|
Statut |
Confirmé |
|
Série |
SEM-LPTHE |
|
Domaines |
cond-mat.stat-mech,hep-th,math-ph |
|
Date |
Jeudi 5 Octobre 2017 |
|
Heure |
11:00 |
|
Institut |
LPTHE |
|
Salle |
Bibliothèque |
|
Nom de l'orateur |
Zuber |
|
Prenom de l'orateur |
Jean-Bernard |
|
Addresse email de l'orateur |
|
|
Institution de l'orateur |
LPTHE |
|
Titre |
Horn's problem, from classical to quantum |
|
Résumé |
Horn's (classical) problem deals with the following question: what can be said about the spectrum
of eigenvalues of the sum C=A+B of two Hermitian matrices of given spectrum ?
Curiously this problem is intimately related to the "quantum" problem : given two irreducible
representations of SU(n), which irreps appear in their tensor product ?
The support of the spectrum of C is well understood, after a long series of works from Weyl (1912) to Knutson and Tao (1999),
and the classical problem is known to provide an asymptotic approach of the quantum one.
Here I show how an explicit computation based on a well-known matrix integral enables one to
determine the probability distribution of the eigenvalues of C, and sheds some new light on the
relation between the classical and quantum problems. |
|
Numéro de preprint arXiv |
|
|
Commentaires |
|
|
Fichiers attachés |
|
