Jean-Philippe Labbé (FU Berlin)

Lundi 14 juin : Jean-Philippe Labbé (FU Berlin)

Titre :Lineup polytopes and applications in quantum physics

Résumé : From a geometric point of view, Pauli's exclusion principle defines a hypersimplex. This convex polytope describes the compatibility of 1-fermion and N-fermion density matrices, therefore it coincides with the convex hull of the pure N-representable 1-fermion density matrices. By employing ideas from convex analysis and combinatorics, we present a comprehensive solution to the convex relaxation of the 1-body N-representability problem. In particular, we adapt and further develop tools such as symmetric polytopes, sweep polytopes, and Gale order. For both fermions and bosons, generalized exclusion principles are discovered. These exclusion principles are expressed as linear inequalities satisfying a hierarchy. The two families of polytopes resulting from these inequalities are part of the new class of so-called lineup polytopes.

This is joint work with physicists Julia Liebert, Christian Schilling and mathematicians Eva Philippe, Federico Castillo and Arnau Padrol.