Newq-derivative andq-logarithm

In this paper a newq-derivative is proposed and its properties are discussed. We defineq-addition and study its axiomatic properties. Theq-exponents andq-logarithmic function are introduced and their algebraic structure discussed.     

<Emphasis Type="Italic">R</Emphasis> soliton in the Wess-Zumino model

The Wess-Zumino model involving a renormalizable interaction potential and possessing R symmetry is considered. It is shown that an R soliton, which is a nontopological soliton state, is present in this model. Characteristic properties of the R soliton are discussed. Problems associated with the stability of the R soliton are considered. The results obtained by numerically calculating the energy and the charge of the R soliton are presented for several values of the model parameters. The scalar field configurations in this supersymmetric model are characterized by the presence of fermionic zero modes. Expressions for the fermionic zero modes of the R soliton are obtained, and some of their properties are considered.     

On Shtelen’s Solution of the Free Linear Schrödinger Equation

Abstract

The solution of the three-dimensional free Schrödinger equation due to W.M. Shtelen based on the invariance of this equation under the Lorentz Lie algebra so(1,3) of nonlocal transformations is considered. Various properties of this solution are examined, including its extension to n ≥ 3 spatial dimensions and its time decay; which is shown to be slower than that of the usual solution of this equation. These new solutions are then used to define certain mappings, F _n, on L ²(?ⁿ) and a number of their properties are studied; in particular, their global smoothing properties are considered. The differences between the behavior of F _n and that of analogous mappings constructed from usual solutions of the free Schrödinger equation are discussed.     

Chemical Evolution of the Universe and its Consequences for Gravitational-Wave Astrophysics

Gravitational waves (GW) emitted by merging black holes (BH) and neutron stars are now routinely detected. Those are the afterlives of massive stars that formed all across the Universe—at different cosmic times and with different metallicities. Birth metallicity plays an important role in the evolution of massive stars. Consequently, the population properties of mergers are sensitive to the metallicity dependent cosmic star formation history (f_SFR(Z,z)). In particular, within the isolated formation scenarios (the focus of this paper), a strong low metallicity preference of the formation of BH mergers is found. The origin of this dependence and its consequences are discussed. Most importantly, uncertainty in the f_SFR(Z,z) (substantial even at low redshifts) cannot be ignored in the models. This poses a challenge for the interpretation of the observed GW source population properties. Possible improvements and the role of future GW detectors are considered. Recent efforts to determine f_SFR(Z,z) and the factors that dominate its uncertainty are summarized. Many of those factors stem from the uncertain properties of faint and distant galaxies. The fact that they leave imprint on the redshift-dependent properties of mergers makes GW a promising (and complementary to electromagnetic observations) tool to study galaxy chemical evolution.     

Monte Carlo analysis of electron heating in Si/SiO2 superlattices

In this work, we investigate the transport properties of Si/SiO₂ superlattices with a multiband one-particle Monte Carlo simulator. Using the envelope function approximation, we solve the Krönig–Penney potential along the growth direction z using a tight-binding-like analytical form; we also consider parabolic dispersion along the xy plane. The scattering mechanisms introduced in the simulator are confined optical phonons, both polar and nonpolar.Owing to the very flat shape of the bands along the growth direction, very low drift velocities are found for vertical transport. However, the simulation shows that, for oblique fields, the transport properties along the vertical direction are strongly influenced by the in-plane component of the electric field: in this way higher vertical drift velocities can be obtained. The results point out that in-plane carrier heating and multiband properties are responsible for this behavior.     

Coexistence of Partially Disordered/Ordered Phases in an Extended Potts Model

We consider a generalization of the standard Potts model in which there are q=r+s states with an interaction that distinguishes the two subspecies. We develop a graphical representation (of the FK type) for the system and show that this representation may be incorporated directly into reflection positivity arguments. Using combinations of these techniques, we establish detailed properties of the phase diagram including the existence of sharp triple points. Whenever relevant, the phases are characterized by the percolation properties of the underlying representation.     

A study on the determination of mechanical properties of a power law material by its indentation force–depth curve

In this study a novel optimization approach is proposed to extract mechanical properties of a power law material whose stress–strain relationship may be expressed as a power law from its given experimental indentation P–h curve. A set of equations have been established to relate the P–h curve to mechanical properties E, σ _y and n of the material. For the loading part of a P–h curve this approach is based on the assumption that the indentation response of an elastic–plastic material is a linear combination of the corresponding elastic and elastic–perfect plastic materials. For the unloading part of the P–h curve it is based on the assumption that the unloading response of the elastic–plastic material is a linear combination of the full contact straight line and the purely elastic curve. Using the proposed optimization approach it was found that the mechanical properties of an elastic–plastic material usually cannot be decided uniquely by using only a single indentation P–h curve of the material. This is because in general a few matched sets of mechanical properties were found to produce a given P–h curve. It is however possible to identify the best matched set of mechanical properties by knowing some background information of the material. If the best matched material is identified, the predictions of mechanical properties are quite accurate.     

