DFG-Project "Numerics and asymptotics of microscopic and mascrocopic
equations for quantum systems"
Principal Investigators: A. Jüngel(Konstanz), A. Arnold
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.