An iterative method for calculating the polar component of the molecular solvation Gibbs energy under a smooth change in the dielectric permittivity of a solution

An iterative method for calculating the polar component of the solvation Gibbs energy under a smooth change in dielectric permittivity, both between a substrate and a solvent and in a solvent is formulated on the basis of a previously developed model. The method is developed in the approximation of the local relationship D = ɛ(r)E between the displacement vectors D and the electric field intensity E.     

Location of the minimum of the differential tunneling resistance in a superconductor-degenerate semiconductor Schottky contact

Measurements of differential resistance in a superconductor-degenerate semiconductor junction Nb - n ^{+ +} GaAs at T = 1.6 K show close similarity to those for a conventional superconductor-insulator- normal metal junction, except for the position of the minimum which is located at 3.6 meV. Using a simple model for the charge screening at the Schottky barrier, we give an argument why this minimum is by far displaced with respect to the superconducting gap energy ( Δ _g = 1.5 meV for bulk Nb). We argue that a rebuilding of the density of states takes place at the barrier, due to the imperfect metal screening in the degenerate semiconductor. Energy states close to the degenerate semiconductor Fermi energy are depleted at the barrier and are not available for tunneling, up to an energy E_g which adds to the superconducting gap Δ _g . Received 11 November 2002 / Received in final form 21 February 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: c.nappi@cib.na.cnr.it     

Calculation of the force characteristics of a multi-coil suspension of a superconducting sphere

The theory presented in the accompanying paper [Ref. 1: Zh. Tekh. Fiz. 67(1), 3 (1997); Tech. Phys. 42, 1 (1997)] for the calculation of the magnetic field and the force characteristics of an electromagnetic suspension for a superconducting body is used to carry out specific calculations of the force characteristics of a multi-coil suspension of a superconducting sphere. Formulas are obtained for the dependence of the force and the stiffness, from which it is possible to approach the problem of the stable suspension of a superconducting sphere in the field of a system of circular currents. The problem of determining the magnetic field at the sphere is analyzed and the conditions are found for which it is less than the critical field. Zh. Tekh. Fiz. 67, 10–16 (January 1997)     

On the Superdiffusive Behavior of Passive Tracer with a Gaussian Drift

In the present article we consider a motion of a passive tracer particle, whose trajectory satisfies the Itô stochastic differential equation d x(t) = V(t, x(t)) dt + d w(t), where w(·) is a Brownian motion, V is a stationary Gaussian random field with incompressible realizations independent of w(·) and >0. We prove the superdiffusive character of the motion under certain conditions on the energy spectrum of the velocity field. The result is shown both for steady (time independent) and time dependent and Markovian velocity fields. In addition, we provide explicit upper and lower bounds for the Hurst exponent of the trajectory. All previous rigorous results concerned explicitely solvable shear flows cases.     

Exact solution for a degenerate Anderson impurity in the limit embedded into a correlated host

We consider the one-dimensional t - J model, which consists of electrons with spin S on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J = t. Without spoiling the integrability we introduce an Anderson-like impurity of spin S (degenerate Anderson model in the limit), which interacts with the correlated conduction states of the host. The lattice model is defined by the scattering matrices via the Quantum Inverse Scattering Method. We discuss the general form of the interaction Hamiltonian between the impurity and the itinerant electrons on the lattice and explicitly construct it in the continuum limit. The discrete Bethe ansatz equations diagonalizing the host with impurity are derived, and the thermodynamic Bethe ansatz equations are obtained using the string hypothesis for arbitrary band filling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter related to the Kondo exchange coupling. The impurity can localize up to one itinerant electron and has in general mixed valent properties. Groundstate properties of the impurity, such as the energy, valence, magnetic susceptibility and the specific heat coefficient, are discussed. In the integer valent limit the model reduces to a Coqblin-Schrieffer impurity. Received: 31 December 1997 / Accepted: 17 March 1998     

Calculating coefficients for a system of moment equations used to describe the magnetization kinetics of a superparamagnetic particle in a fluctuating field

A system of equations is derived for moments [averages of spherical harmonics 〈Y _l,m 〉(t)] that determine the dynamics of the magnetization M of a superparamagnetic particle in a fluctuating field. The system is derived by representing the Gilbert equation in a fluctuating field, and the corresponding Fokker-Planck equation for the distribution function of M, in terms of angular momentum operators, which in turn makes it possible to express the coefficients of the system of moment equations in terms of Clebsch-Gordan coefficients. Fiz. Tverd. Tela (St. Petersburg) 41, 2020–2027 (November 1999)     

Selectivity in the aggregates of the chiral organolithium N-Boc-2-lithiopiperidine with a chiral ligand: a DFT study

