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The Riemannium

P. Leboeuf·A. G. Monastra·O. Bohigas
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Abstract

The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up to a Fermi energy $E_F$. The distribution of the total energy is shown to be non-Gaussian, asymmetric, and independent of $E_F$ in the limit $E_F\to\infty$. The moments of the limit distribution are computed analytically. The autocorrelation function, the finite energy corrections, and a comparison with random matrix theory are also discussed.

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P. Leboeuf, A. G. Monastra, O. Bohigas. 2001-01-08. The Riemannium. https://arxiv.org/abs/nlin/0101014

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