Calculation of electrostatic fields in periodic structures of complex shape

A universal algorithm is presented for calculating electrostatic fields in an infinite periodic structure consisting of electrodes of arbitrary shape which are located in mirror-symmetrical manner along the axis of electron-beam propagation. The method is based on the theory of R-functions, and the differential operators which are derived on the basis of the functions. Numerical results are presented and the accuracy of the results is examined

On a complex differential Riccati equation

We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schrodinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation as, e.g., the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical "one-dimensional" results we discuss new features of the considered equation like, e.g., an analogue of the Cauchy integral theorem

On a factorization of second order elliptic operators and applications

We show that given a nonvanishing particular solution of the equation (divpgrad+q)u=0 (1) the corresponding differential operator can be factorized into a product of two first order operators. The factorization allows us to reduce the equation (1) to a first order equation which in a two-dimensional case is the Vekua equation of a special form. Under quite general conditions on the coefficients p and q we obtain an algorithm which allows us to construct in explicit form the positive formal powers (solutions of the Vekua equation generalizing the usual powers of the variable z). This result means that under quite general conditions one can construct an infinite system of exact solutions of (1) explicitly, and moreover, at least when p and q are real valued this system will be complete in ker(divpgrad+q) in the sense that any solution of (1) in a simply connected domain can be represented as an infinite series of obtained exact solutions which converges uniformly on any compact subset of . Finally we give a similar factorization of the operator (divpgrad+q) in a multidimensional case and obtain a natural generalization of the Vekua equation which is related to second order operators in a similar way as its two-dimensional prototype does

On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory

Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We show that real parts of the solutions of one of these Vekua-type operators are solutions of the considered Klein-Gordon equation. Using hyperbolic pseudoanalytic function theory, we then obtain explicit construction of infinite systems of solutions of the Klein-Gordon equation with potential. Finally, we give some examples of application of the proposed procedure

Magnetic Field Suppression of the Conducting Phase in Two Dimensions

The anomalous conducting phase that has been shown to exist in zero field in dilute two-dimensional electron systems in silicon MOSFETs is driven into a strongly insulating state by a magnetic field of about 20 kOe applied parallel to the plane. The data suggest that in the limit of T -> 0 the conducting phase is suppressed by an arbitrarily weak magnetic field. We call attention to striking similarities to magnetic field-induced superconductor-insulator transitions

Spin Degree of Freedom in a Two-Dimensional Electron Liquid

We have investigated correlation between spin polarization and magnetotransport in a high mobility silicon inversion layer which shows the metal-insulator transition. Increase in the resistivity in a parallel magnetic field reaches saturation at the critical field for the full polarization evaluated from an analysis of low-field Shubnikov-de Haas oscillations. By rotating the sample at various total strength of the magnetic field, we found that the normal component of the magnetic field at minima in the diagonal resistivity increases linearly with the concentration of ``spin-up'' electrons.Comment: 4 pages, RevTeX, 6 eps-figures, to appear in PR

R-Functions and WA-Systems of Functions in Modern Information Technologies

The review report consists of five parts. It describes the main physical applications of atomic, WA-systems and R-functions

Realistic model of correlated disorder and Anderson localization

A conducting 1D line or 2D plane inside (or on the surface of) an insulator is considered.Impurities displace the charges inside the insulator. This results in a long-range fluctuating electric field acting on the conducting line (plane). This field can be modeled by that of randomly distributed electric dipoles. This model provides a random correlated potential with decaying as 1/k . In the 1D case such correlations give essential corrections to the localization length but do not destroy Anderson localization

Magnetoresistance of a two-dimensional electron gas in a parallel magnetic field

The conductivity of a two-dimensional electron gas in a parallel magnetic field is calculated. We take into account the magnetic field induced spin-splitting, which changes the density of states, the Fermi momentum and the screening behavior of the electron gas. For impurity scattering we predict a positive magnetoresistance for low electron density and a negative magnetoresistance for high electron density. The theory is in qualitative agreement with recent experimental results found for Si inversion layers and Si quantum wells.Comment: 4 pages, figures included, PDF onl