Transport properties in resonant tunneling heterostructures

TL;DR

This paper develops a theoretical model for electron transport in biased resonant tunneling heterostructures using an adiabatic approximation, leading to a nonlinear Schrödinger equation framework that captures steady-state and dynamic behaviors.

Contribution

It introduces a novel adiabatic approximation approach to model transport in resonant tunneling heterostructures with a nonlinear Schrödinger equation formulation.

Findings

Model captures steady-state transport properties.

Framework applicable to time-dependent phenomena.

Connects semiclassical approximation with nonlinear dynamics.

Abstract

We use an adiabatic approximation in terms of instantaneous resonances to study the steady-state and time-dependent transport properties of interacting electrons in biased resonant tunneling heterostructures. This approach leads, in a natural way, to a transport model of large applicability consisting of reservoirs coupled to regions where the system is described by a nonlinear Schr\"odinger equation. From the mathematical point of view, this work is non-rigorous but may offer some fresh and interesting problems involving semiclassical approximation, adiabatic theory, non-linear Schr\"odinger equations and dynamical systems.