Information Geometry and its Applications III

Abstract Christophe Vignat

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Christophe Vignat  (Université d'Orsay, France)
Thursday, August 05, 2010, room Hörsaal 1
Orthogonal polynomials and geometry of the quantum harmonic oscillator on constant curvature surfaces

In this talk, starting from results by Carinena et al. [Ann. Phys. 322, 434, 2007] about the quantum harmonic oscillator on constant (positive or negative) curvature surfaces, I will show some properties of the orthogonal polynomials associated with the corresponding wavefunctions. These polynomials have a strong connection with the hyperspherical polynomials, from which they inherit some properties. Moreover, a geometric transformation between the cases of a positive and a negative curvature surface can be made explicit: this transformation can be given an algebraic interpretation in terms of these orthogonal polynomials. Finally, a link can be exhibited with the canonical probability measures involved in the theory of nonextensive statistics.

Date and Location

August 02 - 06, 2010
University of Leipzig
04103 Leipzig

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
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Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
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František Matúš
Academy of Sciences of the Czech Republic
Institute of Information Theory and Automation
Czech Republic
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Scientific Committee

Shun-ichi Amari
Brain Science Institute, Mathematical Neuroscience Laboratory
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
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Administrative Contact

Antje Vandenberg
Max Planck Institute for Mathematics in the Sciences
Contact by Email
Phone: (++49)-(0)341-9959-552
Fax: (++49)-(0)341-9959-555

05.04.2017, 12:42