Higher-Order Nonclassicality in Photon Added and Subtracted Qudit States

Higher-order nonclassical properties of r photon added and t photon subtracted qudit states (referred to as rPAQS and tPSQS, respectively) are investigated here to answer: How addition and subtraction of photon can be used to engineer higher-order nonclassical properties of qudit states? To obtain the answer, higher-order moment of relevant bosonic field operators is first obtained and subsequently used to study the higher-order nonclassical properties (e.g., higher-order antibunching, higher-order squeezing, and higher-order sub-Poissonian photon statistics) of the corresponding states. These witnesses establish that rPAQS and tPSQS are highly nonclassical. To quantitatively establish this observation and to make a comparison between rPAQS and tPSQS, volumes of the negative part of Wigner function are computed. Finally, for the sake of verifiability of the obtained results, optical tomograms are also reported. Throughout the study, a particular type of qudit state named as a new generalized binomial state is used as an example.     

Three-particle correlations from PHENIX to investigate the properties of the QGP at RHIC

There is now a consensus of opinion that in heavy ion collisions at RHIC energies a strongly interacting state of matter resembling a near-perfect liquid (termed sQGP) is formed. Attention is now being focused on elucidating the properties of this medium e.g. size, shape, collectivity, viscosity, closeness to the critical point etc. In this work we describe the efforts in the soft and hard sectors to quantify these properties. In particular, the study of jet-medium interactions are described via correlation based studies. Details of three particle correlation studies of RHIC data will be discussed. Such studies are important as they provide an avenue for estimates of the viscosity and the sound speed of the medium.     

Two theorems on energy-momentum conservation

The mathematical meaning of the law of conservation of energy-momentum is examined. A distinction is made between the intrinsic properties of the metric tensor (i.e., those properties that are independent of the coordinate system), and the nonintrinsic properties of this tensor (i.e., those properties that depend upon the coordinate system). The covariance of the energy-momentum law is used to demonstrate that if one is given (a) any analytic contravariant energy-momentum tensor density in a given coordinate systemx and (b) an analytic specification of the intrinsic properties of the metric tensor, no matter what these properties may be, one can always choose the nonintrinsic properties of the metric tensor in such manner as to satisfy the law of conservation of energy-momentum in the coordinate systemx and thereby in every coordinate system. This result is proved only in the case where the contravariant components of the energy-momentum tensor density are given. Neither the covariant, nor the mixed energy-momentum tensor densities are considered. Other theorems similar to that described above are also derived. Many of the results obtained are nontrivial even when space-time is flat.     

Charge-carrier lifetimes in high-resistance GaAs doped by chromium diffusion

Application of high-resistance GaAs for the formation of ionizing radiation detectors calls for investigation of physical properties of this material. Studying the photoelectrical properties makes it possible to establish the recombination mechanisms of charge carriers and peculiarities of their transport in the electric fields as well as to evaluate the charge-carrier lifetimes. In this work, the results of studying the photoconductivity and Hall photoeffect are discussed for high-resistance GaAs doped by chromium diffusion. A typical lux-ampere characteristic is shown to consist of two parts: a superlinear part and a sublinear one. Changes in the Hall mobility under illumination are studied. A number of simplifications are made and the electron (τ _n) and hole (τ _p) lifetimes are estimated for high and low excitation levels. It is found that τ_p > τ _n. It is shown that the photoelectrical properties of high-resistance GaAs:Cr can be explained using the model of “ curved bands.” It is assumed that the potential barriers are transformed under photoexcitation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 84–88, May, 2008.     

Properties of the self-consistent field treatment of conjugated molecules

The polarizability properties of π electron systems are treated by the self-consistent field method, as modified by Pople for application to conjugated molecules. An analytical treatment of the π electron configuration of substituted hydrocarbons deduces certain universal symmetry properties of this method, and contains the Hückel treatment of inductive substituents as a simplified special case. Whereas the usual Hückel theory derives results by approximate perturbation methods, the treatment given here is formally exact. In a later section s.c.f. polarizability coefficients, as calculated on an Elliott 402 digital computer, are given for benzene, naphthalene, anthracene and phenanthrene, and the predictions of chemical properties are shown to be in better agreement with experiment than predictions derived from Hückel theory.     

