Is there quantum chaos in the prime numbers - Quantum PhysicsReport as inadecuate

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Abstract: A statistical analysis of the prime numbers indicates possible traces ofquantum chaos. We have computed the nearest neighbor spacing distribution,number variance, skewness, and excess for sequences of the first N primes forvarious values of N. All four statistical measures clearly show a transitionfrom random matrix statistics at small N toward Poisson statistics at large N.In addition, the number variance saturates at large lengths as is common foreigenvalue sequences. This data can be given a physical interpretation if theprimes are thought of as eigenvalues of a quantum system whose classicaldynamics is chaotic at low energy but regular at high energy. We discuss somedifficulties with this interpretation in an attempt to clarify what kind ofphysical system might have the primes as its quantum eigenvalues.

Author: Todd Timberlake, Jeffery Tucker


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