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.     

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.     

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.     

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.     

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.     

Proper quantization rule as a good candidate to semiclassical quantization rules

In this article, we present proper quantization rule, ∫k(x) dx ‐ ∫k₀(x) dx = nπ, where and study solvable potentials. We find that the energy spectra of solvable systems can be calculated only from its ground state obtained by the Sturm‐Liouville theorem. The previous complicated and tedious integral calculations involved in exact quantization rule are greatly simplified. The beauty and simplicity of proper quantization rule come from its meaning – whenever the number of the nodes of the logarithmic derivative ?(x) = ψ(x)^‐1dψ(x) /dx or the number of the nodes of the wave function ψ(x) increases by one, the momentum integral will increase by π. We apply two different quantization rules to carry out a few typically solvable quantum systems such as the one‐dimensional harmonic oscillator, the Morse potential and its generalization as well as the asymmetrical trigonometric Scarf potential and show a great advantage of the proper quantization rule over the original exact quantization rule.     

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.     

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.     

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.     

DFT study and NBO analysis of the mutual interconversion of cumulene compounds

The B3LYP/6‐31G* method was used to investigate the configurational properties of allene (1,2‐propadiene) ( 1 ), 1,2,3‐butatriene ( 2 ), 1,2,3,4‐pentateriene ( 3 ), 1,2,3,4,5‐hexapentaene ( 4 ), 1,2,3,4,5,6‐heptahexaene ( 5 ), 1,2,3,4,5,6,7‐octaheptaene ( 6 ), 1,2,3,4,5,6,7,8‐nonaoctaene ( 7 ), and 1,2,3,4,5,6,7,8,9‐decanonaene ( 9 ). The calculations at the B3LYP/6‐31G* level of theory showed that the mutual interconversion energy barrier in compounds 1 – 8 are: 209.73, 131.77, 120.34, 85.00, 80.91, 62.19, 55.56, and 46.83 kJ mol^?1, respectively. The results showed that the difference between the average C?C double bond lengths ( ) values in cumulene compounds 1 and 2 , is larger than those between 7 and 8 , which suggest that with large n (number of carbon atoms in cumulene chain), the values approach a limiting value. Accordingly, based on the plotted data, the extrapolation to n = ∞, gives nearly the same limiting (i. e., ). Also, NBO results revealed that the sum of π‐bond occupancies, , decrease from 1 to 8 , and inversely, the sum of π‐antibonding orbital occupancies, , increase from compound 1 to compound 8 . The decrease of values for compounds 1 – 8 , is found to follow the same trend as the barrier heights of mutual interconversion in compounds 1 – 8 , while the decrease of the barrier height of mutual interconversion in compounds 1 – 8 is found to follow the opposite trend as the increase in the number of carbon atom. Accordingly, besides the previously reported allylic resonant stabilization effect in the transition state structures, the results reveal that the values, , Δ(E_HOMO ? E_LUMO), and the C atom number could be considered as significant criteria for the mutual interconversion in cumulene compounds 1 – 8 . This work reports also useful predictive linear relationships between mutual interconversion energy barriers ( ) in cumulene compounds and the following four parameters: , , Δ(E_HOMO ? E_LUMO), and C_Number. Copyright © 2007 John Wiley & Sons, Ltd.     

Hierarchy of the non‐covalent interactions in the alanine‐based secondary structures. DFT study of the frequency shifts and electron‐density features

The alanine (Ala)‐based cluster models of C5, C7, and C10 H‐bonds are studied at the DFT/B3LYP level. CPMD/BLYP simulations of the infinite polyalanine α‐helix (C13 H‐bond) and the two‐stranded β‐sheets are performed. Combined use of frequency shifts and electron‐density features enable us to detect and describe quantitatively the non‐covalent interactions (H‐bonds) defining the intrinsic properties of Ala‐based secondary structures. The energies of the primary N? H O H‐bonds are decreasing in the following way: C13 > C5 ≥ C7 > C10. The energies of the secondary N? H O, N?H N, and H H interactions are comparable to those of the primary H‐bonds (～4.5 kcal/mol). Side chain–backbone C? H O interaction is found to be the weakest non‐covalent interaction in the considered species. Its energy is ～0.5 kcal/mol in the infinite polyalanine α‐helix. Quantum‐topological electron‐density analysis is found to be a powerful tool for the detection of secondary non‐covalent interactions (C?O H? C and H H) and bifurcated H‐bonds, while the frequency shift study is useful for the identification and characterization of primary or secondary H‐bonds of the N? H O type. Copyright © 2008 John Wiley & Sons, Ltd.     

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)     

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.     

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.     

Degenerate and two‐color resonant four‐wave mixing of C2− in a molecular beam environment

In this paper, we demonstrate that degenerate and two‐color resonant four‐wave mixing spectroscopy is applicable for the sensitive and selective characterization of negative ions in a molecular beam environment. Results are shown for C , which is produced by discharging a mixture of acetylene and argon prior to supersonic expansion. Substantial signal‐to‐noise ratios of ≈ 150 show that the method is generally applicable for high‐resolution optical double‐resonance spectroscopy of negative ions. A detection sensitivity for C of ≈ 10⁷ ions/cm³ is estimated. Copyright © 2010 John Wiley & Sons, Ltd.     

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*) $.     

Epitaxy of m ‐plane ZnO on (112) LaAlO3 substrate

Heteroepitaxial growth of non‐polar m ‐plane (10 0) ZnO has been demonstrated on (112) LaAlO₃ single crystal substrates using the pulsed laser deposition method. X‐ray diffraction, reflection high energy electron diffraction, and cross‐sectional transmission electron microscopy with selected‐area diffraction, have been used to characterize the structural properties of deposited ZnO films. The epitaxial relationship between ZnO and LAO is shown to be (10 0)_ZnO ∥ (112)_LAO, (11 0)_ZnO ∥ ( 1)_LAO and [0001]_ZnO ∥ [ 10]_LAO. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An ab initio study of CX3‐substitution (X = H,F, Cl,Br, I) effects on the static electric polarizability and hyperpolarizability of diacetylene

We report a systematic ab initio and density functional theory (DFT) study of the electric properties of the X₃C? C≡C? C≡C? H (X = H, F, Cl, Br, and I) sequence of substituted diacetylenes. We rely on finite‐field Møller–Plesset perturbation theory and coupled‐cluster calculations with large, flexible basis sets. Our best values at the second‐order Møller–Plesset perturbation theory level for the mean dipole polarizability and second hyperpolarizability are $\overline {{\alpha} } $ /e²aE = 64.46 (? CH₃), 65.59 (? CF₃), 110.11 (? CCl₃), 138.90 (? CBr₃), 184.98 (? CI₃) and $\overline {{\gamma} } $ /e⁴aE = 21020 (? CH₃), 13469 (? CF₃), 32708 (? CCl₃), 57599 (? CBr₃), and 105251 (? CI₃). For comparison, the analogous MP2 values for diacetylene [P.Karamanis and G.Maroulis, Chem. Phys. Lett. 2003 , 376, 403.] are $\overline {{\alpha} } $ /e²aE = 49.17, and $\overline {{\gamma} } $ /e⁴aE = 16227. For the mean first hyperpolarizability we report $\overline {{\beta} } $ /e³aE = ?205.8 (? CH₃), ?55.7 (? CF₃), 120.8 (? CCl₃), 443.8 (? CBr₃), and 725.4 (? CI₃). Copyright © 2010 John Wiley & Sons, Ltd.