The metal‐insulator transitions of VO2: A band theoretical approach

The results of first principles electronic structure calculations for the metallic rutile and the insulating monoclinic phase of vanadium dioxide are presented. In addition, the insulating phase is investigated for the first time. The density functional calculations allow for a consistent understanding of all three phases. In the rutile phase metallic conductivity is carried by metal orbitals, which fall into the one‐dimensional band, and the isotropically dispersing bands. Hybridization of both types of bands is weak. In the phase splitting of the band due to metal‐metal dimerization and upshift of the bands due to increased p‐d overlap lead to an effective separation of both types of bands. Despite incomplete opening of the optical band gap due to the shortcomings of the local density approximation, the metal‐insulator transition can be understood as a Peierls‐like instability of the band in an embedding background of electrons. In the phase, the metal‐insulator transition arises as a combined embedded Peierls‐like and antiferromagnetic instability. The results for VO₂ fit into the general scenario of an instability of the rutile‐type transition‐metal dioxides at the beginning of the d series towards dimerization or antiferromagnetic ordering within the characteristic metal chains. This scenario was successfully applied before to MoO₂ and NbO₂. In the compounds, the and bands can be completely separated, which leads to the observed metal‐insulator transitions.     

Electrons with alternating on-site and correlated hopping interactions

The 1 D one-band Hubbard model with different repulsive on-site interactions on even (U+V > 0) and odd (U-V > 0) sites, supplemented by the correlated-hopping term (t* > 0), describing the modification of the electron hopping by the presence of other particles on the sites, is considered as a 1 D model for CuO systems. The ground state phase diagram is studied within the framework of the bosonization technique and renormalization group analysis valid for weak coupling. Depending on the choice of model parameters, the following sequences of phase transitions with increasing bandfilling occur: 1) metal-insulator-metal (for t* ? U/4); 2) metal-insulator-metal-superconductor $ ({\rm for}U/4 < t * \le U/\sqrt 8);3) $metal-superconductor-metal-insulator-metal-superconductor $ ({\rm for}U/\sqrt 8 \le t * < (U + V)/\sqrt 8){\rm and}4) $metal-superconductor $ ({\rm for}(U + V)/\sqrt 8 \le t*) $.     

A shortcut to general tree‐level scattering amplitudes in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} = 4$\end{document} SYM via integrability

We combine recent applications of the two‐dimensional quantum inverse scattering method to the scattering amplitude problem in four‐dimensional $ \mathcal{N} = 4$ Super Yang‐Mills theory. Integrability allows us to obtain a general, explicit method for the derivation of the Yangian invariants relevant for tree‐level scattering amplitudes in the $ \mathcal{N} = 4$model.     

Über die Schwere des Lichtes in der Newtonschen und in der Einsteinschen Gravitationstheorie

The gravity theories of Newton and Einstein are giving opposite sentences about the velocity of light in gravitational field. According to the Newtonian theory the velocity v in gravitational field is greater than the velocity c in a field-free space: v > c. According to general relativity theory we have a smaller velocity: v < c. For a spherical symmetric gravitational field Newton's theory gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 + \frac{{fM}}{{c^2 r}}} \right) $\end{document} but Einstein's theory of 1911 gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 - \frac{{fM}}{{c^2 r}}} \right) $\end{document} and general relativity gives \documentclass{article}\pagestyle{empty}\begin{document}$ v \approx c\left({1 - 2\frac{{fM}}{{rc^2 }}} \right) $\end{document}. Therefore, the radarecho-measurations of Shapiro are the experimentum crucis for Einstein's against Newton's theory.     

Measurements of Plasma Potential and Electron Temperature Fluctuation in a Low‐Temperature Magnetized Plasma

Measurements of fluctuations of plasma potential and electron temperature in a toroidal magnetized plasma is carried out by applying a cylindrical probe with insulating end plugs oriented parallel to the B‐field in conjunction with another cylindrical probe oriented perpendicularly. Coherency and cross‐phase between and are estimated, and typically have values close to 0.6 and π respectively. Power‐law spectra are found for frequencies well above the poloidal rotation frequency with spectral index typically around 4.0 for and around 2.5 for . The density gradient is above the threshold for flute interchange instability, and the results are consistent with theory and global numerical simulations of this plasma.     

