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A generalized statistical complexity measure: applications to quantum systems. (English) Zbl 1373.81116
Summary: A two-parameter family of complexity measures $$\tilde C(\alpha,\beta)$$ based on the Rényi entropies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous version of the Lopez-Ruiz-Mancini-Calbet complexity, which is recovered for $$\alpha=1$$ and $$\beta=2$$. These complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system. When one of the parameters, $$\alpha$$ or $$\beta$$, goes to infinity, one of the global factors becomes a local factor. For this special case, the complexity is calculated on different quantum systems: H-atom, harmonic oscillator, and square well.