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.     

Boundaries Immersed in a Scalar Quantum Field

We study the interaction between a scalar quantum field $\hat \phi (x)$, and many different boundary configurations constructed from (parallel and orthogonal) thin planar surfaces on which $\hat \phi (x)$ is constrained to vanish, or to satisfy Neumann conditions. For most of these boundaries the Casimir problem has not previously been investigated. We calculate the canonical and improved vacuum stress tensors $ \langle \hat T_{\mu \nu } (x)\rangle\$ and $ \langle \Theta _{\mu \nu (x)} \rangle\$ of $\hat \phi (x)$; for each example. From these we obtain the local Casimir forces on all boundary planes. For massless fields, both vacuum stress tensors yield identical attractive local Casimir forces in all Dirichlet examples considered. This desirable outcome is not a priori obvious, given the quite different features of $ \langle \hat T_{\mu \nu } (x)\rangle\$ and $ \langle \Theta _{\mu \nu (x)} \rangle\$. For Neumann conditions. $ \langle \hat T_{\mu \nu } (x)\rangle\$ and $ \langle \Theta _{\mu \nu (x)} \rangle\$ lead to attractive Casimir stresses which are not always the same. We also consider Dirichlet and Neumann boundaries immersed in a common scalar quantum field, and find that these repel. The extensive catalogue of worked examples presented here belongs to a large class of completely solvable Casimir problems. Casimir forces previously unknown are predicted, among them ones which might be measurable.     

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.     

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.     

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.     

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.     

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.     

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.     

Probing the phase transition behavior of acetonitrile confined in mesoporous silica by FT Raman spectroscopy

Phase transitions of acetonitrile confined in mesoporous silica SBA‐15 and mesocellular silica foam (MCF) having different pore diameters of 39.0, 39.9, 28.4, 8.7, and 4.6 nm with corresponding pore openings of 20.9, 12.1, 10.0, 8.7, and 4.6 nm were investigated by FT Raman spectroscopy. Melting and freezing temperature depressions were found for acetonitrile confined in mesoporous silica with pore opening sizes of 20.9, 12.1, 10.0 and 8.7 nm. A thermal hysteresis between the cooling and heating cycles was also observed. It appears that the smaller the pore opening, the larger the depression of melting or freezing temperature. Although two solid ( and ) phases exist in bulk acetonitrile, only the liquid →β phase transition was detected for acetonitrile confined in the nanopores of mesoporous silica. The solid‐to‐solid phase transition was not observed. For the mesoporous silica with the smallest pore size of 4.6 nm, neither the liquid nor the transition was observed for the confined acetonitrile. The results demonstrate that FT Raman spectroscopy is a useful technique for studying the phase transition behavior of organic compounds confined in silica‐based hosts. Copyright © 2011 John Wiley & Sons, Ltd.     

Zur unitarisierten Gravitationstheorie mit lang- und kurzrechweitigen Termen (mit ruhmasselosen und schweren Gravitonen)

In our papers, TREDER [1, 2] we have formulated a unified electrodynamics of the fourth order with bi-wave equations for the vector potential A. In this electrodynamics EINSTEIN ian photon and heavy W-mesons are the field quanta. In correspondence to this field theory we are able to formulate a unified theory of gravitation, too. The field equations for the gravitational metrics grr in this theory are corresponding with the EINSTEIN equations of General Relativity in the same way like the electromagnetic bi-wave equations are corresponding with the MAXWELL equations. The metric g_μν is a linear functional of an EINSTEIN ian long-range potential g_μν and of a subatomic short-range potential definierte Materie-Tensor die gemeinsame Quelle für alle drei Felder ist. Dann ist g1_μν, g2_μν und g_μν und es gelten die Funktional-Bedingungen wobei hier g2_μν Feldgleichungen vom “kosmologischen Typ” befriedigt. By these conditions, the short-range interaction becomes a repulsive force and the action of the NEWTON -EINSTEIN ian attraction and of the subatomic repulsion makes the matter point-like (as in the E.-I.-H.-method) but self-consistent. The gravitational metrics g2_μν become regulary. P. e., in the EINSTEIN approximation the field of a point-like mass M is given by a SCHWARZSCHILD     

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*) $.     

Kinetic Study of the Emission of the First Negative System in an Argon-Nitrogen Plasma at Atmospheric Pressure

Quantitative optical spectroscopy measurements of the emission spectra of the N(B²∑_u,)ν′→X²∑_gν″ transition (first negative system) in an Ar-N₂ microwave discharge at atmospheric pressure have allowed determination of the rate coefficient of the production of N molecules in the B² ∑_u, state with vibrational level ν′ = 0. The N(B²∑_u, ν′) molecules are produced by the reaction in a surface-wave-induced microwave discharge (2450 MHz) sustained in an open-ended dielectric tube. The rate coefficient K (T) has been obtained for ν′ν″ = 0 for different gas temperatures by varying the incident microwave power. The K₀₀(T) values are between 7.10^?10 and 4.10^?10 cm³ s^?1 for the temperature range 2500 to 3450K.     

