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Entropy and Complexity Analyses of D-dimensional Quantum Systems

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Book cover Statistical Complexity

Abstract

This chapter briefly reviews the present knowledge about the analytic information theory of quantum systems with non-standard dimensionality in the position and momentum spaces. The main concepts of this theory are the power and entropic moments, which are very fertile largely because of their flexibility and multiple interpretations. They are used here to study the most relevant information-theoretic one-element (Fisher, Shannon, Rényi, Tsallis) and some composite two-elements (Fisher-Shannon, LMC shape and Cramér-Rao complexities) measures which describe the spreading measures of the position and momentum probability densities farther beyond the standard deviation. We first apply them to general systems, then to single particle systems in central potentials and, finally, to hydrogenic systems in D-dimensions.

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Acknowledgements

This work was partially supported by the projects FQM-2445 and FQM-4643 of the Junta de Andalucia (Spain, EU), and the grant FIS2008-2380 of the Ministerio de Innovación y Ciencia. We belong to the Andalusian research group FQM-207. We are very grateful to C. Vignat and S. Zozor for their critical reading of the manuscript.

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  1. Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071, Granada, Spain

    J. S. Dehesa, S. López-Rosa & D. Manzano

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  1. J. S. Dehesa
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  2. S. López-Rosa
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  3. D. Manzano
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Correspondence to J. S. Dehesa .

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  1. School of Chemistry, University of Hyderabad, Hyderabad, 500046, India

    K.D. Sen

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Dehesa, J.S., López-Rosa, S., Manzano, D. (2011). Entropy and Complexity Analyses of D-dimensional Quantum Systems. In: Sen, K. (eds) Statistical Complexity. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3890-6_5

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