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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

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
Mathématiques/Physique mathématique

Physique/Physique mathématique

Physique/Physique Quantique
harmonic oscillators – Hilbert spaces – probability – quantisation (quantum theory) – Schrodinger equation
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