Nonclassical Degrees of Freedom in the Riemann Hamiltonian

Details Nonclassical Degrees of Freedom in the Riemann Hamiltonian Nonclassical Degrees of Freedom in the Riemann Hamiltonian

2011-05-12

arxiv.org/abs/1105.2342v6

Phys. Rev. Lett. 107, 100201 (2011)

Physics

Mathematical Physics

4 pages, no figures; v3-6 have minor corrections to v2, v2 has a more complete solution of the sign problem than v1

Scientific paper

The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so, conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.

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