Upper bounds for Shannon and Rényi entropies for central potentials - CICS Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Physics Année : 2011

Upper bounds for Shannon and Rényi entropies for central potentials

Résumé

The Rényi and Shannon entropies are information-theoretic measures, which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation. Moreover, they are closely related to various energetic density functionals of quantum systems. Here we derive upper bounds on these quantities in terms of the second-order moment for general central potentials. This improves previous results of this type. The proof uses the Rényi maximization procedure with a covariance constraint due to Costa et al. [in Proceedings of the Fourth International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), edited by A. Rangarajan, M. A. T. Figueiredo, and J. Zerubia (Springer-Verlag, Lisbon, 2003), [Lect. Notes Comput. Sci. 52, 211 (2003).]] The contributions to these bounds coming from the radial and angular parts of the physical wave functions are taken into account. Finally, the application to the d-dimensional (d ≥ 3) hydrogenic and oscillator-like systems is provided.
Fichier non déposé

Dates et versions

hal-00623689 , version 1 (14-09-2011)

Identifiants

Citer

Pablo Sanchez-Moreno, Steeve Zozor, Jesus S. Dehesa. Upper bounds for Shannon and Rényi entropies for central potentials. Journal of Mathematical Physics, 2011, 52 (2), pp.022105. ⟨10.1063/1.3549585⟩. ⟨hal-00623689⟩
135 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More