a)H_0ρ_(de),(iii) Q = b(a)H_0ρ_c,(iv) Q = b(a)Hρ_0,(v) Q = b(a)Hρ_(de), and(vi) Q = b(a)Hρ_c.The current observational data sets we use to constrain the models include the JLA compilation of type Ia supernova data, the Planck 2015 distance priors data of cosmic microwave background observation, the baryon acoustic oscillations measurements,and the Hubble constant direct measurement. We find that, for all the models, we have b_0 0 and b_e 0 at around the 1σ level,and b_0 and b_e are in extremely strong anti-correlation. Our results show that the coupling changes sign during the evolution at about the 1σ level, i.e., the energy transfer is from dark matter to dark energy when dark matter dominates the universe and the energy transfer is from dark energy to dark matter when dark energy dominates the universe.     

Extremal points for fractional boundary value problems

This article is concerned with characterizing the first extremal point, b₀, for a Riemann–Liouville fractional boundary value problem, D^α₀₊y + p(t)y = 0, 0 < t < b, y(0) = y′(0) = y″(b) = 0, 2 < α ≤ 3, by applying the theory of u₀-positive operators with respect to a suitable cone in a Banach space. The key argument is that a mapping, which maps a linear, compact operator, depending on b to its spectral radius, is continuous and strictly increasing as a function of b. Furthermore, an application to a nonlinear case is given.     

Diagnosing holographic type dark energy models with the Statefinder hierarchy,composite null diagnostic and <Emphasis Type="Italic">w</Emphasis>-<Emphasis Type="Italic">w′</Emphasis> pair

The main purpose of this work is to distinguish various holographic type dark energy (DE) models, including the ΛHDE, HDE, NADE, and RDE model, by using various diagnostic tools. The first diagnostic tool is the Statefinder hierarchy, in which the evolution of Statefinder hierarchy parmeter S ⁽¹⁾ ₃(z) and S ⁽¹⁾ ₄(z) are studied. The second is composite null diagnostic (CND), in which the trajectories of {S ⁽¹⁾ ₃, ?} and {S ⁽¹⁾ ₄, ?} are investigated, where ? is the fractional growth parameter. The last is w-w′ analysis, where w is the equation of state for DE and the prime denotes derivative with respect to lna. In the analysis we consider two cases: varying current fractional DE density Ω _de0 and varying DE model parameter C. We find that: (1) both the Statefinder hierarchy and the CND have qualitative impact on ΛHDE, but only have quantitative impact on HDE. (2) S ⁽¹⁾ ₄ can lead to larger differences than S ⁽¹⁾ ₃, while the CND pair has a stronger ability to distinguish different models than the Statefinder hierarchy. (3) For the case of varying C, the {w,w′} pair has qualitative impact on ΛHDE; for the case of varying Ω _de0, the {w, w′} pair only has quantitative impact; these results are different from the cases of HDE, RDE, and NADE, in which the {w,w′} pair only has quantitative impact on these models. In conclusion, compared with HDE, RDE, and NADE, the ΛHDE model can be easily distinguished by using these diagnostic tools.     

Testing the Distance-Duality Relation from Hubble,Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D _L(1+z)^?2/D _A by combining the angular diameter distance D _A(or comoving distances D _c ) with the luminosity distance D _L. The D _A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D _c are obtained from Hubble parameter data and D _L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z?z _SNe|<0.005, and method B: reconstructing the D _L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D _L associated with the redshits of the observed D _A or D _c. Four parameterizations for η(z), i.e., η(z)=1+η ₀ z, η(z)=1+η ₀ z/(1+z), η(z)=1+η ₀ z/(1+z)² and η(z)=1?η ₀ ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.     

Surface Microparticles in Liquid Helium. Quantum Archimedes’ Principle

Deviations from Archimedes’ principle for spherical molecular hydrogen particles with the radius R₀ at the surface of ⁴He liquid helium have been investigated. The classical Archimedes’ principle holds if R₀ is larger than the helium capillary length L_cap ? 500 μm. In this case, the elevation of a particle above the liquid is h₊ ~ R₀. At 30 μm < R₀ < 500 μm, the buoyancy is suppressed by the surface tension and h₊ ~ R³₀/L²_cap. At R₀ < 30 μm, the particle is situated beneath the surface of the liquid. In this case, the buoyancy competes with the Casimir force, which repels the particle from the surface deep into the liquid. The distance of the particle to the surface is h_- ~ R^5/3_c/R^2/3₀ if R₀ > R_c. Here, \({R_c} \cong {\left( {\frac{{\hbar c}}{{\rho g}}} \right)^{1/5}} \approx 1\), where ? is Planck’s constant, c is the speed of light, g is the acceleration due to gravity, and ρ is the mass density of helium. For very small particles (R₀ < R_c), the distance h_ to the surface of the liquid is independent of their size, h_ = R_c.     

