The Riemannium

Leboeuf, P.; Monastra, A. G.; Bohigas, O.

The Riemannium

Authors

Leboeuf, P.

Monastra, A. G.

Bohigas, O.

Description

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.
10 pages, 2 figures, 1 table