Einfluß des Randes auf das effektive Verhalten heterogener Körper - Anwendung auf Rayleighwellen

Effective Elastic Properties of Finite Heterogeneous Media - Application to Rayleigh-waves Rayleigh waves in a heterogeneous material (multiphase mixtures, composite materials, polycrystals) are governed by integrodifferential equations derived by the aid of known methods for infinite heterogeneous media. According to this wave equation the velocity depends on the frequency, and the waves are damped. After some simplifications (isotropy, nonrandom elastic constants) the following is obtained: if the fluctuations of the mass density are restricted to the vicinity of the boundary, the frequency dependent part of the velocity behaves like \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^3 \omega ^3}}{{{\mathop c\limits^\circ} _t^3}} $\end{document} and the damping is proportional to \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^4 \omega ^5}}{{{\mathop c\limits^\circ} _t^5}} $\end{document}, whereas \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^2 \omega ^2}}{{{\mathop c\limits^\circ} _t^2}} $\end{document} respectively \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^3 \omega ^4}}{{{\mathop c\limits^\circ} _t^4}} $\end{document} is found if the fluctuations are present in the whole half-space. From this it is seen, what assumptions are necessary to describe the waves by differential equations with frequenc y-dependent mass density.     

A search for an \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} =2 $\end{document} inflaton potential

We consider $ \mathcal{N} =2 $ supergravity theories that have the same spectrum as the R + R² supergravity, as predicted from the off‐shell counting of degrees of freedom. These theories describe standard $ \mathcal{N} =2 $ supergravity coupled to one or two long massive vector multiplets. The central charge is not gauged in these models and they have a Minkowski vacuum with $ \mathcal{N} =2 $ unbroken supersymmetry. The gauge symmetry, being non‐compact, is always broken. α‐deformed inflaton potentials are obtained, in the case of a single massive vector multiplet, with α = 1/3 and 2/3. The α = 1 potential (i.e. the Starobinsky potential) is also obtained, but only at the prize of having a single massive vector and a residual unbroken gauge symmetry. The inflaton corresponds to one of the Cartan fields of the non‐compact quaternionic‐Kähler cosets.     

Comments on the Pressure Dissociation of Deuterium as Related to the Nova Laser Hugoniot

The recent Nova laser experimental Hugoniot for deuterium can be justified by a simple model which involves only very general properties of this material and which highlights the role of the molecular dissociation. The region of maximal compression along the principal Hugoniot is characterized by , , , where E_B is the binding energy of a molecule, and ρ_o is the initial density.     

Off‐shell supergravity in five dimensions and supersymmetric brane world scenarios

We review the construction of off‐shell Poincaré supergravity in five dimensions. We describe in detail the minimal multiplet, which is the basic building block, containing the propagating fields of supergravity. All matter multiplets containing (8 + 8) components, being the smallest matter multiplets in five dimensions, are constructed. Using these multiplets the complete tensor calculus for supergravity is developed. As expected it turns out, that there exist three distinct minimal (i.e. containing (48 + 48) field components) off‐shell supergravities. The lagrangians for these theories and their gauged variants are given explicitly. These results are used in the second part to develop a tensor calculus on the orbifold $S^1/\mathbb{Z}_2$. Gauged supergravity on the orbifold $S^1/\mathbb{Z}_2$ with additional cosmological constants at the fixpoints, is constructed. This generalizes the work of Randall‐Sundrum to local supersymmetry. The developed tensor calculus is used to extend this model to include matter located at the fixpoints. Chiral and super Yang‐Mills multiplets at the fixpoints are considered.     

A Remark about the Point Interaction in one Dimension

The zero range limit of one dimensional Schrödinger operator is studied by scaling technique and new results are obtained for potentials V with \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \smallint \limits_{\rm R} $\end{document} V(x)dx = 0.     

A new approach to correcting theoretical emitted intensities for absorption and enhancement effects

This paper introduces the possibility of replacing the usual additive corrections for absorption and enhancement by multiplicative factors. The possibility of deriving simple multiplicative factors to correct for inter‐element matrix effects, namely and , to correct for absorption of primary and secondary radiation, respectively, and enhancement ( ), is demonstrated. The use of the new coefficients, , and , derived directly from mass attenuation coefficients, simplifies the understanding of, and allows the stepwise evaluation of, the excitation of theoretical emitted intensities in XRF spectrometry. The approach is especially useful in providing a more consistent definition of theoretical intensity emitted from an infinitely thick sample, as compared with the classical formalism involving the use of mass attenuation coefficients. The approach has proved particularly useful in the classroom. Copyright © 2004 John Wiley & Sons, Ltd.     