Graviton mass,quintessence, and oscillatory character of Universe evolution

On the basis of the field relativistic theory of gravity, an upper limit on the graviton mass, m_g≤1.6×10^?66 g, is obtained at a 95% C.L. by using data on the density parameter Ω_tot. Within one standard deviation, the probable value of the graviton mass is m_g=1.3×10^?66 g. It is indicated that, according to the relativistic theory of gravity, the existence of quintessence is needed for explaining the accelerated expansion of the Universe. Experimental data on the age of the Universe and on the density of cold matter make it possible to determine the allowed interval of the parameter ν that enters into the equation of state for the quintessence and to indicate the instants of time that correspond to the beginning and cessation of the era of accelerated expansion, as well as the maximum-expansion time, which corresponds to the half-period of the oscillatory evolution of the Universe.     

Temperature Dependence of the Thermal Conductivity of a Trapped Dipolar Bose-Condensed Gas

The thermal conductivity of a trapped dipolar Bose condensed gas is calculated as a function of temperature in the framework of linear response theory. The contributions of the interactions between condensed and noncondensed atoms and between noncondensed atoms in the presence of both contact and dipole-dipole interactions are taken into account to the thermal relaxation time, by evaluating the self-energies of the system in the Beliaev approximation. We will show that above the Bose-Einstein condensation temperature (T?>?T _BEC ) in the absence of dipole-dipole interaction, the temperature dependence of the thermal conductivity reduces to that of an ideal Bose gas. In a trapped Bose-condensed gas for temperature interval k _B T?<<?n ₀ g _B , E _p ?<<?k _B T (n ₀ is the condensed density and g _B is the strength of the contact interaction), the relaxation rates due to dipolar and contact interactions between condensed and noncondensed atoms change as \( {\tau}_{dd12}^{-1}\propto {e}^{-E/{k}_BT} \) and τ _c12?∝?T ^?5, respectively, and the contact interaction plays the dominant role in the temperature dependence of the thermal conductivity, which leads to the T ^?3 behavior of the thermal conductivity. In the low-temperature limit, k _B T?<<?n ₀ g _B , E _p ?>>?k _B T, since the relaxation rate \( {\tau}_{c12}^{-1} \) is independent of temperature and the relaxation rate due to dipolar interaction goes to zero exponentially, the T ² temperature behavior for the thermal conductivity comes from the thermal mean velocity of the particles. We will also show that in the high-temperature limit (k _B T?>?n ₀ g _B ) and low momenta, the relaxation rates \( {\tau}_{c12}^{-1} \) and \( {\tau}_{dd12}^{-1} \) change linearly with temperature for both dipolar and contact interactions and the thermal conductivity scales linearly with temperature.     

Elastische und unelastische Streuung von Elektronen an Gasen

The theoretical differential cross section for the elastic scattering and for the excitation of optical transitions in helium by electron impact has been refined in Born approximation by use of the two parameter Eckart eigenfunction for the ground state and for the excited states. The angular distributions of 25 kev electrons scattered elastically and inelastically by helium were measured in the angular range 2·3·10^?4≦?≦4·10^?2. The intensity distribution of the elastically scattered electrons is in accordance with the theoretical curve for?>7·10^?3 and is disturbed at smaller angles by the primary beam. Normalization of the experimental values to the theoretical elastic differential cross section leads to agreement between the experimental differential cross section for the excitation of the 2¹ P and 3¹ P state and the scattering formulae given in this paper. There are small systematic deviations (<20%) for the 2¹ P differential cross section in the angular range 3·10^?3<?<1·10^?2 only. The oscillator strength of these two transitions has been determined from the scattering measurements:f ₂₁=0·312±0·04 andf ₃₁=0·0898±0·006.     

