Effect of Magnetic Field on Resonant Tunneling in 3D Waveguides of Variable Cross-Section

Abstract

In this chapter, we consider a three-dimensional waveguide that, far from the coordinate origin, coincides with a cylinder G containing the axis x. The cross-section of G is a two-dimensional domain (of an arbitrary form) with smooth boundary. The waveguide has two narrows of small diameter $\varepsilon$. The waveguide part between the narrows plays the role of a resonator and there can arise conditions for electron resonant tunneling. We take $\varepsilon$ as small parameter and obtain asymptotic formulas for characteristics of the resonant tunneling as $\varepsilon \rightarrow 0$.