Aspects of stability and phenomenology in type IIA orientifolds with intersecting D6‐branes

Intersecting branes have been the subject of an elaborate string model building for several years. After a general introduction into string theory, this work introduces in detail the toroidal and $\mathbb{Z}_N$‐orientifolds. The picture involving D9‐branes with B‐fluxes is shortly reviewed, but the main discussion employs the T‐dual picture of intersecting D6‐branes. The derivation of the R‐R and NS‐NS tadpole cancellation conditions in the conformal field theory is shown in great detail. Various aspects of the open and closed chiral and non‐chiral massless spectrum are discussed, involving spacetime anomalies and the generalized Green‐Schwarz mechanism. An introduction into possible gauge breaking mechanisms is given, too. Afterwards, both 𝒩 = 1 supersymmetric and non‐supersymmetric approaches to low energy model building are treated. Firstly, the problem of complex structure instabilities in toroidal ΩR‐orientifolds is approached by a $\mathbb{Z}_3$‐orbifolded model. In particular, a stable non‐supersymmetric standard‐like model with three fermion generations is discussed. This model features the standard model gauge groups at the same time as having a massless hypercharge, but possessing an additional global B‐L symmetry. The electroweak Higgs mechanism and the Yukawa couplings are not realized in the usual way. It is shown that this model descends naturally from a flipped SU(5) GUT model, where the string scale has to be at least of the order of the GUT scale. Secondly, supersymmetric models on the $\mathbb{Z}_4$‐orbifold are discussed, involving exceptional 3‐cycles and the explicit construction of fractional D‐branes. A three generation Pati‐Salam model is constructed as a particular example, where several brane recombination mechanisms are used, yielding non‐flat and non‐factorizable branes. This model even can be broken down to a MSSM‐like model with a massless hypercharge. Finally, the possibility that unstable closed and open string moduli could have played the role of the inflaton in the evolution of the universe is being explored. In the closed string sector, the important slow‐rolling requirement can only be fulfilled for very specific cases, where some moduli are frozen and a special choice of coordinates is taken. In the open string sector, inflation does not seem to be possible at all.     

On Static Asymptotically Flat Solutions of Fourth Order Gravitational Field Equations

It is shown that each non-flat regular static asymptotically flat solution of the gravitational field equation following from the Lagrangian has in a certain sense positive energy. Further, for a set of parameters including the BACH -EINSTEIN theory some results concerning the full nonlinear behaviour of the solutions of the field equation will be given.     

Intensity Effects in Scattering of Electromagnetic Waves by Electrons Moving in External Magnetic Field

In this paper we consider the emission processes of a relativistic electron moving in the field of a plane electromagnetic wave and in a homogeneous magnetic field. A detailed analysis of the most important characteristics of the radiation properties for arbitrary values of the magnetic field, compared with \documentclass{article}\pagestyle{empty}\begin{document}$ [H_0 = \frac{{m^2 c^3}}{{e\hbar}}]$\end{document} = 4.41.10¹³ gauss, is presented.     

Na‐site energy of P2‐type NaxM O2 (M = Mn and Co)

P2‐type Na_xM O₂ (M = Mn and Co) is a promising cathode material for low‐cost sodium ion secondary batteries. In this structure, there are two different crystallographic Nai (i = 1 and 2) sites with different Coulomb potential $ (\varphi _i)$ provided by M^4–x and O^2–. Here, we experimentally determine a difference ${(\rm \Delta }\varepsilon \equiv \varepsilon _1 - \varepsilon _2)$ of Na‐site energies ${(}\varepsilon _i \equiv e\varphi {\kern 1pt} _i)$ based on the temperature dependence of the site occupancies. We find that ${\rm \Delta }\varepsilon \;{=}\;56\;{K}$ for Na_0.52MnO₂ is significantly smaller than 190 K for Na_0.59CoO₂. We interpret the suppressed ${\rm \Delta }\varepsilon $ in Na_0.52MnO₂ in terms of the screening effect of the Na⁺ charge. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calibration of the electrical aerosol analyzer at subambient pressures

A commercial Electrical Aerosol Analyzer (EAA, TSI Inc. model 3030) was calibrated experimentally at three subambient pressures (i. e., 0.901, 0.878, and 0.853 atm). Each calibration resulted in a 19 × 11 response matrix and a size dependent sensitivity curve $ \left({\frac{{pA}}{{{\# \mathord{\left/ {\vphantom {\# {cm^3}}} \right. \kern-\nulldelimiterspace} {cm^3}}}}} \right) $. The results of the calibration were incorporated into a data reduction computer program for size distribution inversion. The accuracy of the calibration was tested by measuring the size distribution of a NaCl polydisperse aerosol at the three subambient pressures. All the tests gave good agreement in the inverted mean geometric diameter and geometric standard deviation of the aerosol number size distribution.     

