Superintegrability on N-dimensional spaces of constant curvature from so(N + 1) and its contractions

The Lie—Poisson algebra so(N + 1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the N-dimensional spherical, Euclidean, hyperbolic, Minkowskian, and (anti-)de Sitter spaces. We firstly present a Hamiltonian which is a superposition of an arbitrary central potential with N arbitrary centrifugal terms. Such a system is quasi-maximally superintegrable since this is endowed with 2N — 3 functionally independent constants of motion (plus the Hamiltonian). Secondly, we identify two maximally superintegrable Hamiltonians by choosing a specific central potential and finding at the same time the remaining integral. The former is the generalization of the Smorodinsky—Winternitz system to the above six spaces, while the latter is a generalization of the Kepler—Coulomb potential, for which the Laplace—Runge—Lenz N vector is also given. All the systems and constants of motion are explicitly expressed in a unified form in terms of ambient and polar coordinates as they are parametrized by two contraction parameters (curvature and signature of the metric). The text was submitted by the authors in English.     

Green’s functions in quantum chemistry I. The Σ perturbation method

As an improvement over the Hartree-Fock approximation, we investigate a Green’s Function method—theΣ perturbation method—for molecular calculations. The method is applied to hydrogen molecule and to theπ-electron system of ethylene under PPP approximation. When the algebraic approximation is used, the energy obtained is better than that of the HF approach, but is not as good as that of the configuration-interaction method. The main advantage of this procedure is that it is devoid of the most serious defect of HF method, viz. incorrect dissociation limits.     

Memory electrical switching in hydrated amorphous vanadium dioxide

Experimental data for the effect of memory electrical switching in a metal—oxide—metal structure based on hydrated vanadium dioxide obtained by the method of anodic—cathodic polarization are discussed. A model that assumes the key role of the ion current in the switching mechanism is suggested. This model makes it possible to determine the critical parameters of the material (the concentration and mobility of impurity ions) that influence the origination of the effect. The field dependence of the ion mobility derived by simulating the switching effect is explained through the hopping transfer mechanism in terms of the percolation theory.     

Connecting cluster dynamics and protein folding

The relaxation dynamics of clusters can be interpreted in terms of the topographies of their potential surfaces. Systems with short-range potentials have sawtooth-like potential surfaces with small drops in energy from one local minimum to the next and few-body motions as the clusters move from one minimum to another; such systems readily take on amorphous structures. These are called “glass-formers". Systems with long-range forces have potentials whose topographies are like rough staircases, with some large drops in energy from one minimum to the next; their well-to-well passages involve very collective motions and such systems are excellent structure-seekers. They find their way to well-ordered, highly selective structures under almost all circumstances. These characteristics generalize to describe the potential surfaces and folding behavior of polypeptides and proteins. The forces are effective long-range forces due to the polymer chain. Staircase topographies emerge both from direct sampling of potential surfaces and from the inversion of the kinetics generated by a much more aaabstract topological model, from which folding pathways can be inferred. Received 4 December 2000     

Erosion of the GaAs target under irradiation by a high-power pulsed ion beam

The results of examination of the GaAs-target erosion under irradiation by a high-power pulsed ion beam are reported. In the experiments, use was made of a high-power pulsed ion source with the following parameters: ion energy — 250 keV, target current density — 350 A/cm², pulse duration — 80 ns, target energy density — up to 7 J/cm². The target erosion coefficient and its dependence on the number of successive pulses are measured. It is found that the surface roughness parameter is increased with the number of successive beam pulses. A regular structure of surface relief is observed to form in the case where the number of pulses > 20–40. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 66–70, January, 2007.     

Multilayer mirror systems to form hard X-ray beams

This paper is an overview of the research activities carried out in the past five years at the Institute for Physics of Microstructures RAS and “X-ray” Company towards the manufacture of multilayer mirror systems capable of forming X-ray beams in the subnanometer range of wavelengths. The systems fabrication technology is presented, including techniques for producing supersmooth surfaces of specified shape, methods of graded multilayer structure deposition on such surfaces, and the principles of designing optimal mirror parameters. The characteristics of a quadrelliptical reflector—a novel high light-gathering power four-corner focusing system—are reported.     

Development of inelastic effects in the transport characteristics of spin nanostructures

The influence of inelastic spin-dependent effects on the transport of a spin-polarized electron through model nanostructures of two-, four- and six-spi n clusters was investigated. It was shown that the spin—flop processes induced by the s-d(f)-exchange interaction of an electron and a nanocluster lead to changes in the potential profile and to qualitative changes in the transport characteristics’ energy dependence.     

