Non-commutative reading of the complex plane through Delone sequences

S. Twareque Ali L. Balkova 1 E. M. F. Curado J.-P. Gazeau 2 M.A. Rego-Monteiro L.M.C.S. Rodrigues K. Sekimoto 3
1 APC - UMR 7164 - AstroParticule et Cosmologie
2 APC - THEORIE
APC - UMR 7164 - AstroParticule et Cosmologie, Institut für theoretische Physik
3 MSC - Matière et Systèmes Complexes
Abstract : 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.
Keywords : harmonic oscillators Hilbert spaces probability quantisation (quantum theory) Schrodinger equation
Type de document :
Article dans une revue
Journal of Mathematical Physics, American Institute of Physics (AIP), 2009, 50, pp.043517. <10.1063/1.3095772>
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http://hal.in2p3.fr/in2p3-00352734
Contributeur : Simone Lantz <>
Soumis le : mardi 13 janvier 2009 - 16:04:58
Dernière modification le : mardi 11 octobre 2016 - 13:27:25

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S. Twareque Ali, L. Balkova, E. M. F. Curado, J.-P. Gazeau, M.A. Rego-Monteiro, et al.. Non-commutative reading of the complex plane through Delone sequences. Journal of Mathematical Physics, American Institute of Physics (AIP), 2009, 50, pp.043517. <10.1063/1.3095772>. <in2p3-00352734>

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