The type-problem on the average for random walks on graphs

When averages over all starting points are considered, the type problem for the recurrence or transience of a simple random walk on an inhomogeneous network in general differs from the usual “local" type problem. This difference leads to a new classification of inhomogeneous discrete structures in terms of recurrence and transience on the average, describing their large scale topology from a “statistical" point of view. In this paper we analyze this classification and the properties connected to it, showing how the average behavior affects the thermodynamic properties of statistical models on graphs. Received 8 October 1999     

Nuclear vertex constants and asymptotic normalization coefficients for the tritium nucleus

The properties of the nuclear vertex constant for virtual triton decay to a deuteron and a neutron (T → d + n) are investigated along with the properties of the asymptotic normalization coefficient defined for the triton wave function and related to this constant. These quantities are calculated numerically on the basis of an equation that relates the asymptotic normalization coefficient to the triton effective radius ρ _T, which was introduced in the present study. The values of G _T² = 1.244(68) fm and C _T² = 2.958(162) found from our calculations are in good agreement with experimental and theoretical estimates obtained for these quantities in other studies. Physical properties of the triton virtual state are also discussed.     

Integrable nonlinear equations and Liouville's theorem,II

A symplectic structure is constructed and the Liouville integration carried out for a stationary Lax equation [L, P]=0, whereL is a scalar differential operator of an arbitrary order.n ^th order operators are included into the variety of first-order matrix operators, and properties of this inclusion are studied.     

Electric field effects on the linear and nonlinear intersubband optical properties of double semi-parabolic quantum wells

In this work, the effects of the electric field on the optical properties of the symmetric and asymmetric double semi-parabolic quantum wells (DSPQWs) are investigated numerically for typical GaAs/Al_xGa_1−xAs. Optical properties are obtained using the compact density matrix approach. Our calculations for the asymmetric DSPQW show that the resonant peak values of the total refractive index change and total optical absorption coefficient are maximum for a certain value of the applied electric field, due to the anti-crossing effect. However, for the symmetric DSPQW, the resonant peak values of these optical properties decrease monotonically with increasing the applied electric field. Also, our results indicate that a larger value of the optical rectification coefficient of the symmetric DSPQW can be induced by applying a small electric field.     

Stability properties and the KMS condition

First we derive stability properties of KMS states and subsequently we derive the KMS condition from stability properties. New results include a convergent perturbation expansion for perturbed KMS states in terms of appropriate truncated functions and stability properties of ground states. Finally we extend the results of Haag, Kastler, Trych-Pohlmeyer by proving that stable states ofL ¹-asymptotically abelian systems which satisfy a weak three point cluster property are automatically KMS states. This last theorem gives an almost complete characterization of KMS states, ofL ¹-asymptotic abelian systems, by stability and cluster properties (a slight discrepancy can occur for infinite temperature states).Supported during this research by the Norwegian Research Council for Science and Humanities     

Photoluminescence of TlCu<Subscript>1−x</Subscript>GaSe<Subscript>2</Subscript> single crystals

The results of the study of photoluminescence and its excitation spectra in Tl _x Cu_1−x GaSe₂ single crystals are presented. The crystals under study are layered and characterized by anisotropic optical properties. In this respect, it is important to investigate optical properties of the crystals under study.     

Magnetic properties of lithium intercalation compounds

Magnetic experiments are powerful tools to study fundamental properties and to check the qualities of samples. Temperature, stress, and impurities of materials can all affect magnetic properties and play an important role in the utilization of these materials for engineering applications. The estimation and analysis of the spontaneous magnetization can reveal ferromagnetic particles as impurities in samples. The shape of the temperature dependence of magnetization is indicative of the origin of the magnetic properties. However, it is necessary to correlate the χ _m (T) curves and isothermal M(H) plots to achieve a complete analysis of the electronic properties of the materials. Highlights of magnetic properties of lithium intercalation compounds are briefly described. Intrinsic and extrinsic properties are considered as useful parameters to determine the purity of electrode materials for rechargeable Li-ion batteries.     

Representation Theorem of Observables on a Quantum System

An orthomodular lattice (OML) with a conditional state can be used as a model for noncompatible events (a quantum system). In this paper we will study some properties of a conditional state and an s-map which are defined on an OML. We show conditions when a quantum system has the same properties as the classical probability space.