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Multiparticle Distribution of Fermi Gas System in Any Dimension

  • Shigenori Tanaka
Chapter
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 22)

Abstract

The multiparticle distribution functions and density matrices for ideal Fermi gas system in the ground state are calculated for any spatial dimension. The results are expressed as determinant forms, in which a correlation kernel plays a vital role. The expression obtained for the one-dimensional Fermi gas is essentially equivalent to that observed for the eigenvalue distribution of random unitary matrices, and thus to that conjectured for the distribution of the non-trivial zeros of the Riemann zeta function. Their implications are discussed briefly.

Keywords

Zeta Function Riemann Zeta Function Random Matrix Theory Pair Distribution Function Correlation Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Wigner E, Seitz F (1933) Phys Rev 43:804CrossRefGoogle Scholar
  2. 2.
    Pines D (1963) Elementary excitations in solids. Benjamin, New YorkGoogle Scholar
  3. 3.
    Dyson FJ (1962) J Math Phys 3:140CrossRefGoogle Scholar
  4. 4.
    Dyson FJ (1962) J Math Phys 3:157CrossRefGoogle Scholar
  5. 5.
    Dyson FJ (1962) J Math Phys 3:166CrossRefGoogle Scholar
  6. 6.
    Montgomery HL (1973) Proc Symp Pure Math 24:181CrossRefGoogle Scholar
  7. 7.
    Keating JP, Snaith NC (2003) J Phys A 36:2859CrossRefGoogle Scholar
  8. 8.
    Mahan GD (1990) Many-Particle physics. Plenum, New YorkCrossRefGoogle Scholar
  9. 9.
    Abramowitz M, Stegun IA (1965) Handbook of mathematical functions. Dover Publications, New YorkGoogle Scholar
  10. 10.
    Gradshteyn IS, Ryzhik IM (1994) Table of integrals, series, and products. Academic, San DiegoGoogle Scholar
  11. 11.
    Wigner EP (1951) Ann Math 53:36CrossRefGoogle Scholar
  12. 12.
    Titchmarsh EC, Heath-Brown DR (1986) The theory of the Riemann Zeta-function. Clarendon, OxfordGoogle Scholar
  13. 13.
    Odlyzko AM (2001) In: van Frankenhuysen M, Lapidus ML (ed) Dynamical, spectral, and arithmetic zeta functions. Am Math Soc, Contemporary Math Series, Providence, RI, vol 290. p. 139Google Scholar
  14. 14.
    Rudnick Z, Sarnak P (1996) Duke Math J 81:269CrossRefGoogle Scholar
  15. 15.
    Bogomolny EB, Keating JP (1995) Nonlinearity 8:1115CrossRefGoogle Scholar
  16. 16.
    Bogomolny EB, Keating JP (1996) Nonlinearity 9:911CrossRefGoogle Scholar
  17. 17.
    Hardy GH, Littlewood JE (1923) Acta Math 44:1CrossRefGoogle Scholar
  18. 18.
    Katz NM, Sarnak P (1999) Bull Am Math Soc 36:1CrossRefGoogle Scholar
  19. 19.
    Berry MV, Keating JP (1999) SIAM Rev 41:236CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Shigenori Tanaka
    • 1
  1. 1.Department of Computational Science, Graduate School of System InformaticsKobe UniversityHyōgoJapan

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