A self-consistent method of constructing an effective rotational Hamiltonian

Methods have become widely used in molecular spectroscopy that involve the construction of effective rotational Hamiltonians [1, 2]. One of these methods has been developed by one of us over several years [3, 4]. A simple basis is provided for this method and it is shown that the scheme for constructing the effective operator for the rotational energy is substantially self-consistent.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 68–72, May, 1981.     

Solution of the thermoelastoplastic problem for a thin disk of plastically compressible material subjected to thermal loading

Elastoplastic solutions for thin plates and disks are sensitive to loading and plasticity conditions [1–5]. The plasticity condition for a number of metal materials depends on the mean stress [6–8]. In this case, when using the associated flow rule, plastic deformations do not satisfy the incompressibility condition, which is commonly accepted in statements of boundary-value problems for thin elastoplastic plates and disks [9–13]. It is of interest to determine the effect of plastic compressibility on the behavior of solutions for such structures. In this paper, a hollow disk in a rigid container subjected to a uniform temperature field is considered. The plasticity condition proposed in [14] is accepted. A general study of the set of equations including this plasticity condition and the associated flow rule was performed in [15]. The solution under the Mises plasticity condition was obtained in [1].     

多变量Master方程及其波动解

本文讨论了线性反应过程:A→X多变量Master方程的波动解。除了可以由反应扩散方程得到的密度波以及由之耦合而成的多波解外,不可能得到类似于文献[2]中得到的涨落波分支。在考虑压力效应后,情况基本不变。本文讨论了由于化学反应及扩散的空间尺度(自由程)一般差别很大,多变量Master方程所存在的问题。 关键词：     

The effective dielectric constant of plasmas — A mean field theory built from the electromagnetic ionic T-matrix

This work aims to obtain the effective dielectric constant tensor of a warm plasma in the spirit of the derivation of a mixing law. The medium is made of non point-like ions immersed in an electron gas with usual conditions relating the various lengths which define the problem. In this paper the ion dielectric constants are taken from their RPA responses as developed in a previous paper [1]. Furthermore the treatment of the screening effects is made through a mathematical redefinition of the initial problem as proposed in Ref. [1]. Here the complete calculation of the T-matrix describing the scattering of an electromagnetic wave on an isolated ion immersed in an “effective medium” is given. It is used for building , in the spirit of a mixing law, a self-consistent effective medium theory for the plasma dielectric tensor. We then extend the results obtained in Ref. [1] to higher orders in ion or dielectric inclusion densities. The techniques presented are generic and can be used in areas such as elasticity, thermoelasticity, and piezoelectricity.     

Time-dependent solutions with localized energy of the Einstein system of equations and a nonlinear scalar field

A soliton-like time-dependent solution in the form of a running wave is derived of a self-consistent system of the gravitational field equations of Einstein and Born-Infeld type of equations of a nonlinear scalar field in a conformally flat metric. This solution is localized in space and possesses a localized energy. It is shown that both the gravitational field and the nonlinearity of the scalar field are essential to the presence of such a localized solution. In recent years various classical particle models have been widely discussed which are static or time-independent solutions of nonlinear equations with localization in space and which possess a finite field energy. In particular, soliton solutions [1], solutions in the form of eddies [2], and so on have been derived and investigated. All these solutions were treated in a flat space-time. It is of interest to derive the analogous particle-like solutions with the gravitational field taken into account; in particular it is of interest to investigate the roles of the gravitational field in connection with the formation of localized objects. These problems have been discussed in [3] in the static case. We will present below a soliton-like time-dependent solution in the form of a solitary running wave as an example of the inter-action of a Born-Infeld type of nonlinear scalar field and an Einstein gravitational field in a conformally flat metric.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 12–17, May, 1979.     

Generation of static solutions of the self-consistent system of Einstein-Maxwell equations

A theorem is proved, according to which to each solution of the Einstein equations with an arbitrary momentum-energy tensor in the right hand side there corresponds a static solution of the self-consistent system of Einstein-Maxwell equations. As a consequence of this theorem, a method is established of generating static solutions of the self-consistent system of Einstein-Maxwell equations with a charged grain as a source of vacuum solutions of the Einstein equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 98–102, February, 1988.     

