Abstract:
Usually, quantum systems are described by microscopic quantum models,
like the Schroedinger or Wigner equation. In order to reduce
the computational effort and to improve the modeling of the boundary
conditions, macroscopic quantum models have been derived. In this
talk we present three of these models: the quantum drift-diffusion,
quantum hydrodynamic and viscous quantum hydrodynamic equations.
We sketch the derivation of these models, give some results on the
existence and non-existence of the solutions and show some
numerical simulation results for a one-dimensional semiconductor
tunneling diode.