Desorptions- und Reaktionskinetik der Erdalkalien Calcium und Strontium mit Chlor an Wolfram. Part II: Kinetics of the Elementary Steps of the Surface Reaction M + Cl ⇌ MCl (M = Ca,Sr)

Desorption- and Reactionkinetics of the Alkaline Earth Elements Calcium and Strontium with Chlorine on a Tungsten Surface — Part II: Kinetics of the Elementary Steps of the Surface Reaction M + Cl ? MCl (M = Ca, Sr) Utilizing pulsed molecular-beam-technique the kinetics of desorption of Strontium, Calcium, and Chlorine as well as that of the molecules SrCl and CaCl, which are formed at the hot tungsten surface, was investigated. Thereby, the following values were obtained for the activation energies of desorption: ? = (3.76 ± 0.05) eV, ? = (3.32 ± 0.07) eV, ? = (4.16 ± 0.05) eV, ? = (4.2 ± 0.3) eV and ? = (3.9 ± 0.3) eV. Combining these results with the steady-state-results from part I [1] the temperature dependency of the rate constants of dissociation and recombination of MCl-molecules at the tungsten surface could be determined. The values obtained for the dissociation energies D of SrCl and CaCl on tungsten are (0.5 ± 0.5) eV and (0.3 ± 0.5) eV, respectively. The molecules are stabilized on the surface by the activation barrier for dissociation D? only, which was found to be (2.8 ± 0.5) eV for SrCl and (2.3 ± 0.5) eV for CaCl.     

Gibt es Plancksche Sekunden des Kosmos?

On Planckian Seconds of the Universe According to the Planckian limites for quantum energies the cosmological scenaria break-down for space dimensions (or for life times of the universe) and for Planckian lengths, not till.     

Hyperfine Structure of the Configuration lll

The matrix elements for the hyperfine structure of the configuration lll in SL-Kopplung are expressed as linear combinations of the electron coupling constants α_li(10), α_li(01), α_li(12).     

On the Generalized πN Potential A New Representation from Fixed-t Dispersion Relations

Starting from a recent paper [13] we derive a new representation of the left-hand cut contribution for the πN system. This representation makes it possible to calculate the generalized πN potential accurately from phase shifts and high energy models, because it contains only the imaginary parts of the partial wave amplitudes in the physical region. The analytic properties, the region of convergence and the physical content of this representation is discussed. We propose to use this left-hand cut contribution in bootstrap calculations, because it is more reliable than the approximate expressions which have been used in previous papers. – The left-hand cut contributions are calculated and compared with the nucleon and Δ (1236) approximation for the ƒ, ƒ, ƒ and ƒ partial wave amplitudes.     

On the Nuclear Energy Generation Rate in a Simple Analytic Stellar Model

This paper is concerned with the hydrostatic equilibrium of a purely gaseous star generating energy at a rate . By the common technique of integration theory of special functions the total net rate of nuclear energy generation is evaluated analytically for a linear density distribution function assumed for a simple stellar model.     

Desorptions- und Reaktionskinetik der Erdalkalien Calcium und Strontium mit Chlor an Wolfram. Teil I: Chemisches Gleichgewicht der Oberflächenreaktion M + Cl = MCl im stationären Zustand (M = Ca,Sr)

Desorption- and Reactionkinetics of the Alkaline Earth Elements Calcium and Strontium with Chlorine on a Tungsten Surface — Part I: Chemical Equilibrium of the Surface Reaction M + Cl ? MCl in the Steady State (M = Ca, Br) Utilizing positive and negative surface ionization the reaction M + Cl = MCl (M = Ca, Sr) was studied at a hot tungsten surface under steady state conditions. Comparing the results obtained either by simultaneous M- and Cl₂ -exposures or by MCl₂ -exposure the existence of chemical equilibrium could be confirmed for the reaction in the temperature interval 1600 K.2000 K; at higher temperatures this equilibrium can be disturbed considerably by the desorption of the reacting components. From the experimental results we obtained under conditions of chemical equilibrium the energy of dissociation of MCl-molecules in the gasphase (D = (3.9 ± 0.15) eV, D = (4.2 ± 0.15)eV) and in the case of a strong disturbance of the equilibrium the difference between the activation energies of desorption and of dissociation of MCl-molecules on the surface (? - D? = (1.6 ± 0.2) eV, ? - D? = (1.4 ± 0.2) eV).     

Gravitationskollaps und Lichtgeschwindigkeit im Gravitationsfeld

An elementary criterion of the stability of a matter sphere against gravitational collapse is given by the circular velocity condition of POINCARÉ : In a space with a spherically symmetric gravitation potential ? (r) and with a spherically symmetric metric gik (e.g., a SCHWARZSCHILD space time) the circular velocity V^* of a particle on the surface r = R of the matter-sphere must be (This condition is a consequence of the virial theorem and of the POINCARÉ theorem.) - However, EINSTEIN 's axiom of causality implies that this velocity V^* must be smaller than the local velocity of light v: V^*2 < v². And this local velocity v is a function of the gravitation potential ?, too: v = v [?]. In the case of NEWTON 's or EINSTEIN 's theory the spherically symmetric gravitation potential is given by the NEWTON ian function ? = fM/r. In the special theory of relativity, we would have v = c (c = EINSTEIN 's fundamental velocity) and grr = 1. Therefore, the specialrelativistic stability condition is R > fMc^?2. - But in the NEWTON ian theory v is depending of the gravitation potential and depends of the boundary condition for the light propagation, also. According to the ansatz of LAPLACE (1799) we have: (emanation-theory of light). But, according to SOLDNER (1801), we have Therefore, we are finding in the case of LAPLACE the same condition R > fMc^?2 as in the SRT. But, in the case of SOLDER 's ansatz non condition for stability is resulting. - In the general relativistic theories the local velocity of light is given by EINSTEIN 's expression According to EINSTEIN 's theory of “static gravitation” (1911/12) we have grr = 1 and therefore the formula and according to the GRT (with - g_ω = grr^?1) we have the formula Therefore, the Hilbert-Laue condition r= R > 3fMc^?2 results as stability condition. From the gravo-optical point of view, in GRT and for the classical ansatz of LAPLACE “black-holes” with bounding states of light result for R ≤ 2fM^?2. But, no “black-holes” are existing according to SOLDNER 's ansatz. However, in GRT each black-hole must be a “collapsar”. But according to the classical theory of LAPLACE we have uncollapsed “black- holes” for the domain .