Rational Solutions of the Master Symmetries¶of the KdV Equation

In this article we characterize a certain class of rational solutions of the hierarchy of master symmetries for KdV. The result is that the generic rational potentials that decay at infinity and remain rational by all the flows of the master-symmetry KdV hierarchy are bispectral potentials for the Schr?dinger operator. By bispectral potentials we mean that the corresponding Schr?dinger operators possess families of eigenfunctions that are also eigenfunctions of a differential operator in the spectral variable. This complements certain results of Airault–McKean–Moser [4], Duistermaat–Grünbaum [10], and Magri–Zubelli [40]. As a consequence of bispectrality, the rational solutions of the master symmetries turn out to be solutions of a (generalized) string equation. Received: 28 January 1999 / Accepted: 22 October 1999     

Characteristic features of exact solutions of the problem of an electron in the quantized field of a plane wave

The physical and mathematical features of exact solutions of the problem of an electron moving in the field of a quantized, plane electromagnetic wave [1–4] are investigated. In particular, the problem of constructing solutions for all values of the total energy of the system is solved. A new interpretation is given to the limiting approach to Volkov solutions [5, 6]. The completeness and orthogonality of the solutions are proven in the reference plane formalism. The notation of [4] is used in this paper.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 7–14, March, 1977.     

Stationary self-consistent distributions for a charged particle beam in the longitudinal magnetic field

A review of analytical solutions of the Vlasov equation for a beam of charged particles is given. These results are analyzed on the basis of a unified approach developed by the authors. In the context of this method, a space of integrals of motion is introduced in which the integrals of motion of particles are considered as coordinates. In this case, specifying a self-consistent distribution is reduced to defining a distribution density in this space. This approach allows us to simplify the construction and analysis of different self-consistent distributions. In particular, it is possible, in some cases, to derive new solutions by considering linear combinations of well-known solutions. This approach also makes it possible in many cases to give a visual geometric representation of self-consistent distributions in the space of integrals of motion.     

A class of exact solutions for coupled electromagnetic and scalar fields for einstein-rosen metric. II

This paper is a continuation of the author's earlier work entitled “A class of exact solutions for coupled electromagnetic and scalar fields for Einstein-Rosen metric. I.” [Ann. Physics69 (1972), 473]. In this paper we have interpreted some of the solutions from different viewpoints with special reference to singular behavior. It has been observed that the presence of zero mass scalar meson fields does not affect the singular behavior as when the electromagnetic field only is present.     

The correspondence principle between classical and quantum quantities

Questions of the reestablishment of a classical quantity from the known quantum operator are investigated in this article, in that case when the operators are constructed according to the rule proposed in article [15]. The existence of a twofold limiting transition is proved, in which the investigated rule satisfies the requirements of the correspondence principle.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 18–23, June, 1974.The author expresses his deep gratitude to V. V. Kuryshkin for suggesting the topic and for systematic aid in the work.     

Solution formulas for the two-dimensional Toda lattice and particle-like solutions with unexpected asymptotic behaviour

The first main aim of this article is to derive an explicit solution formula for the scalar two-dimensional Toda lattice depending on three independent operator parameters, ameliorating work in [31]. This is achieved by studying a noncommutative version of the 2d-Toda lattice, generalizing its soliton solution to the noncommutative setting.

The purpose of the applications part is to show that the family of solutions obtained from matrix data exhibits a rich variety of asymptotic behaviour. The first indicator is that web structures, studied extensively in the literature, see [4] and references therein, are a subfamily. Then three further classes of solutions (with increasingly unusual behaviour) are constructed, and their asymptotics are derived.     

Spontaneously broken symmetries in gravitational fields

In the present work we study models with material and gravitational fields unified in a self-consistent manner [2, 3]. We use a semiclassical approach, where the gravitational field is classical, but the other fields may be quantum ones. The mechanism of spontaneous symmetry breaking is due to the conformai generalization of the Higgs fields in a curved spacetime. Gravitation will be considered as a gauge field and then in the usual Einstein version.     

A modified equation for single-mode superradiance kinetics

A new method is proposed for decoupling the chain of quantum equations, which incorporates the fluctuations in the population difference between levels in the atoms near the maximum in the superradiance intensity. A new system of equations is derived that describes a broader and more unsymmetrical superradiance pulse than does the results of [1–4]. The new solutions improve the agreement between theory and experiment [5].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 27, No. 1, pp. 28–33, January, 1984.     

