SEMINAIRE MERCREDI 20 JUIN 2007
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Jean-Bernard Bru
Fakultät für Physik, Universität Wien, Austria

Titre: Flow equations for operators and non-autonomous evolution equations

Abstract: The so-called ``flow equations for operators" are non-linear
operator value first order differential equations. They were formally
defined independently by Brockett in 1991 for symmetric real matrices
to solve linear programming problems and by Wegner in 1994 to obtain
diagonal Hamiltonians. The main interest of these differential
equations is to realize an appropriate isospectral flow on a
self-adjoint operator acting on Hilbert spaces. However, their
mathematical foundations are still missing and rigorous results in
that direction will be discussed in this talk. As an example, we will
then give an application of this technique to quadratic Hamiltonians
acting on Boson Fock spaces.