Thermooxidative degradation of blends based on poly(3-Hydroxybutyrate). Specifics of the process

The relationship between the structure and the kinetics of the thermal oxidation of the poly(3-hydroxybutyrate) — ethylene propylene rubber and polyethylene — poly(3-hydroxybutyrate) systems is studied. For the first system containing 30–50 wt % poly(3-hydroxybutyrate), phase inversion is observed, which affects its reactivity. For the compositions with polyethylene, two stages of oxidation manifest themselves: before and after poly(3-hydroxybutyrate) degradation.     

Models for the 3D singular isotropic oscillator quadratic algebra

We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential—differential or differential—difference and difference—difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.     

Revealing Bell’s nonlocality for unstable systems in high energy physics

Entanglement and its consequences—in particular the violation of Bell inequalities, which defies our concepts of realism and locality—have been proven to play key roles in Nature by many experiments for various quantum systems. Entanglement can also be found in systems not consisting of ordinary matter and light, i.e. in massive meson–antimeson systems. Bell inequalities have been discussed for these systems, but up to date no direct experimental test to conclusively exclude local realism was found. This mainly stems from the fact that one only has access to a restricted class of observables and that these systems are also decaying. In this Letter we put forward a Bell inequality for unstable systems which can be tested at accelerator facilities with current technology. Herewith, the long awaited proof that such systems at different energy scales can reveal the sophisticated “dynamical” nonlocal feature of Nature in a direct experiment gets feasible. Moreover, the role of entanglement and CP\mathcal{CP} violation, an asymmetry between matter and antimatter, is explored, a special feature offered only by these meson–antimeson systems.     

Structure of quantum-mechanical relativistic two-body interactions for spinning particles

Relativistic constraint mechanics yields consistent systems of coupled Dirac equations for pairs of spinning particles. We explicitly connect these equations to the Bethe-Salpeter equation of quantum field theory and to the interactions of classical Fokker-Tetrode dynamics (and hence to classical relativistic field theory) to obtain versions of these equations governed by systems of (possibly noncoulombic) relativistic potentials whose detailed structures contain important relativistic effects like correct Darwin interactions. We recast the defining pair of Dirac equations in a number of equivalent but important forms—“external potential,” Sazdjian, hyperbolic, and Breit— and examine their interconnection. Since the potentials in these equations are no more singular than — 1/4r² we are able to solve appropriate versions of them nonperturbatively for the qˉq system to obtain a very good fit to the entire meson spectrum and for the e ⁺ e ⁻ system to calculate the positronium spectrum of QED correct through order α ⁴ .     

Neutron-, ion-, and electron-energy spectra in a 1 kJ plasma focus

The neutron energy spectrum (4 Torr deuterium) was determined from 30 m flight histograms.—An average energy of approximately 100±20 keV of the neutron producing deuterons within an assumed cone angle of approximately 40 degrees along thez-axis was calculated by means of the target beam model.—Shadow bar techniques reveal that only 10% of the neutrons are produced in the ≈1 cm long focus.—Experimental time of flight analysis confirms that the ion spectrum extends from less than 70 to greater than 400 keV. The electron spectrum in 8 Torr hydrogen follows a ≈3 keV Boltzmann distribution, but demonstrates the presence of nonthermal >100 keV electrons.     

Computer simulation of interdiffusion in polycrystalline thin film couples

Computer simulation of superimposed lattice, grain boundary and surface diffusion, characteristic for polycrystalline thin film diffusion systems, was performed by way of discretisation of the nonlinear diffusion law. In order to give a vivid impression how such a complex process takes place under some typical conditions we have chosen pseudo three-dimensional computer plots of the spacial distribution of the concentration instead of the commonly used iso-concentration diagrams. The following cases are considered:

Organic thin-film transistors of pentacene films fabricated from a supersonic molecular beam source

Top-contact organic thin-film transistors (OTFTs) of pentacene have been fabricated on bare SiO₂ and SiO₂ modified with hexamethyldisilazane (HMDS) and octadecyltrichlorosilane (OTS). The pentacene films were deposited from a supersonic molecular beam source with kinetic energy of incident molecules ranging from 1.5 to 6.7 eV. The field-effect mobility of OTFTs was found to increase systematically with increasing kinetic energy of the molecular beam. The improvements are more important on HMDS- and OTS-treated surfaces than on bare SiO₂. Tapping mode atomic force microscopy images reveal that pentacene thin films deposited at high kinetic energy form with significantly larger grains—independent of surface treatment—than films deposited using low-energy beams.     

