Constrained orthogonal polynomials; coordinates, modes and maps for the density functional
Jul 6, 2006
3:30PM to 4:30PM
Date(s) - 06/07/2006
3:30 pm - 4:30 pm
Title: Constrained orthogonal polynomials; coordinates, modes and maps for the density functional
Speaker: Dr. Bertrand Giraud
Institute: CEN Saclay, France
Location: ABB 163
We describe a new family of orthogonal polynomials; these are constrained by the condition of matter conservation. They are tuned to the description of density fluctuations of closed systems, and in particular the density responses, linear or not, to external perturbations. Such phenomena, classical or quantal, range from nuclear, atomic and molecular vibrations to instabilities in centrifuges and tokomaks, internal dynamics of stars when mass is constant, etc.
The seminar includes a mathematical part, giving a few main properties of such polynomials, and a physical part, illustrating their use in a few elementary models of nuclear or atomic physics. In particular, toy models are shown for the “density functional”. A hierarchy of “density modes” replaces the usual particle-hole hierarchy for wave functions.