Multiparticle Distribution of Fermi Gas System in Any Dimension

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


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.


Zeta Function Riemann Zeta Function Random Matrix Theory Pair Distribution Function Correlation Kernel 
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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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