In this paper the aggregates of the chiral organolithium N-Boc-2-lithiopiperidine [Boc=CO₂C(CH₃)₃], which play an important role in the formation of chiral 2-substituted piperidines found in many alkaloid structures and medicinal compounds, have been investigated within the framework of Density Functional Theory (DFT) calculations. In the complex structures, the lithium atoms are tetra-coordinated, the diaminoalkoxide ligand is tridentate to one lithium atom and forms a chelate with the substrate which is stabilized by the solvent diethyl ether. The same type of bonding was observed for all the different ligand-bound structures; for ligands 6 and 7, which have bulky substituents, selectivity was in agreement with experiment. The results shed light on the microscopic structures of these species and suggest a potential ligand, 11, to yield high enantioselectivity.     

Bose-Einstein condensation in a static scalar field from the standpoint of the Goursat problem

The Goursat problem, developed by the present authors in previous papers [Ukr. Fiz. Zh. (Russ. Ed.) 27, 1602 (1982); Differentsial’nye Uravneniya 20, 302 (1984); J. Math. Phys. 33, 233 (1996)], is used to study the energy spectrum of a scalar relativistic particle in a static axisymmetric external scalar field of an attractive nature. This is obviously a model. It is shown that the problem formulated in this way has no unstable solutions, i.e., solutions increasing with time, in contrast to the Cauchy problem, where such solutions appear when the square of the particle frequency (energy) vanishes (in other words, in a Bose-Einstein condensation) Zh. éksp. Teor. Fiz. 112, 1167–1175 (October 1997)     

A novel electron scattering apparatus combining a laser photoelectron source and a triply differentially pumped supersonic beam target: characterization and results for the resonance

A novel electron scattering apparatus for high resolution studies of angle-differential elastic and inelastic electron scattering from atoms and molecules in the gas phase is described and its performance characterized. It combines a laser photoelectron source, a triply differentially pumped collimated supersonic beam target (half angle 0.015 rad, background to beam density ratio < 0.01), and several electron multipliers for simultaneous detection of elastically scattered electrons and metastable atoms (or molecules) due to inelastic scattering. In detailed test measurements of the yield for the production of metastable He^*(2³S₁) atoms around its threshold, the dependence of the overall energy width on various experimental parameters has been investigated. So far a resolution down to 7 meV (FWHM) has been obtained. Under such conditions we have investigated the profile of the He^- (1 s 2 s ^{2 2} S _1/2 ) resonance at the scattering angles 22 ^° , 45 ^° , and 90 ^° . From a consistent fit of the measured profiles by resonant scattering theory we determine a new value for the resonance energy ( E _r = 19.365(1) eV) and an accurate resonance width ( Γ = 11.2(5) meV). These results are consistent with the previously recommended values. Received 23 July 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: hotop@physik.uni-kl.de RID="b" ID="b"Permanent address: Department of Physics and Astronomy, Drake University, Des Moines, IA 50311, USA.     

Spatial structure of a particle collision region and its relationship with the angular distribution of a detectable particle

Within the framework of the SO(2.1) algebra formalism, a relationship is obtained between the differential cross section over the transverse particle momentum and the differential distribution over the spatial parameter b describing coordinates of the production region of this particle. The relationship obtained between the cross sections over q _⊥ and b is exact and is not related with a definite model; therefore, the spatial target structure can be analyzed on the basis of experimental data on the angular distributions of the detectable particle. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 33–37, June, 2008.     

On a Mathematical Framework for the Constitutive Equations of Anisotropic Dielectric Relaxation

Three classes of time-domain non-relativistic anisotropic dielectric constitutive equations of increasing generality are discussed. In each class dissipativity is ensured by the choice of a class of convolution kernels in the D-to-E constitutive equation expressing the electric field E in terms of the electric displacement field D. Defining properties of the inverse (E-to-D) kernels and their Fourier-Laplace transforms (complex dielectric functions) are determined by inversion of the D-to-E constitutive equation. By this procedure it is shown that dielectric functions of the dipolar dielectrics are tensor-valued Bernstein functions while the dielectric functions of the Drude-Lorentz type are tensor-valued negative definite functions. The properties of the complex dielectric permittivities are also determined for either class. The theory is applied to an exhaustive review of empirical response functions of real dielectric materials encountered in the literature. Each class of convolution kernels is consistent with existence of a conserved energy, but in one case a strictly dissipative energy can be constructed.     

