Lecture Notes on Numerical Methods in Engineering and Sciences / Resonant Tunneling

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

"The book is concerned with mathematical models for resonant tunneling in two- and three-dimensional quantum waveguides of variable cross-section. ... The book does not require an advanced background and is practically self-consistent. It is addressed to a wide audience and can interest, in particular, mathematicians, physicists and engineers involved in research activity in the field of resonant quantum waveguides." (Vittorio Romano, Mathematical Reviews, October, 2016)