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Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems. (English) Zbl 1457.82010

Summary: In this work we find that not only the Heisenberg-like uncertainty products and the Rényi-entropy-based uncertainty sum have the same first-order values for all the quantum states of the \(D\)-dimensional hydrogenic and oscillator-like systems, respectively, in the pseudoclassical \((D \to \infty)\) 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 difference in the high dimensional limit already at first order.

MSC:

82B05 Classical equilibrium statistical mechanics (general)

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