HAL : in2p3-00352734, version 1

arXiv : 0811.4400

DOI : 10.1063/1.3095772

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Journal of Mathematical Physics 50 (2009) 043517

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

(2009)

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.

1 :	APC - UMR 7164 - AstroParticule et Cosmologie
2 :	MSC - Matière et Systèmes Complexes

équipe(s) de recherche : APC - THEORIE

Thème(s)

:

Mathématiques/Physique mathématique Physique/Physique mathématique Physique/Physique Quantique

Mot(s)-clé(s) : harmonic oscillators – Hilbert spaces – probability – quantisation (quantum theory) – Schrodinger equation

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Contributeur : Simone Lantz <>

Soumis le : Mardi 13 Janvier 2009, 16:04:58

Dernière modification le : Lundi 25 Juin 2012, 11:15:20