0000000000246169
AUTHOR
Boris Plamenevskii
showing 7 related works from this author
The Impact of a Finite Waveguide Work Function on Resonant Tunneling
2021
To describe electron transport in a waveguide, we assume that the electron wave functions vanish at the waveguide boundary. This means that, being in the waveguide, an electron can not cross the waveguide boundary because of the infinite potential barrier. In reality, the assumption has never been fulfilled: generally, electrons can penetrate through the waveguide boundary and go some distance away from the waveguide. Therefore, we have to clarify how this phenomenon affects the resonant tunneling.
Resonant Tunneling in 2D Waveguides in Magnetic Field
2021
Chapter 7 presents an asymptotic and numerical studies of resonant tunneling in a two-dimensional waveguide with two-narrows in magnetic field. It is supposed that the electron energy is between the first and the second thresholds.
Asymptotic and Numerical Studies of Resonant Tunneling in 2D-Waveguides for Electrons of Small Energy
2021
Chapter 5 is devoted to asymptotic studies of electron resonant tunneling in a two-dimensional waveguide with two narrows. The narrow diameter plays the role of a small parameter. The asymptotics of basic characteristics of resonant tunneling are presented for electrons with energy between the first and the second thresholds. Moreover, the asymptotics results are compared with numerical ones obtained by approximate calculation of the scattering matrix.
Waveguides. Radiation Principle. Scattering Matrices
2021
Chapter 2 exposes a mathematical model of a waveguide with several cylindrical ends going to infinity, basic notions and mathematical results (with complete proofs) needed in successive chapters: waves, continuous spectrum eigenfunctions, intrinsic radiation principle, and scattering matrices.
Resonant Tunneling in 2D-Waveguides with Several Resonators
2021
In this chapter, we consider a two-dimensional waveguide that coincides with a strip having \(n+1\) narrows of small diameter \(\varepsilon \). All narrows are of the same shape and are spaced from each other by equal distances. Parts of the waveguide between two neighboring narrows play the role of resonators. The wave function of a free electron satisfies the Dirichlet boundary value problem for the Helmholtz equation in the waveguide. Near a simple eigenvalue of the closed resonator there are n resonant peaks of height close to 1. We let \(\varepsilon \rightarrow 0\) and obtain asymptotic formulas for the resonant energies and for the widths of the resonant peaks at their half-height. Th…
Method for Computing Scattering Matrices
2021
Chapter 4 presents statement and justification of a method for approximate computing a waveguide scattering matrix. As an approximation to a row of such a matrix, a minimizer of a quadratic functional is suggested. To construct the functional, one has to solve a boundary value problem in a bounded domain obtained by cutting off the cylindrical ends of the waveguide at distance R. The minimizer tends to the scattering matrix row at exponential rate as R increases to infinity.
Properties of Scattering Matrices in a Vicinity of Thresholds
2021
Chapter 3 is devoted to various properties of a waveguide scattering matrix, which is a matrix function on the waveguide continuous spectrum. There is a sequence of threshold values of the spectral parameter where the scattering matrix changes its size; the thresholds accumulate at infinity. In particular, both two-sided limits of the scattering matrix are calculated at every threshold.