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Finite-dimensional Hilbert space and frame quantization
Cotfas N., Gazeau J.-P., Vourdas A.
Journal of Physics A: Mathematical and Theoretical 44 (2011) 175303 - http://hal.archives-ouvertes.fr/hal-00739314
Physique/Physique mathématique
Mathématiques/Physique mathématique
Finite-dimensional Hilbert space and frame quantization
N. Cotfas1, J.-P. Gazeau2, A. Vourdas
1 :  Faculty of Physics
University of Bucharest
2 :  APC - UMR 7164 - AstroParticule et Cosmologie
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
The quantum observables used in the case of quantum systems with finite-dimensional Hilbert space are defined either algebraically in terms of an orthonormal basis and discrete Fourier transformation or by using a continuous system of coherent states. We present an alternative approach to these important quantum systems based on the finite frame quantization. Finite systems of coherent states, usually called finite tight frames, can be defined in a natural way in the case of finite quantum systems. Novel examples of such tight frames are presented. The quantum observables used in our approach are obtained by starting from certain classical observables described by functions defined on the discrete phase space corresponding to the system. They are obtained by using a finite frame and a Klauder-Berezin-Toeplitz-type quantization. Semi-classical aspects of tight frames are studied through lower symbols of basic classical observables.

Journal of Physics A: Mathematical and Theoretical
Publisher Institute of Physics: Hybrid Open Access
ISSN 1751-8113 (eISSN : 1751-8121)
Articles dans des revues avec comité de lecture