Letters in Mathematical Physics

, Volume 68, Issue 2, pp 103–112

Gaussian Quantum Fluctuations in Interacting Many Particle Systems

  • Michael Hartmann
  • Günter mahler
  • Ortwin Hess
Article

Abstract

We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state becomes a Gaussian normal distribution in the limit of infinite number of particles. We indicate some possible applications.

quantum central limit theorem quantum many-body systems quantum fluctuations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lieb, E.and Mattis, D.: Mathematical Physics in One Dimension, Academic Press, New York, 1966.Google Scholar
  2. 2.
    Thirring, W.: Quantum Mathematical Physics, 2nd edn, Springer, Berlin, 2002.Google Scholar
  3. 3.
    Lieb, E.: The Stability of Matter: From Atoms to Stars, Springer, Berlin, 2001.Google Scholar
  4. 4.
    Goldstein, M.Sh.: J.Statist.Phys. 40 (1985), 329.Google Scholar
  5. 5.
    Goldstein M.Sh.: Theoret.Math.Phys. 1 (1985), 412.Google Scholar
  6. 6.
    Cushen, C.D.and Hudson, R.L.: J.Appl.Probab. 8 (1971), 454.Google Scholar
  7. 7.
    Accardi, L.and Bach, A.: Z.Wahrsch.verw.Geb. 68 (1985), 393.Google Scholar
  8. 8.
    Goderis, D., Verbeure, A.and Vets, P.: Probab.Theory Related Fields 82 (1989), 527.Google Scholar
  9. 9.
    Goderis, D.and Vets, P.: Comm.Math.Phys. 122 (1989), 249.Google Scholar
  10. 10.
    Kuperberg G.: math-ph/0202035.Google Scholar
  11. 11.
    Michoel, T. and Nachtergaele, B.: math-ph/0310027.Google Scholar
  12. 12.
    Sakurai, J.J.: Modern Quantum Mechanics, Addison-Wesley, Reading, Mass, 1994.Google Scholar
  13. 13.
    Ibargimov, I.A.and Linnik, Y.V.: Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen, 1971.Google Scholar
  14. 14.
    Billingsley, P.: Probability and Measure, 3rd edn, Wiley, New York, 1995.Google Scholar
  15. 15.
    Fick, E. and Sauermann, G.: The Quantum Statistics of Dynamic Processes, Springer, Berlin, 1990.Google Scholar
  16. 16.
    D¨urr, D., Goldstein, S.and Zanghi, N.: J.Stat.Phys. 67 (2003), 843.Google Scholar
  17. 17.
    D¨urr, D., Goldstein, S. and Zanghi, N.: J.Stat.Phys. to be published, quant-ph/0308038.Google Scholar
  18. 18.
    Mahler, G.and Weberruß, V.: Quantum Networks, Springer, Berlin, 2001.Google Scholar
  19. 19.
    Jordan, A.N.and B¨uttiker, M.: Phys.Rev.Lett. 92 (2004), 247901.Google Scholar
  20. 20.
    Hartmann, M., Mahler, G.and Hess, O.: Phys.Rev.Lett., to be published.quant-ph/0312214.Google Scholar
  21. 21.
    Hartmann, M., Mahler, G.and Hess, O.: cond-mat/0406100.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Michael Hartmann
    • 1
  • Günter mahler
    • 2
  • Ortwin Hess
    • 3
  1. 1.Institute of Thechnical Physics, DLR Stuttgart and Institute of Theoretical Physics IUniversity of StuttgartGermany
  2. 2.Institute of Theoretical Physics IUniversity of StuttgartGermany
  3. 3.Advanced Technology InstituteUniversity of SurreyUnited Kingdom

Personalised recommendations