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Few-Body Systems

, 58:158 | Cite as

Higher-Order Statistical Correlations and Mutual Information Among Particles in a Quantum Well

  • V. S. Yépez
  • R. P. Sagar
  • H. G. Laguna
Article
  • 71 Downloads

Abstract

The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more correlated than the antisymmetric ones with same quantum numbers. This holds in position as well as in momentum space. This behavior is opposite to that observed for the correlation between pairs of variables in this model, and the two-particle system, where the antisymmetric wave functions are in general more correlated. These results are also consistent with those observed in a system of three uncoupled oscillators. The use of higher-order mutual information as a correlation measure, is monitored and examined by considering a superposition of states or systems with two Slater determinants.

Notes

Acknowledgements

V. S. Y. thanks CONACyT for a fellowship. H. G. L. thanks DGAPA-UNAM for a postdoctoral fellowship. The authors acknowledge CONACyT for support to the Red de Fisicoquímica Teórica (RedFQT) through Project 0250976.

References

  1. 1.
    M.C. Tichy, M. Tiersch, F. Mintert, A. Buchleitner, New J. Phys. 14, 093015 (2012)ADSCrossRefGoogle Scholar
  2. 2.
    E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, G. Fève, Science 339, 1054 (2013)ADSCrossRefGoogle Scholar
  3. 3.
    S. Bose, D. Home, Phys. Rev. Lett. 110, 140404 (2013)ADSCrossRefGoogle Scholar
  4. 4.
    J.-J. Ma, X.-X. Yuan, C. Zu, X.-Y. Chang, P.-Y. Hou, L.-M. Duan, New. J. Phys. 16, 083011 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    Z. Gong, S. Deffner, H.T. Quan, Phys. Rev. E 90, 062121 (2014)ADSCrossRefGoogle Scholar
  6. 6.
    M.C. Tichy, J. Phys. B Atomic Mol. Opt. Phys. 47, 103001 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    R. Lopes, A. Imanaliev, A. Aspect, M. Cheneau, D. Boiron, C.I. Westbrook, Nature 520, 66 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    E.P. Wigner, F. Seitz, Phys. Rev. 43, 804 (1933)ADSCrossRefGoogle Scholar
  9. 9.
    E.P. Wigner, F. Seitz, Phys. Rev. 46, 509 (1934)ADSCrossRefGoogle Scholar
  10. 10.
    W. Kutzelnigg, G. Del Re, G. Berthier, Phys. Rev. 172, 49 (1968)ADSCrossRefGoogle Scholar
  11. 11.
    M. Belloni, M.A. Doncheski, R.W. Robinett, Am. J. Phys. 72, 1183 (2004)ADSCrossRefGoogle Scholar
  12. 12.
    W.D. Hobey, J. Org. Chem. 37, 1137 (1972)CrossRefGoogle Scholar
  13. 13.
    C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948)CrossRefGoogle Scholar
  14. 14.
    V. Majerník, L. Richterek, Eur. J. Phys. 18, 79 (1997)CrossRefGoogle Scholar
  15. 15.
    V. Majerník, L. Richterek, J. Phys. A Math. Gen. 30, L49 (1997)ADSCrossRefGoogle Scholar
  16. 16.
    V. Majerník, R. Charvot, E. Majerníková, J. Phys. A Math. Gen. 32, 2207 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    J. Sánchez-Ruiz, Phys. Lett. A 226, 7 (1997)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    O. Olendski, Ann. Phys. (Berlin) 528, 882 (2016)ADSCrossRefGoogle Scholar
  19. 19.
