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arXiv · 1806.00982

Exact Rényi entropies of $D$-dimensional harmonic systems

D. Puertas-Centeno·I. V. Toranzo·J. S. Dehesa
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Abstract

The determination of the uncertainty measures of multidimensional quantum systems is a relevant issue \textit{per se} and because these measures, which are functionals of the single-particle probability density of the systems, describe numerous fundamental and experimentally accessible physical quantities. However, it is a formidable task (not yet solved, except possibly for the ground and a few lowest-lying energetic states) even for the small bunch of elementary quantum potentials which are used to approximate the mean-field potential of the physical systems. Recently, the dominant term of the Heisenberg and Rényi measures of the multidimensional harmonic system (i.e., a particle moving under the action of a $D$-dimensional quadratic potential, $D > 1$) has been analytically calculated in the high-energy (i.e., Rydberg) and the high-dimensional (i.e., pseudoclassical) limits. In this work we determine the exact values of the Rényi uncertainty measures of the $D$-dimensional harmonic system for all ground and excited quantum states directly in terms of $D$, the potential strength and the hyperquantum numbers.

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D. Puertas-Centeno, I. V. Toranzo, J. S. Dehesa. 2018-06-04. Exact Rényi entropies of $D$-dimensional harmonic systems. https://doi.org/10.1140/epjst%2Fe2018-00092-4

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