Double resonance Raman effects in InN nanowires

We study the excitation wavelength dependence of the Raman spectra of InN nanowires. The $ E_1 ({\rm LO})$ phonon mode, which is detected in backscattering configuration because of light entering through lateral faces, exhibits an upward fre‐ quency shift that can be explained by Martin's double resonance. The $ E_1 ({\rm LO})$ /$ E_2^h $ intensity ratio increases with the excitation wavelength more rapidly than the $A_1 ({\rm LO})/E_2^h $ ratio measured in InN thin films. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Die Lorentz-Transformation als Ausdruck der Superposition gegenläufiger Raum-Zeit-Beziehungen,Preisgabe des Relativitätsprinzips

The Lorentz Transformation as an Expression of Opposite Spacetime Relations. Abandonment of the Principle of Relativity Any increase of the characteristic energy of any body endowed with a clock, ΔE = E — E₀ (E₀ being the rest energy), is connected with an increase of its time lapse, t/t₀ = E/E₀ (EINSTEIN 1907). Effective observation of this accelerating influence on the speed of any clock is restricted on the increase of the potential energy only. Increase of the kinetic energy \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{E}{{E_0 }}\, = \,\frac{1}{{\sqrt{1 - \frac{v}{{c^2 }}} }}} \right) $\end{document} is, on the contrary, connected with a decrease of the time lapse, a decrease of exactly the same but inverse (reciprocal) amount to the increase of the energy: \documentclass{article}\pagestyle{empty}\begin{document}$ t/t_0{\rm = }E_0 /E{\rm = }\sqrt {1 - \frac{{v^2 }}{{c^2 }}.} $\end{document}. Moreover this amount is that one postulated by the Lorentz Transformation. This effect is the well-known “time dilatation” of the Special Theory of Relativity, the “transversal Doppler effect”. The Lorentztransformation is of exclusively kinematical meaning and therefore takes no account of the energy increase connected with any motion. There is no reason, why the time accelerating effect of any energy rises should be absent in the case of kinetic energy, paying regard to is seem indispensable. Therefore the actual effect \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {1 - \frac{{v^2 }}{{c^2 }}} $\end{document} has to be given as a superposition of the time accelerating energy effect \documentclass{article}\pagestyle{empty}\begin{document}$ 1/\sqrt {1 - \frac{{v^2 }}{{c^2 }}} $\end{document} and a decelerating kinematic effect of “double” (inverse square) amount: 1 – v²/c². Modified transformation equations are derived which pay regard to this subdivision of the actual relations concerning times and local scales, and whose interated form is nevertheless identical with the classical Lorentz Transformation, if kinetic energy is the sole one being present. Of course this new subdivision of the content of meaning in the transformations is in contradiction with the ?principle of relativity”?, it presumes the existence of an inertial frame absolutely at rest related to the universe, A series of arguments is asserted which let appear the existence of such an absolute frame more fascinating than the equivalence of the variety of all inertial frames.     

Analysis of Three-Dimensional Motion of Relativistic Electrons in Ion-Focused Electrostatic System

Three-dimensional motion of relativistic electrons in ion-focused electrostatic system, which is the basis of investigating the ion-channel electron cyclotron maser (ICECM) or circular polarized ion-channel laser (CPICL), is analyzed through nonlinear numerical simulation. The results show that the projection of electron orbit in cross-section is, in general, a precessing ellipse with a center on the axis of the ion-channel in a cylindrical ion-focuse electrostatic system. When injection electrons satisfy a specific condition, the electrons can have a steady circular orbit. The effect of relativistic factor on electrons' motion is discussed. Using the perturbation method, the eigenfrequency of this system is derived as Equation $ \sqrt {4 - \beta _ \bot ^2 } \omega _0 $ where wo is the cyclotron frequency of the electrons. This implies that there may exist a new kind of instability in ICECM or CPICL.