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Table of Contents
Preface
1 Introduction
2 Waveguides. Radiation Principle. Scattering Matrices
2.1 Boundary Value Problem in a Cylinder
2.2 Problem in a Domain G with Cylindrical Ends
2.3 Waves and Scattering Matrices
3 Properties of Scattering Matrices in a Vicinity of Thresholds
3.1 Augmented Space of Waves
3.2 Continuous Spectrum Eigenfunctions. Scattering Matrices
3.3 Other Properties of the Scattering Matrices
4 Method for Computing Scattering Matrices
4.1 A Method for Computing Scattering Matrices outside Thresholds
4.2 A Method for Computing Scattering Matrices in Vicinity of Thresholds
5 Asymptotic and Numerical Studies of Resonant Tunneling in 2D-Waveguides for Electrons of Small Energy
5.1 Statement of the Problem
5.2 Limit Problems
5.3 Special Solutions to the First Kind Homogeneous Problems
5.4 Asymptotic Formulas
5.5 Justification of the Asymptotics
5.6 Comparison of Asymptotic and Numerical Results
5.7 The Impact of a Finite Waveguide Work Function on Resonant Tunneling
6 Asymptotics of Resonant Tunneling in 3D Waveguides for Electrons of Small Energy
6.1 Statement of the Problem and Outline of the Results
6.2 Limit Problems
6.3 Tunneling in a Waveguide with One Narrow
6.4 Tunneling in a Waveguide with Two Narrows
7 Resonant Tunneling in 2D Waveguides in Magnetic Field
7.1 Statement of the Problem
7.2 The Limit Problems
7.3 Special Solutions to Homogeneous First Kind Limit Problems
7.4 Asymptotic Formulas
7.5 Justification of the Asymptotics
7.6 Comparison of Asymptotic and Numerical Approaches
8 Effect of Magnetic Field on Resonant Tunneling in 3D Waveguides of Variable Cross-Section
8.1 Introduction
8.2 Statement of the Problem
8.3 Limit Problems
8.4 Special Solutions of Limit Problems
8.5 Asymptotic Formulas
8.6 Justification of the Asymptotics
9 Numerical Simulation of High Energy Electron Transport
9.1 Numerical Simulation of Multichannel Resonant Tunneling
9.2 Fano Resonances
10 Asymptotic Analysis of Multichannel Resonant Tunneling
10.1 Statement of the Problem and Limit problems
10.2 Tunneling in a Waveguide with One Narrow
10.3 Tunneling in a Waveguide with Two Narrows
11 Electronics Devices Based on Resonant Tunneling
11.1 Magnetic Field Sensors Based on Quantum Waveguides.- 11.2 Transistors Based on Quantum Waveguides
11.3 Electron Flow Switch for Quantum Nets
Bibliography.
1 Introduction
2 Waveguides. Radiation Principle. Scattering Matrices
2.1 Boundary Value Problem in a Cylinder
2.2 Problem in a Domain G with Cylindrical Ends
2.3 Waves and Scattering Matrices
3 Properties of Scattering Matrices in a Vicinity of Thresholds
3.1 Augmented Space of Waves
3.2 Continuous Spectrum Eigenfunctions. Scattering Matrices
3.3 Other Properties of the Scattering Matrices
4 Method for Computing Scattering Matrices
4.1 A Method for Computing Scattering Matrices outside Thresholds
4.2 A Method for Computing Scattering Matrices in Vicinity of Thresholds
5 Asymptotic and Numerical Studies of Resonant Tunneling in 2D-Waveguides for Electrons of Small Energy
5.1 Statement of the Problem
5.2 Limit Problems
5.3 Special Solutions to the First Kind Homogeneous Problems
5.4 Asymptotic Formulas
5.5 Justification of the Asymptotics
5.6 Comparison of Asymptotic and Numerical Results
5.7 The Impact of a Finite Waveguide Work Function on Resonant Tunneling
6 Asymptotics of Resonant Tunneling in 3D Waveguides for Electrons of Small Energy
6.1 Statement of the Problem and Outline of the Results
6.2 Limit Problems
6.3 Tunneling in a Waveguide with One Narrow
6.4 Tunneling in a Waveguide with Two Narrows
7 Resonant Tunneling in 2D Waveguides in Magnetic Field
7.1 Statement of the Problem
7.2 The Limit Problems
7.3 Special Solutions to Homogeneous First Kind Limit Problems
7.4 Asymptotic Formulas
7.5 Justification of the Asymptotics
7.6 Comparison of Asymptotic and Numerical Approaches
8 Effect of Magnetic Field on Resonant Tunneling in 3D Waveguides of Variable Cross-Section
8.1 Introduction
8.2 Statement of the Problem
8.3 Limit Problems
8.4 Special Solutions of Limit Problems
8.5 Asymptotic Formulas
8.6 Justification of the Asymptotics
9 Numerical Simulation of High Energy Electron Transport
9.1 Numerical Simulation of Multichannel Resonant Tunneling
9.2 Fano Resonances
10 Asymptotic Analysis of Multichannel Resonant Tunneling
10.1 Statement of the Problem and Limit problems
10.2 Tunneling in a Waveguide with One Narrow
10.3 Tunneling in a Waveguide with Two Narrows
11 Electronics Devices Based on Resonant Tunneling
11.1 Magnetic Field Sensors Based on Quantum Waveguides.- 11.2 Transistors Based on Quantum Waveguides
11.3 Electron Flow Switch for Quantum Nets
Bibliography.