Klaus Gärtner, Researcher (Retired from WIAS, Germany)

崔涛 研究员

Discrete dissipative structures, Fermi-statistics particle systems and Delaunay meshes

11月4日（周三）15:30-16:30，腾讯会议：272-818-650

The talk is dealing mainly with electrons and holes in semiconductors under the assumption of Fermi-Dirac-statistics. The restriction of the state space results in the variational formulation naturally in a drift reduction compared with the Boltzmann-statistics case.

For the discrete case and supposing boundary conforming Delaunay meshes a time and space discretization can be derived, fulfilling the same qualitative properties as the classical Boltzmann case. Existence of bounded steady state solutions can be proved and the implicit Euler scheme is dissipative.

To illustrate the generality of the setting, the talks starts with a short overview over some particle systems present on earth, having a steady state and very different energies.

Gibbs free energy is introduced to interpret mass-action-law Chemistry as diffusion problem on a graph. Hence that would naturally lead to semiconductor models, that could treat the high energetic tail of the Fermi- (or Boltzmann-) statistics like different species in mass-action-law chemistry accordingly to locally very strong forces. The overwhelming part of the particles is described by the chosen standard distribution function (Fermi- or Boltzmann statistics).

For a connection to meshing the 'dissipation rate' can be reinterpreted in geometric terms as 'curvature' - hence looking up its maxima in R^3 and the related energy density of the solution would allow to construct locally isodisspation lines on each energy isosurface.

The effort may pay off: the solution defines the metric of the mesh via the free energy and the dissipation rate - hance switching from a mesh based of an 'old' state to the last computed should be possible or would require a shorter distance between two states of the system.

Bio: Klaus Gärtner works in numerical semiconductor simulation. WIAS identifies him as a member of the m4sim spin-off project, which developed industrial microelectronics simulation software from the Oskar3 research simulator. The workshop materials list his affiliation as M4SIM, Germany.