Relaxation of a hard-sphere gas and criteria of validity of the calculations

The isotropic Boltzmann equation is solved using the Sonin moment system of equations. The main task here is the construction of a matrix describing the particle interaction. Such a matrix has been constructed analytically for various interaction cross sections in a number of papers [M. Barnsley and G. Turchetti, Lett. Nuovo Cimento 33, 347 (1982); G. Turchetti and M. Paolilli, Phys. Lett. A 90, 123 (1982); F. Schürrer and G. Kügerl, Phys. Fluids A 2, 609 (1990); A. Ya. énder and I. A. énder, Tech. Phys. 39, 997 (1994)]. Calculations of matrix elements arrived at by different methods for the hard-sphere model are compared. Some general properties of the matrix are found that can be used as criteria of the validity of the calculations. With the help of such criteria it is shown that the nonlinear matrix elements were calculated incorrectly by Schürrer and Kügerl (op. cit.). Zh. Tekh. Fiz. 68, 18–26 (May 1998)     

Bias and temperature dependence of the noise in a single electron transistor

Models generalizing the su (2) XX spin-chain were recently introduced. These XXC models also have an underlying su (2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the A_m Lie algebras. Integrability of the new models is shown in the context of the quantum inverse scattering method. Their R-matrix is found and shown to yield a representation of the Hecke algebra. The diagonalization of the transfer matrices is carried out using the algebraic Bethe Ansatz. I comment on eventual generalizations and possible links to reaction-diffusion processes. Received: 24 June 1998 / Received in final form: 8 September 1998 / Accepted: 10 September 1998     

On the possibility of investigating the dispersion of the energy bands of a crystal using resonant x-ray emission spectra

It is shown that, when the dispersion of the energy bands of crystals is investigated by resonant x-ray emission (RXE), an ambiguity can arise in the determination of k _tr — the transition point in k space — as a result of the characteristic features of the band structure and the value of the matrix elements. It is proposed that calculations of the distribution of partial contributions to interband optical transitions in the Brillouin zone (BZ) be used as a means of obtaining a simplified estimate of k _tr. The basic properties of this distribution are examined for lithium hydride, which is a convenient model object having a simple band structure and interband transitions which have been studied in detail. It is shown that the k points of the general position, which form a complex figure in the BZ, make the main contribution to the interband transitions. The contribution of high-symmetry points is much smaller mainly because of their small representativeness. This make it easier to understand the reason for the possible nonmonotonic variation of k _tr in RXE measurements of the dispersion of the energy bands of crystals or the sharp changes in the resonance-fluorescence intensity. Fiz. Tverd. Tela (St. Petersburg) 41, 1597–1601 (September 1999)     

Electrodynamics Under a Possible Alternative to the Lorentz Transformation

A generalization of the classical electrodynamics for systems in absolute motion in presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate two inertial frames: the privileged frame S and the moving frame S with velocity v with respect to S. b) The transformation of the fields from S to the moving frame S is given by H = a(H – v × D) and E = a(E + v × B), where a is a matrix whose elements depend of the absolute velocity of the system. c) The constitutive relations in the moving frame S are given by D = E, B = H and J = E. It is found that Maxwell's equations, which are transformed to the moving frame, take a new form depending on the absolute velocity of the system. Moreover, differing from classical electrodynamics, it is proven that the electrodynamics proposed explains satisfactorily the Wilson effect.     

Shaping of the electron distribution function in a striated solution

Numerous papers have been devoted to the investigation of striations in inert gases at low pressures (p⩽2 Torr) and small currents (i<100 mA) [A. V. Nedospasov, Sov. Phys. Usp. 11, 174 (1968); L. Pekarek, Sov. Phys. Usp. 11, 188 (1968); N. L. Oleson and A. W. Cooper, Adv. Electron. Electron Phys. 24, 155 (1968); P. S. Landa, N. A. Miskinova, and Yu. V. Ponomarev, Sov. Phys. Usp. 23, 813 (1980)]. Since the nature of striations is determined under these conditions by the nonlocal kinetics of the electrons in spatially periodic fields [L. D. Tsendin, Sov. J. Plasma Phys. 8, 228 (1982)], an investigation of the electron distribution function in space and time would be very interesting. The purpose of the present work is to experimentally investigate the potential profiles and distribution functions in S and P striations and to analyze the mechanism which shapes the distribution functions for striations of these types. Zh. Tekh. Fiz. 67, 14–21 (September 1997)     

Stability of a bubble in a dielectric liquid in an external electrostatic field

Critical instability conditions are found for a gas bubble in a liquid dielectric in a uniform external electrostatic field E ₀. It is shown that they depend both on the magnitude of E ₀ and on the properties of the liquid, as well as on the gas pressure in the bubble. In a linear approximation with respect to the square of the eccentricity of an equilibrium spheroidal form, the equilibrium eccentricity of the bubble exceeds the equilibrium eccentricity of a drop in the field E ₀. The gas pressure in the bubble lowers the critical electric field E ₀ for development of an instability in the bubble. Zh. Tekh. Fiz. 69, 43–48 (August 1999)     

