Non-commutative reading of the complex plane through Delone sequences

S. Twareque Ali; L. Balkova; E. M. F. Curado; J.-P. Gazeau; M.A. Rego-Monteiro; L.M.C.S. Rodrigues; K. Sekimoto

doi:10.1063/1.3095772

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

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

Document type :

Journal articles

Journal of Mathematical Physics, American Institute of Physics (AIP), 2009, 50, pp.043517. <10.1063/1.3095772>

Domain :

Mathematics / Mathematical Physics

Physics / Mathematical Physics

Physics / Quantum Physics

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Contributor : Simone Lantz <>
Submitted on : Tuesday, January 13, 2009 - 4:04:58 PM
Last modification on : Tuesday, October 28, 2014 - 6:18:15 PM

Non-commutative reading of the complex plane through Delone sequences

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