Room Temperature Phosphorimetry as a New Spectrochemical Method of Analysis

Abstract

Luminescence spectroscopy has been extensively applied in the fields of clinical chemistry, biochemistry, and environmental chemistry. Proteins, nucleic acids, enzymes, drugs, and pollutants all show characteristic luminescence properties. The unexcelled sensitivity, selectivity, ease of sampling, and breadth of application of this method is of considerable interest to every analytical researcher and analyst. Whereas fluorimetry has become a well-established method for analysis [11, phosphorimetry has been used during the past decade only for a limited number of quantitative analyses, including the analysis of poly-nuclear aromatic compounds [2–41, coal tar fractions [5], air pollutants [6-8], impurities in petroleum fractions [9–111, detection of pesticides, and fungicides in foods [12–17], and the analysis of amino acids and pharmaceutical compounds in biological fluids [18–26]. Only recently has phosphorimetry been extensively developed into a practical qualitative and quantitative analytical method. Several papers have appeared in which the progress in instrumentation and methodology as well as the analytical uses of phosphorimetry were given [27–30]. In the 1960s the lack of use of phosphorimetry for quantitative analysis was primarily due to the great complexity and time needed to prepare and carry out an analysis at low temperature, and the poor precision and accuracy of measurements of snowed, opaque, or cracked inhomogeneous samples. In the early 1970s, improvements were achieved with techniques to enable the measurement of opaque matrices of organic solvents [31] and the development of time-resolved and phase-resolved phosphorimetry [32-361. However, in most phosphorimetric studies, the analysis still had to be performed using either low temperature rigid solvents of organic glasses, polymer matrices, or carefully degassed and purified solutions in order to minimize collisional triplet quenching. These requirements still are the main disadvantages which make this spectro-chemical method less-widely used than fluorimetry. Recently, the observed phenomenon of intense phosphorescence at room temperature (RTP) from ionic organic compounds adsorbed on a variety of supports, such as silica, alumina, paper, and asbestos [36, 37], has been proposed as a new analytical technique [38–42]. A large variety of ionic compounds of biological and clinical interest [38-40] has been investigated by this new method. The use of external heavy atom perturbers has also been investigated for the determination of trace nonionic compounds, such as the polyaromatic hydrocarbons [41]. Significant progress has been achieved with the development of a simple device for automated RTP measurement [42].     

Bianchi Type VI0 Cosmological Models with Perfect Fluid and Dark Energy

We consider a self-consistent system of Bianchi Type VI₀ cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=??? with ????[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein??s field equations are obtained as a quadrature. Models with power-law and exponential expansion have discussed in detail.     

Renormalisation of out-of-equilibrium quantum fields

We consider the initial value problem and its renormalisation in the framework of the two-particle-irreducible (2PI) effective action. We argue that in the case of appropriately chosen self-consistent initial conditions, the counterterms needed to renormalise the system in equilibrium are also sufficient to renormalise its time evolution. In this way we improve on Gaussian initial conditions which have the disadvantage of generically not showing a continuum limit. For a more detailed discussion see [Sz. Borsányi and U. Reinosa, arXiv:0809.0496].     

Electronic transport for pristine and doped crossed graphene nanoribbon junctions with zigzag interfaces

Using the fully self-consistent non-equilibrium Green?s function (NEGF) method combined with density functional theory, we investigate numerically the electronic transport property for pristine and doped crossed graphene nanoribbon (GNR) junctions. It is demonstrated that in the case of zigzag interfaces, the I–V characteristics of the junction with or without doping always show semiconducting behavior, which is different from that in the case of armchair interfaces [Zhou, Liao, Zhou, Chen, Zhou, Eur. Phys. J. B 76 (2010) 421]. Interestingly, negative differential resistance (NDR) behavior can be clearly observed in a certain bias region for nitrogen-doped shoulder crossed junction. A mechanism for the NDR behavior is suggested.     

First-principles study of phenyl ethylene oligomers as current-switch

We use a self-consistent method to study the distinct current-switch of 2′-amino-4-ethynylphenyl-4′-ethynylphenyl-5′-nitro-1-benzenethiol, from the first-principles calculations. The switch behavior is in accord with the early experiment [M.A. Reed, J.H. Tour, Sci. Am. 282 (2000) 86]. To further investigate the transport mechanism of the conformational molecular switch, we calculate the switching behavior of p-terphenyl with the rotations of the middle ring as well, the results are consistent with Reed's experiment. We also study the effect of the hydrogen atom substituting one ending sulfur atom on the transport and find that the asymmetry of I–V curves appears and the switch effect still lies in both the positive and negative bias range.     

New exact solutions of the Dirac equation. IX

Exact solutions of the equations of motion of a charge in external electromagnetic fields of seven new types are investigated. The notation and system of units used in this article coincide with those used in [1].Translated from Izvestiya Vysshikh Uchebenykh Zavedenii, Fizika, No. 3, pp. 46–49, March, 1978.