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A Generalized Statistical Complexity Measure: Applications to Quantum Systems

A two-parameter family of complexity measures $\tilde{C}^{(α,β)}$ 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 LMC complexity, which is recovered for $α=1$ and $β=2$. These complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system. When one of the parameters, $α$ or $β$, 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.