Title: Lineup polytopes and exclusion principles
| Speaker: | Federico Castillo |
| Affiliation: | Universidad Catolica de Chile |
| Zoom link: | Contact Logan Crew |
Abstract:
The set of all possible spectra of 1-reduced density operators for systems of N particles on a d-dimensional Hilbert space is a polytope called hypersimplex and this is related to Pauli's exclusion principle. If the spectrum of the original density operators is fixed, the set of spectra (ordered decreasingly) of 1-reduced density operators is also a polytope. A theoretical description of this polytope using inequalities was provided by Klyachko in the early 2000's.
Adapting and enhancing tools from discrete geometry and combinatorics (symmetric polytopes, sweep polytopes, and the Gale order), we obtained such necessary inequalities explicitly, that are also valid for arbitrarily large N and d.
This
approach
leads
to
a
new
class
of
polytopes
called
lineup
polytopes.
This
is
joint
work
with
physicists
Jean
Philippe
Labbe,
Julia
Liebert,
Eva
Philippe,
Arnau
Padrol,
and
Christian
Schilling.