The Integrated Density of States for 1D Nanostructures at Zero Bias Limit

By methods of quasiclassical asymptotics the behaviour of the integrated density of states for 1D periodic nanostructures at the zero bias limit is studied. It is shown that the density of states at the zero bias limit has no regular limit while the integrated density of states has. The rigorous proof of this phenomenon given in the paper is based on a novel approach for the quasiclassical asymptotics on the spectrum of the Stark-Wannier operators. A connection of this phenomenon with the zero bias limits of the current through the nanostructures and their conductivity is briefly discussed.Comment: 18 page

A New Class of Elliptic Finite-Gap Densities of the Polar Operator and Stationary Solutions of the Harry Dym equation

A new family of one- and two-gap elliptic densities of the polar operator has been constructed by modifying the so-called "higher time approach" to constructing finite-gap solutions of the Harry Dym equation. Auto-B\"{a}cklund transformations of the obtained stationary solutions have been constructed and their properties have been studied

Spectral Modelling of Quantum Superlattice and Application to the Mott-Peierls Simulated Transitions

A local perturbation theory for the spectral analysis of the Schr\"odinger operator with two periodic potentials whose periods are commensurable has been constructed. It has been shown that the perturbation of the periodic 1D Hamiltonian by an additional small periodic potential leads to the following spectral deformation: all gaps in the spectrum of the unperturbed periodic Hamiltonian bear shifts while any band splits by arising additional gaps into a set of smaller spectral bands. The spectral shift, the position of additional gaps and their widths have been calculated explicitly. The applications to the operational regime of a nanoelectronic device based on Mott-Peierls stimulated transition have also been discussed.Comment: 14 pages, LaTe

On the point transformations for the second order differential equations. I

Point transformations for the ordinary differential equations of the form $y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) (y')^2+S(x,y) (y')^3$ are considered. Some classical results are resumed. Solution for the equivalence problem for the equations of general position is described.Comment: AmSTeX, Version 2.1, 15 page

Spin-filter modeling by means of extension theory methods

The problem of spin-dependent transport of electrons through a finite array of quantum dots attached to 1D quantum wire (spin gun) for various semiconductor materials is studied. Unlike the model considered in [1] a model proposed here is based on the extension theory model (ETM) and assumes the quantum dots to have an arbitrary internal structure, i.e. the internal energy levels. The presence of internal structure in quantum dots results in energy-dependent interaction between electrons and quantum dots. This interaction changes the transmission mode of the spin current through the spin gun. For the energy-dependent interaction it is shown in this article the difference of transmission probabilities for singlet and triplet channels for several quantum dots in the array due to interference effects can reach approximately 100% percent for some energy intervals. For the same energy intervals the conductance of the device reaches the value in units. As a result a model of the spin-gun which transforms the spin unpolarized electron beam into completely polarized one is suggested.Comment: 18 pages, 6 figure

On some equations that can be brought to the equations of diffusion type

For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.Comment: AmSTeX, Ver. 2.1h,13 pages, amsppt styl

Rigged Hilbert Space Approach to Spectral Analysis of the Frobenius-Perron Operator for the Tent-map

On the basis of an unified theoretical formulation of resonances and resonance states in the rigged Hilbert spaces the spectral analysis of the Frobenius-Perron operators corresponding to the exactly solvable chaotic map has been developed. Tent map as the simplest representative of exactly solvable chaos have been studied in details in frames of the developed approach. An extension the Frobenius-Perron operator resolvent to a suitable rigged Hilbert space has been constructed in particular and the properties of the generalized spectral decomposition have been studied. Resonances and resonance projections for this map have been calculated explicitly.Comment: 25 page

Complete normality conditions for the dynamical systems on Riemannian manifolds

New additional equations for the Newtonian dynamical systems on Riemannian manifolds are found. They supplement the previously found weak normality conditions up to the complete normality conditions for Newtonian dynamical systems.Comment: AMS-TeX, version 2.1, 7 pages, size 23K (ASCII), Published in book "Dynamical systems accepting the normal shift", (R.A. Sharipov, ed.), Bashkir State University, Ufa, 1994, pp. 20-3

On a point symmetry analysis for generalized diffusion type equations

Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with theory of these equation.Comment: AmSTeX, Ver. 2.1h, 51 pages, amsppt styl

Information Scientific and Educational Resource "Electrophysics"

The paper discusses an advanced level information system to support educational, research and scientific activities of the Department "Electrophysical Facilities" (DEF) of the National Research Nuclear University "MEPhI" (NRNU MEPhI), which is used for training of specialists of the course "Physics of Charged Particle Beams and Accelerator Technology"