HAL : hal-00003426, version 2
 arXiv : quant-ph/0411210
 International Journal of Modern Physics B 20, 11/13 (2006) 1778 - 1791
 Versions disponibles : v1 (30-11-2004) v2 (12-04-2005)
 Finite dimensional quantizations of the (q,p) plane : new space and momentum inequalities
 (2006)
 We present a N-dimensional quantization a la Berezin-Klauder or frame quantization of the complex plane based on overcomplete families of states (coherent states) generated by the N first harmonic oscillator eigenstates. The spectra of position and momentum operators are finite and eigenvalues are equal, up to a factor, to the zeros of Hermite polynomials. From numerical and theoretical studies of the large $N$ behavior of the product $\lambda_m(N) \lambda_M(N)$ of non null smallest positive and largest eigenvalues, we infer the inequality $\delta_N(Q) \Delta_N(Q) = \sigma_N \overset{<}{\underset{N \to \infty}{\to}} 2 \pi$ (resp. $\delta_N(P) \Delta_N(P) = \sigma_N \overset{<}{\underset{N \to \infty}{\to}} 2 \pi$) involving, in suitable units, the minimal ($\delta_N(Q)$) and maximal ($\Delta_N(Q)$) sizes of regions of space (resp. momentum) which are accessible to exploration within this finite-dimensional quantum framework. Interesting issues on the measurement process and connections with the finite Chern-Simons matrix model for the Quantum Hall effect are discussed.
 équipe(s) de recherche : APC - THEORIE
 Domaine : Physique/Physique Quantique
 Mots Clés : Quantization – coherent states – localisation – Chern-Simons
Liste des fichiers attachés à ce document :
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 FinoscJHEP1.ps(1.7 MB)
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 FinoscJHEP1.pdf(778.9 KB)
 hal-00003426, version 2 http://hal.archives-ouvertes.fr/hal-00003426 oai:hal.archives-ouvertes.fr:hal-00003426 Contributeur : Jean-Pierre Gazeau <> Soumis le : Mardi 12 Avril 2005, 18:05:09 Dernière modification le : Lundi 6 Mai 2013, 16:16:57