Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series SEM-LPTHE
Subjects cond-mat.stat-mech,hep-th,math-ph
Date Thursday 5 October 2017
Time 11:00
Institute LPTHE
Seminar Room Bibliothèque
Speaker's Last Name Zuber
Speaker's First Name Jean-Bernard
Speaker's Email Address
Speaker's Institution LPTHE
Title Horn's problem, from classical to quantum
Abstract 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.
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