Resumen de Analysis of a Quantum Subband Model for the Transport of Partially Confined Charged Particles

Florián Méhats

• This paper is devoted to the analysis of a quantum subband model, which is presented as an alternative to the standard 3D Schrödinger-Poisson system for modeling the transport of electrons strongly confined along one direction. This subband model is composed of quasistatic 1D Schrödinger equations in the direction of the confinement, coupled to 2D time-dependent Schrödinger equations describing the transport in the non-confined directions. Selfconsistent electrostatic interactions are also taken into account via the Poisson equation. This system is studied in the framework of the strong partial confinement asymptotics introduced in the article ¿Adiabatic approximation of the Schrödinger-Poisson system with a partial confinement¿, by Ben Abdallah, Méhats and Pinaud (SIAM J. Math. Anal. 36 (2005), 986¿1013).