Numerics and asymptotics of microscopic and macroscopic equations for quantum systems

01.09.2005 - 31.08.2008

Research funding project

Quantummechanical systems can be described by an hierarchy of macroscopic (quantum hydrodynamic) and of microscopic (Schrödinger-Poisson, quantum kinetic) models, which differ in their mathematical complexity and which contain different time and length scales. The first aim of the project is to derive these models mathematically rigorously, in order to obtain the limits of validity of the reduced models. The second aim is the development of efficient numerical schemes for these equations for the simulation of quantum wave guides and radio-transmission problems. Finally a numerical comparison of these models (Wigner-Fokker-Planck, Madelung, Schrödinger, quantum-drift-diffusion) will be made for the simulation of a tunneldiode.

People

Project leader

Anton Arnold (E101)

Project personnel

Jens Geier (E101)

Institute

E101 - Institute of Analysis and Scientific Computing

Grant funds

Deutsche Forschungsgemeinschaft e.V (EU) German Research Foundation (DFG)

Research focus

Quantum Modeling and Simulation: 70%
Mathematical and Algorithmic Foundations: 30%

Keywords

German	English
partielle Differentialgleichungen	Partial differential equations
Quantensysteme	quantum systems
mathematische Analyse	mathematical analysis
numerische Simulationen	numerical simulations
Halbleitermodelle	semiconductor models

External partner

Universität Mainz

Publications

Publications