Thermosynthetic Life

Two categories of life are currently recognized—chemosynthetic and photosynthetic—indicating their principal free energy resource as either chemicals or electromagnetic radiation. Building on recent developments in thermodynamics, we posit a third category of life—thermosynthetic life (TL)—which relies on environmental heat rather than traditional free energy sources. Since thermal energy is more abundant than chemicals or light in many settings, thermosynthesis offers compelling evolutionary possibilities for new life forms. Based on variants of standard cellular machinery, a physical model is proposed for the conversion of thermal energy into biochemical work. Conditions favorable to thermosynthetic life and prospects for its discovery are assessed. Terrestrially, deep-subsurface unicellular anaerobic superthermophiles are deduced to be likely TL candidates.     

Structure and melting of dipole clusters

Two-dimensional microclusters made up of particles repelled by the dipole law and confined by an external quadratic potential are considered. The model describes a number of physical systems, in particular, electrons in semiconductor structures near a metallic electrode, indirect excitons in coupled semiconductor dots etc. Two competing types of particle ordering in clusters have been revealed: formation of a triangular lattice and of a shell structure. Equilibrium configurations of clusters with N=1–40 particles are calculated. Temperature dependences of the structure, potential energy, and mean-square radial and angular displacements are studied. These characteristics are used to investigate cluster melting. Melting occurs in one or two stages, depending on N. Melting of a two-shell microcluster takes place in two stages: at low temperatures—from the frozen phase to a state with rotationally reoriented “crystalline” shells with respect to one another, followed by a transition involving breakdown of radial order. Melting in a cluster made up of a larger number of shells occurs in one stage. This is due to the fact that the potential barrier to intershell rotation is substantially lower than that to particle jumping from one shell to another for small N, and of the same order of magnitude for large N. A method is proposed for predicting the character of melting in shell clusters by comparing the potential barriers for shell rotation and intershell particle jumping. Fiz. Tverd. Tela (St. Petersburg) 40, 1379–1386 (July 1998)     

The potential energies of the Na** + He quasi-molecule

The special features of the behavior of the potential energy surfaces of the system comprising a highly excited A** atom and a neutral B atom with a filled electronic shell were thoroughly analyzed. This was done using the integral variant of theory combined with the generalized finite radius potential method correctly describing the scattering of a weakly bound electron by the B atom. The method allows P scattering to be taken into account. This scattering causes the additional splitting of potential energy surfaces into separate groups of interacting terms classified according to the projection m of the electron angular momentum l onto the quasimolecular axis. Calculations of the nl(^{2s + 1}Λ) state potential curves of the Na** + He quasi-molecule (n, l, and Λ are the principal quantum number, angular momentum, and its projection onto the molecular axis, and s is the spin of the system) were performed. The calculation results were compared to those obtained by other authors.     

Spin excitons — a new mechanism of superconducting pairing in copper oxides

The Fermi and Bose quasiparticle spectrum in copper oxides is studied in a many-band p-d model taking account of the strong electronic correlations. It is shown that hole-doped systems possess a Bose mode — a spin exciton — which is associated with the singlet-triplet excitation of the two-hole ground-state term of CuO₄ clusters. Intercluster hopping leads to fermion-boson interaction with a spin exciton as the intermediate boson. Such a mechanism does not exist for n-type systems. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 23–28 (10 July 1996)     

Studies of phase transitions and quantum chaos relationships in extended Casten triangle of IBM-1

A precise solution of the classical energy functional E(N, η, χ; β) minimum problem with respect to deformation parameter β is obtained for the simplified Casten version of the standard interacting boson model (IBM-1) Hamiltonian. The first-order phase transition lines as well as the critical points of X(5), -X(5), and E(5) symmetries are considered. The dynamical criteria of quantum chaos—the basis state fragmentation width and the wave function entropy—are studied for the (η, χ) parameter space of the extended Casten triangle, and the possible relationships between these criteria and phase transition lines are discussed. The text was submitted by the authors in English.     

Studies of the classical energy limit of the interacting boson model in the case of three-body interactions

In this study of the classical energy limit of an interacting boson model with three-body interactions, two variants are considered: the inclusion of cubic d-boson interaction terms and the inclusion of three-body O(6) symmetric quadrupole operator terms. The solutions of the corresponding energy minimum condition equations are used for analysis of the triaxiality of the nuclear shape in the first case and for analysis of spherical—prolate—oblate shape phase transitions in the second case. The text was submitted by the authors in English.