Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems
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2017-08-14
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IOP Publishing
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In this work we find that not only the Heisenberg-like uncertainty products and the Rényi-entropy-based uncertainty sum have the same firstorder values for all the quantum states of the D-dimensional hydrogenic and oscillator-like systems, respectively, in the pseudoclassical (D → ∞) limit but a similar phenomenon also happens for both the Fisher-information-based uncertainty product and the Shannon-entropy-based uncertainty sum, as well as for the Crámer–Rao and Fisher–Shannon complexities. Moreover, we show
that the López–Ruiz–Mancini–Calvet (LMC) and LMC-Rényi complexity measures capture the hydrogenic-harmonic dierence in the high dimensional limit already at first order.
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Sobrino-Coll, N., Puertas-Centeno, D., Toranzo, I. V., & Dehesa, J. S. (2017). Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems. Journal of Statistical Mechanics: Theory and Experiment, 2017(8), 083102. 10.1088/1742-5468/aa7df4