Dielectric relaxations,magnetodielectric and magnetoelectric interactions in Bi0.6La0.4MnO3 ceramics

Complex permittivity ε*/ε₀ = ε′/ε₀–iε″/ε₀ of the bismuth–lanthanum manganite Bi_0.6La_0.4MnO₃ ceramics has been measured in the temperature range of 10–220 K at frequencies f = 20–10⁶ Hz and magnetic inductions B = 0–0.846 T. At a temperature of 80 K, the spectra ε′/ε₀(t) and ε″/ε₀(t) demonstrate the dielectric relaxation that is a superposition of contributions of several relaxation processes, each of which is dominant in its frequency range: I (f < 10³ Hz, II (10³ < f < 10⁵ Hz), and III (10⁵ < f < 10⁶ Hz). In the range of 10–120 K, anomalous behavior of ε′/ε₀(T) and ε″/ε₀(T) is observed near the temperature of the transition from the paramagnetic to ferromagnetic phase and is due to the Anderson localization of charge carrier on a spin disorder.     

Maslov index for power-law potentials

The Maslov index in the semiclassical Bohr–Sommerfeld quantization rule is calculated for one-dimensional power-law potentials V (x) = ?V ₀/x ^s, x > 0, 0 < s < 2 The result for the potential V(x)=-V ₀/x ^1/2 is compared with the recently reported exact solution. The case of a spherically symmetric power-law potential is also considered.     

Über Kristallstruktur und elektrische Eigenschaften der Wismutselenide Bi2Se2 und Bi2Se3

The properties of bismuth triselenide (Bi₂Se₃) are already known to a certain extent through the work of several authors, while it was still an open question whether there exists an individual solid phase of BiSe. Further information on this subject could be obtained by the successful growth and investigation of single crystals of both Bi₂Se₃ and Bi₂Se₂. X-ray analysis by means of goniometry, Weißenberg, Laue, and Debye-Scherrer diagrams confirmed the known crystal structure of Bi₂Se₃ (ditrigonal scalenohedral;D _3d ⁵ ?R—m; with the hexagonal axes:a=4·15 Å andc=28·55 Å, and 3 molecules per unit cell). As to Bi₂Se₂ it can be shown that it belongs to the same class but to a different space group (D _3d ¹ ?P— 1m orD _3d ³ ?P—m 1; hexagonal axes:a=4·15 Å,c=22·84 Å, unit cell: 3 molecules, if the formula Bi₂Se₂ is adopted). Common to both is a subcell with the dimensions:a′=a=4·15 Å andc′=5·71 Å. The temperature dependence of electrical conductivity and Hall coefficient was measured on several specimens having different crystal orientations. The most striking difference is the high anisotropy of Bi₂Se₃ (σ _a σ _c =10) as compared with Bi₂Se₂ (σ _a /σ _c <2). All specimens turned out to ben-type. The room temperature carrier concentration observed was:n (Bi₂Se3)=8·10¹⁸ cm^?3 andn (Bi₂Se₂)=4·10²⁰ cm^?3, the carrier mobility:μ(Bi₂Se3)=2·10³ cm²/V·s andμ(Bi₂Se₃)=20 cm²/V·s.     

Zur Chronologie des alten Ägypten

The velocityv of the propagation of discharge along the anode of a self-quenchingG—M-counter is a function of total pressureP, pressure of the quenching gasP _D, radius of the cathoder _a and of the anoder _i andV _ü the difference between working- and starting-potential. For the mixtures argon-methylal, argon-alcohol and helium-alcohol isv=v ₀·exp[k·(V _ü/V _e)^1/2] withv ₀ the velocity at the starting potentialV _e v ₀=(a+b·P _D/P)·V _n ^1/2 ·exp [(c?d·P_D/P·V _n ^?1/2 ] andV _n=V _e·(lnr _a/r _i)^?1.k, a, b, c andd are characteristical constants of the filling gas.     

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.     

<Emphasis Type="Italic">nd</Emphasis> scattering at low energies in the two-body potential model

The S-wave phase shift δ(E) for the spin-doublet nd scattering at low energy E is calculated in the framework of the two-body approach. The effective-range-theory formula k cot δ = (1+k²/k ₀ ² )^?1(?1/α+C₂k²+C₄k⁴) is used to obtain approximate analytical results with different potentials. The corresponding coefficients C₂ and C₄ are obtained from our previous calculations of the asymptotic normalization parameter function C _t ² (aκ), where κ is the triton wave number and a is the doublet nd scattering length. The model reasonably describes δ(E), the results being quite sensitive to the choice of the effective nd potential.