Weyl-Titchmarsh Matrix Functions and Spectrum of Non-selfadjoint Dirac Type Equation

2010 ◽  
pp. 539-551 ◽  
Author(s):  
L. Sakhnovich
Keyword(s):  
Type Equation ◽  
Matrix Functions ◽  
Dirac Type

RELATIVISTIC CORRECTIONS TO BALLISTIC QUANTUM TUNNELING THROUGH Ga1−xAlxAs BARRIERS

1991 ◽  
Vol 05 (13) ◽  
pp. 881-888
Author(s):  
H. CRUZ ◽  
A. HERNANDEZ-CABRERA ◽  
A. MUÑOZ
Keyword(s):  
Effective Mass ◽  
Transmission Coefficient ◽  
Analytical Solutions ◽  
Quantum Tunneling ◽  
Type Equation ◽  
Hot Electron ◽  
Electron Device ◽  
Relativistic Corrections ◽  
Dirac Type ◽  
Quantum Electron

Analytical solutions of a Dirac-type equation as effective mass equation. for electrons are obtained and by means of these solutions we have analytically calculated the relativistic transmission coefficient for quantum electron ballistic tunneling through Ga 1−x Al x As -GaAs single barriers. This solution for the transmission coefficient is applied to the tunnel injector of a hot electron device finding that relativistic corrections yield small but significant shifts in the transmittance-voltage characteristics.

New quadratic nondifferential Thomas-Fermi-Dirac-type equation for atoms

1988 ◽  
Vol 37 (10) ◽  
pp. 4030-4033 ◽  
Author(s):  
B. M. Deb ◽  
P. K. Chattaraj
Keyword(s):  
Type Equation ◽  
Thomas Fermi ◽  
Dirac Type

FERMIONS IN MAGNETAR'S CRUST IN TERMS OF HEUN DOUBLE CONFLUENT FUNCTIONS

2012 ◽  
Vol 27 (32) ◽  
pp. 1250184 ◽  
Author(s):  
CIPRIAN DARIESCU ◽  
MARINA-AURA DARIESCU
Keyword(s):  
Magnetic Field ◽  
Series Expansion ◽  
Current Density ◽  
Magnetic Induction ◽  
Type Equation ◽  
Periodic Magnetic Field ◽  
Dirac Type ◽  
Particle Momentum ◽  
Magnetic Length

The present paper is devoted to the study of relativistic fermions evolving in a periodic magnetic field frozen in the magnetar's crust. The Heun's Double Confluent functions being the solutions to the Dirac-type equation, their series expansion allows us to write down the expressions of the current density components. For typical values of the magnetic induction, b0~1015 G , so that the magnetic length is much smaller than the extension of the crust, we get a nontrivial quantization law for the particle momentum along Oz.

EXACT SOLUTIONS FOR A DIRAC-TYPE EQUATION WITH N-FOLD DARBOUX TRANSFORMATION

2019 ◽  
Vol 9 (1) ◽  
pp. 200-210 ◽  
Author(s):  
Jinting Ha ◽  
◽  
Huiqun Zhang ◽  
Qiulan Zhao ◽  
Keyword(s):  
Exact Solutions ◽  
Darboux Transformation ◽  
Type Equation ◽  
Dirac Type

scholarly journals Weyl matrix functions and inverse problems for discrete Dirac-type self-adjoint systems: explicit and general solutions

2008 ◽  
pp. 201-231 ◽  
Author(s):  
Bernd Fritzsche ◽  
Bernd Kirstein ◽  
I. Roitberg ◽  
Clément de Seg ins Pazzis
Keyword(s):  
Inverse Problems ◽  
Matrix Functions ◽  
General Solutions ◽  
Adjoint Systems ◽  
Dirac Type ◽  
Weyl Matrix

A result on a Dirac-type equation in spaces of analytic functions

Analysis ◽  
2017 ◽  
Vol 37 (2) ◽  
Author(s):  
Daniel Oliveira da Silva
Keyword(s):  
Initial Data ◽  
Analytic Functions ◽  
Type Equation ◽  
Quadratic Nonlinearity ◽  
Dirac Type ◽  
Gevrey Spaces ◽  
Spaces Of Analytic Functions

AbstractWe consider a Dirac-type equation with a quadratic nonlinearity with initial data in the Gevrey spaces

scholarly journals Cuplength estimates in Morse cohomology

2016 ◽  
Vol 08 (02) ◽  
pp. 243-272 ◽  
Author(s):  
Peter Albers ◽  
Doris Hein
Keyword(s):  
Fixed Points ◽  
Lower Bounds ◽  
Critical Points ◽  
Lagrangian Submanifolds ◽  
Type Equation ◽  
Base Case ◽  
Floer Theory ◽  
Hamiltonian Diffeomorphisms ◽  
Dirac Type ◽  
Bounded Below

The main goal of this paper is to give a unified treatment to many known cuplength estimates with a view towards Floer theory. As the base case, we prove that for [Formula: see text]-perturbations of a function which is Morse–Bott along a closed submanifold, the number of critical points is bounded below in terms of the cuplength of that critical submanifold. As we work with rather general assumptions the proof also applies in a variety of Floer settings. For example, this proves lower bounds (some of which were known) for the number of fixed points of Hamiltonian diffeomorphisms, Hamiltonian chords for Lagrangian submanifolds, translated points of contactomorphisms, and solutions to a Dirac-type equation.

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