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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.