A Generalized Statistical Complexity Measure: Applications to Quantum Systems

Abstract

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 LMC 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.

15 pages, 3 figures

References in corpus (3)

• Information Entropy, Information Distances and Complexity in Atoms
• Statistical complexity, Fisher-Shannon information, and Bohr orbits in the H-atom
• Some features of the statistical complexity, Fisher-Shannon information, and Bohr-like orbits in the Quantum Isotropic Harmonic Oscillator

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