The Riemannium
Leboeuf, P. · Monastra, A. G. · Bohigas, O.
Original · EN
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 EF. The distribution of the total energy is shown to be non-Gaussian, asymmetric, and independent of EF in the limit EF→∞. 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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