Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems

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 ($D\to \infty$) 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 LMC (López-Ruiz-Mancini-Calvet) and LMC-Rényi complexity measures capture the hydrogenic-harmonic difference in the high dimensional limit already at first order.

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• Analytical Shannon information entropies for all discrete multidimensional hydrogenic states
• On Generalized Stam Inequalities and Fisher-Rényi Complexity Measures
• Information-entropic measures for non-zero l states of confined hydrogen-like ions
• Quantum mechanical virial-like theorem for confined quantum systems
• Dynamics of order-disorder and complexity for interacting bosons in optical lattice
• Exact Rényi entropies of $D$-dimensional harmonic systems
• Shell-confined atom and plasma: incidental degeneracy, metallic character and information entropy
• Multidimensional hydrogenic states: Position and momentum expectation values
• Information-Entropic Measures in Confined Isotropic Harmonic Oscillator
• Quantum information measures of the Dirichlet and Neumann hyperspherical dots