Home | About Journal | Web Links | E-mail Alerts | RSS RSS Icon | Browse
Previous Article Next Article

A generalized statistical complexity measure: Applications to quantum systems

Source: J. Math. Phys. 50, 123528 (2010); doi:10.1063/1.3274387

Published 31 December 2009

KEYWORDS and PACS
Keywords
PACS
  • 03.65.Ge
    Solutions of wave equations: bound states in quantum mechanics
  • 02.50.Cw
    Probability theory
  • 31.15.es
    Applications of density-functional theory (atoms and molecules)
  • 03.67.-a
    Quantum information
  • 03.65.Ta
    Foundations of quantum mechanics; measurement theory
  • YEAR: 2010
RELATED DATABASES

To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.
PUBLICATION DATA
Publisher:
AIP is a member of CrossRef AIP
R. López-Ruiz,1 Á. Nagy,2 E. Romera,3 and J. Sañudo4
1DIIS and BIFI, Facultad de Ciencias, Universidad de Zaragoza, E-50009 Zaragoza, Spain
2Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, Hungary
3Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
4Departamento de Física, Facultad de Ciencias, Universidad de Extremadura, E-06071 Badajoz, Spain, and BIFI, Universidad de Zaragoza, E-50009 Zaragoza, Spain
A two-parameter family of complexity measures C-tilde(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. ©2009 American Institute of Physics
History: Received 20 May 2009; accepted 19 November 2009; published 31 December 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/123528/1

REFERENCES (27)

For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. S. Hawking, “I think the next century will be the century of complexity,” in: San José Mercury News, 23 January 2000.
  2. A. N. Kolmogorov, Probl. Inf. Transm. 1, 1 (1965).
  3. G. Chaitin, J. ACM 13, 547 (1966).
  4. A. Lempel and J. Ziv, IEEE Trans. Inf. Theory 22, 75 (1976).
  5. J. P. Crutchfield and K. Young, Phys. Rev. Lett. 63, 105 (1989).
  6. S. R. Gadre, S. B. Sears, S. J. Chakravorty, and R. D. Bendale, Phys. Rev. A 32, 2602 (1985).
  7. K. Ch. Chatzisavvas, Ch. C. Moustakidis, and C. P. Panos, J. Chem. Phys. 123, 174111 (2005).
  8. R. López-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A 209, 321 (1995).
  9. R. G. Catalán, J. Garay, and R. López-Ruiz, Phys. Rev. E 66, 011102 (2002).
  10. M. Perakh, On Talk Reason, www.talkreason.org /articles/complexity.pdf, August (2004)
    11. e-print arXiv:nlin/0701048v1 [nlin.CD].
  11. J. Sañudo and R. López-Ruiz, Phys. Lett. A 372, 5283 (2008).
  12. J. Sañudo and R. López-Ruiz, J. Phys. A 41, 265303 (2008).
  13. C. E. Shannon, Bell. Sys. Tech. J. 27, 379 (1948)
    14. 27, 623 (1948).
  14. M. T. Martin, A. Plastino, and O. A. Rosso, Physica A 369, 439 (2006).
  15. J. Pipek and I. Varga, Phys. Rev. A 46, 3148 (1992).
  16. I. Varga and J. Pipek, Phys. Rev. E 68, 026202 (2003).
  17. A. Rényi, Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1: Contributions to the Theory of Statistics, 1961, p. 547.
  18. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
  19. S. Liu and R. G. Parr, Phys. Rev. A 55, 1792 (1997).
  20. S. Liu, A. Nagy, and R. G. Parr, Phys. Rev. A 59, 1131 (1999).
  21. E. Romera, R. López-Ruiz, J. Sañudo, and A. Nagy, Int. Rev. Phys. 3, 207 (2009).
  22. J. Pipek and I. Varga, Int. J. Quantum Chem. 64, 85 (1997).
  23. R. López-Ruiz, Biophys. Chem. 115, 215 (2005).
  24. L. Debnath and P. Mikusinski, Introduction to Hilbert Spaces with Applications (Elsevier, New York, 2005).
  25. A. Galindo and P. Pascual, Quantum Mechanics I (Springer, Berlin, 1991).
  26. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, Berlin, 1977).
  27. C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, New York, 1977).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.
ADVERTISEMENT