9,960 research outputs found
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
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