Numerics and asymptotics of microscopic and macroscopic equations for quantum systems

01.09.2005 - 31.08.2008
Forschungsförderungsprojekt
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.

Personen

Projektleiter_in

Projektmitarbeiter_innen

Institut

Grant funds

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

Forschungsschwerpunkte

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

Schlagwörter

DeutschEnglisch
partielle DifferentialgleichungenPartial differential equations
Quantensystemequantum systems
mathematische Analysemathematical analysis
numerische Simulationennumerical simulations
Halbleitermodellesemiconductor models

Externe Partner_innen

  • Universität Mainz

Publikationen