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TZID:Europe/Paris
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BEGIN:VEVENT
UID:1-390@lptms.universite-paris-saclay.fr
DTSTART:20151016T103000Z
DTEND:20151016T120000Z
DTSTAMP:20151008T100122Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
 s-viktor-eisler-zdzislaw-burda/
SUMMARY:Séminaire du LPTMS : Viktor Eisler &amp\; Zdzislaw Burda - LPTMS\,
  salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay - 16 Oct 15 10:30
DESCRIPTION:\nEntanglement in mixed states: the negativity\n\n\nDr. Viktor 
 Eisler (TU Graz)\n\nIn pure states of many-body systems\, entanglement is 
 routinely studied via the Renyi entropies\, which give a complete characte
 rization of the bipartite case. The situation becomes more complicated\, i
 f the system is composed of more than two parts\, and one is interested in
  the entanglement between two non-complementary pieces. Such a scenario ca
 n be studied by introducing a new entanglement measure\, the so-called neg
 ativity\, which has been the focus of recent interest. In this talk I woul
 d like to give an overview about the available methods to calculate the ne
 gativity\, and present some new results on mixed-state entanglement.\n----
 -----------------------\nQuaternionic R transform and non-hermitian random
  matrices\nDr. Zdzislaw Burda (AGH University of Science and Technology)\n
 Using the Cayley-Dickson construction we rephrase and review the non-hermi
 tian diagrammatic formalism [R. A. Janik\, M. A. Nowak\, G. Papp and I. Za
 hed\, Nucl.Phys. B 501\, 603 (1997)]\, that generalizes the free probabili
 ty calculus to asymptotically large non-hermitian random matrices. The mai
 n object in this generalization is a quaternionic extension of the R trans
 form which is a generating function for planar (non-crossing) cumulants. W
 e demonstrate that the quaternionic R transform generates all connected av
 erages of all distinct powers of X and its hermitian conjugate X†:  &lt
 \;&lt\;(1/N) Tr [Xa X†b Xc …] &gt\;&gt\;  for N → ∞. We show that
  the R transform for Gaussian elliptic laws is given by a simple linear qu
 aternionic map R(z+wj) = x + σ² (μ e^{2iφ} z + w j) where (z\,w) is th
 e Cayley-Dickson pair of complex numbers forming a quaternion q=(z\,w)≡ 
 z+ wj. This map has five real parameters Re[x]\, Im[x]\, φ\, σ and μ. W
 e use the R transform to calculate the limiting eigenvalue densities of se
 veral products of Gaussian random matrices.
CATEGORIES:seminars
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15 
 Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
 me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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