Calculation of the characteristics of the radiation from a generator with a virtual cathode

A three-dimensional computer model, described by a system of Maxwell-Vlasov equations, for the interaction of a plasma with the electromagnetic field was used to calculate the excitation of a field by a relativistic electron beam with a virtual cathode oscillating in a resonance chamber. The characteristics of the generator radiation are investigated. Zh. Tekh. Fiz. 69, 87–92 (February 1999)     

Search for a Magnetic-Field Dependence of the Interaction of the Nuclear Quadrupole Moment with the Electric-Field Gradient

It is argued that the nuclear quadrupole–electric field gradient (EFG) interaction is, in principle, dependent on the presence of a magnetic fieldB. A rough estimate of the size of this effect yields 10⁻⁴in fields up to 10 T. However, if the site symmetry of the nucleus in question includes time-reversal symmetry, the linear dependence of the EFG onBvanishes. In diamagnetic compounds, time-reversal symmetry is violated only by the presence of nuclear spins. In such compounds, the dominant dependence of the EFG onBshould be quadratic and should be described by a fourth-rank tensor. In ferro- and antiferromagnetic compounds time-reversal symmetry is strongly violated and a linear dependence of the EFG onB, described by a third-rank tensor, is expected. A search for a magnetic field dependence of the EFG was carried out by measuring the quadrupole coupling constants (QCCs) of the²⁷Al and¹⁴N nuclei in corundum and sodium nitroprusside (SNP) by pure NQR, and by NMR in fields of 6.3 and 11 T. These diamagnetic compounds were selected because previous measurements, done in different fields, yielded differing results for the QCCs. A new technique for measuring QCCs by NMR is introduced that circumvents the necessity of precisely orienting the sample crystals. For the QCCs of both the²⁷Al and¹⁴N nuclei in corundum and SNP, respectively, a precision of distinctly better than 10⁻⁴is reached. The results obtained in 0, 6.3, and 11 T fields fully agree with each other which means that, in fields up to 11 T, any possible field dependence of the QCCs is smaller than 10⁻⁴. These results confirm that in diamagnetic compounds a linear dependence of QCCs onBis largely suppressed.     

Potential use of small basis set on the calculations of electronic properties of some four-membered heterocycles: a conformational study

The potential use of small basis sets upon a low level of theory was studied on the calculations of electronic properties (dipole moment, static polarisability and static hyperpolarisabilities) of a series of 16 four-membered heterocycles with an exocyclic double bond at the position 3 (1–16). First, the calculations were performed within the Hartree–Fock (HF) approximation using 6-31G, 6-31G(d,p) and 6-31+G(d,p) as basis sets for the different conformational states of each molecule, and the results obtained were compared with the MP2/6-31+G(d,p) results reported. In the second place, in order to know the real potential of HF calculations, these were compared with those calculated using larger approaches such as MP2/6-311+G(d,p), MP2/aug-cc-pVDZ, CCS/6-311+G(d,p), CCS/aug-cc-pVDZ, CCS/aug-cc-pVTZ, CCSD/6-31+G(d) and CCSD/cc-pVDZ, taken into account only the planar and equilibrium geometries of each molecules. The HF approaches permit us to obtain a good qualitative representation of the dipole moment as a function of puckering angle in comparison with MP2, CCS and CCSD levels for all tested molecules. However, only HF/6-31+G(d,p) provides quantitative values of dipole moment for the heterocycles 1, 5 and 13 in comparison with MP2, CCS and CCSD levels. On the other hand, the polarisability and hyperpolarisabilities were quite sensitive to the quality of level of theory and basis sets. In particular, HF/6-31+G(d,p) predicted a representative approximation of alpha for the molecule 16 in comparison with larger methods as MP2/aug-cc-pVDZ, CCS/aug-cc-pVDZ and CCS/aug-cc-pVTZ, while a detailed analysis showed that HF can be used in the calculation of alpha for the molecules 3, 7, 11 and 15, but it requires the use of extended basis sets. Also, HF/6-31+G(d,p) predicted values of beta very similar to those calculated at the MP2 and CCSD levels used, for the planar and equilibrium geometry of the molecules 10 and 14. Furthermore, HF/6-31+G(d,p) described a representative dependence of this property with the puckering angle for the heterocycles 9, 10 and 14, compared with the MP2 curves.