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Open Quantum Systems Decoherence
Quantum Simulation
Entanglement Theory Quantum Correlations
Nonclassical Degrees of Freedom in the Riemann Hamiltonian
arXiv
Authors: Mark Srednicki
Year
2011
Paper ID
8853
Status
Preprint
Abstract Read
~2 min
Abstract Words
91
Citations
N/A
Abstract
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.
Why This Paper Matters
- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
- It adds a 2011 reference point for readers tracking recent quantum research.
- The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian.
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