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Non-commutative reading of the complex plane through Delone sequences
Twareque Ali S., Balkova L., Curado E.M.F., Gazeau J.-P., Rego-Monteiro M.A. et al
Journal of Mathematical Physics 50 (2009) 043517 - http://hal.in2p3.fr/in2p3-00352734
Mathématiques/Physique mathématique
Physique/Physique mathématique
Physique/Physique Quantique
Non-commutative reading of the complex plane through Delone sequences
S. Twareque Ali, L. Balkova1, E. M. F. Curado, J.-P. Gazeau1, M.A. Rego-Monteiro, L.M.C.S. Rodrigues, K. Sekimoto2
1 :  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
2 :  MSC - Matière et Systèmes Complexes
CNRS : UMR7057 – Université Paris VII - Paris Diderot
Université Paris Diderot, Bât. Condorcet, case postale 7056, 10 rue Alice Domon et Léonie Duquet, 75205 PARIS Cedex 13
The Berezin-Klauder-Toeplitz ("anti-Wick") quantization or "non-commutative reading" of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction properties of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on the natural numbers. This work is an attempt for following the same path by considering sequences of non-negative numbers which are not "too far" from the natural numbers. In particular, we examine the consequences of such perturbations on the non-commutative reading of the complex plane in terms of its probabilistic, functional, and localization aspects.

Articles dans des revues avec comité de lecture
Journal of Mathematical Physics (J. Math. Phys.)
Publisher American Institute of Physics (AIP)
ISSN 0022-2488 

37 pages, 4 figures
harmonic oscillators – Hilbert spaces – probability – quantisation (quantum theory) – Schrodinger equation
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