Multiparticle Distributions of Ideal Fermi Gas: Analogy to Random Matrices and the Riemann Zeros

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概要

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• The multiparticle distribution functions for ideal Fermi gas system in the ground state are calculated for any spatial dimension. The n-particle distribution function is expressed in terms of a determinant form in which a correlation kernel plays a vital role. The expression obtained for the one-dimensional Fermi gas is essentially equivalent to that known for the distribution of the eigenvalues of random unitary matrices, which, in turn, has a mathematical structure analogous to the distribution of non-trivial zeros of the Riemann zeta function. Thus, these analogies may provide deeper insights into the understanding of the individual theories.

• 2011-03-15

著者

• Tanaka Shigenori

  Graduate School Of Engineering Kobe Univ.:crest

• Tanaka Shigenori

  Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan

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