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A. Jüngel:
"Quantum semiconductor modeling and simulation: quantum fluid and Schrödinger models";
Vortrag: Mathematisches Seminar der Universität Innsbruck, Innsbruck (eingeladen); 30.04.2010.

Siehe englisches Abstract.

Numerical simulations of ultrasmall semiconductor devices
are necessary to replace costly experiments and to fulfill the
demands due to the technological progress in microelectronics.
In view of the nanoscale of modern devices, simple correction
factors in the PDE models are no longer sufficient to describe
the quantum effects appropriately, and physically more precise
models have to be incorporated in the device simulators. In this
talk, we present two modeling approaches: quantum fluid
equations and the Schroedinger equation with open boundary
conditions.

A hierarchy of quantum fluid models, derived from the quantum
Wigner equation, is presented and some results on their
mathematical treatment and numerical discretization are given.
The derivation of appropriate a priori estimates for the
nonlinear partial differential equations is reformulated as a
polynomial decision problem from real algebraic geometry.
Furthermore, numerical simulations of a 3D quantum wave guide
using the Schroedinger equation are shown.