Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems. (14th August 2017)

• Record Type: Journal Article
• Authors: Sobrino-Coll, N; Puertas-Centeno, D; Toranzo, I V; Dehesa, J S
• Is Part Of: Journal of statistical mechanics. (2017:Aug.)
• Publication Date: 2017-08-14
• Subjects: 1 -- 2; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa7df4
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: 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 → ∞ ) 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.