    O. Olendski, Ann. Phys. (Berlin) 527, 278 (2015)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    N. Mukerjee, A.K. Roy, Ann. Phys. (Berlin) 528, 412 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    N. Mukerjee, A. Roy, A.K. Roy, Ann. Phys. (Berlin) 527, 825 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    M. Ghafourian, H. Hassanabadi, J. Korean Phys. Soc. 68, 1267 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    S.A. Najafizade, H. Hassanabadi, S. Zarrinkamar, Chin. Phys. B 25, 040301 (2016)CrossRefGoogle Scholar
  24. 24.
    A.J. Fotue, S.C. Kenfack, M. Tiotsup, N. Issofa, A.V. Wirngo, M.P. Tabue Djemmo, H. Fotsin, L.C. Fai, Mod. Phys. Lett. B 29, 1550241 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    G.H. Sun, S.H. Dong, N. Saad, Ann. Phys. (Berlin) 525, 934 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    S. Dong, G.H. Sun, S.H. Dong, J.P. Draayer, Phys. Lett. A 378, 124 (2014)ADSCrossRefGoogle Scholar
  27. 27.
    I. Bialynicki-Birula, J. Mycielski, Commun. Math. Phys. 44, 129 (1975)ADSCrossRefGoogle Scholar
  28. 28.
    D. Deutsch, Phys. Rev. Lett. 50, 631 (1983)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    H. Maasen, J.B.M. Uffink, Phys. Rev. Lett. 60, 1103 (1988)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    S. Wehner, A. Winter, New J. Phys. 12, 025009 (2010)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    J. Zhang, Y. Zhang, C. Yu, Sci. Rep. 5, 11701 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    T.M. Cover, J.A. Thomas, Elements of Information Theory (Wiley, New York, 1991)CrossRefzbMATHGoogle Scholar
  33. 33.
    R.P. Sagar, N.L. Guevara, J. Chem. Phys. 123, 044108 (2005)ADSCrossRefGoogle Scholar
  34. 34.
    R.P. Sagar, N.L. Guevara, J. Chem. Phys. 124, 134101 (2006)ADSCrossRefGoogle Scholar
  35. 35.
    H.G. Laguna, R.P. Sagar, Phys. Rev. A 84, 012502 (2011)ADSCrossRefGoogle Scholar
  36. 36.
    H.G. Laguna, R.P. Sagar, J. Phys. A Math. Theor. 44, 185302 (2011)ADSCrossRefGoogle Scholar
  37. 37.
    H.G. Laguna, R.P. Sagar, Physica A 396, 267 (2014)ADSCrossRefGoogle Scholar
  38. 38.
    H.T. Peng, Y.K. Ho, Entropy 17, 1882 (2015)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    H. Matsuda, Phys. Rev. E 62, 3096 (2000)ADSCrossRefGoogle Scholar
  40. 40.
    H. Matsuda, Physica A 294, 180 (2001)ADSCrossRefGoogle Scholar
  41. 41.
    B.J. Killian, J.Y. Kravitz, M.K. Gibson, J. Chem. Phys. 127, 024107 (2007)ADSCrossRefGoogle Scholar
  42. 42.
    S. Somani, Conformational Sampling and Calculation of Molecular Free Energies using Superposition Approximations,(Ph.D. Thesis, University of Maryland, 2011)Google Scholar
  43. 43.
    Z. Huang, S. Kais, Chem. Phys. Lett. 413, 1 (2005)ADSCrossRefGoogle Scholar
  44. 44.
    S. Kais, Adv. Chem. Phys. 134, 493 (2007)Google Scholar
  45. 45.
    Wolfram Research Inc., Mathematica Version 10.0 (Champaign, IL, USA, 2015)Google Scholar
  46. 46.
    F. M. Fernández, arXiv:1310.5136v2 [quant-ph] (2014)
  47. 47.
    T. Koga, H. Matsuyama, Theor. Chem. Acc. 126, 383 (2010)CrossRefGoogle Scholar
  48. 48.
    T. Koga, M. Sekiya, J. Chem. Phys. 128, 084105 (2008)ADSCrossRefGoogle Scholar
  49. 49.
    P.W. Anderson, Science 177, 393 (1972)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  1. 1.Departamento de QuímicaUniversidad Autónoma MetropolitanaCiudad de MéxicoMexico
  2. 2.Departamento de Matemáticas, Facultad de Ciencias; y Centro de Ciencias de la ComplejidadUniversidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico

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