Huyghens, Bohr, Riemann and Galois: Phase-Locking

Details Huyghens, Bohr, Riemann and Galois: Phase-Locking Huyghens, Bohr, Riemann and Galois: Phase-Locking

2005-10-11

arxiv.org/abs/math-ph/0510044v1

International Journal of Modern Physics B 20 (2006) 1833-1850

Physics

Mathematical Physics

18 pages paper written in relation to the ICSSUR'05 conference held in Besancon, France to be published at a special issue of

Scientific paper

10.1142/S0217979206034340

Several mathematical views of phase-locking are developed. The classical Huyghens approach is generalized to include all harmonic and subharmonic resonances and is found to be connected to 1/f noise and prime number theory. Two types of quantum phase-locking operators are defined, one acting on the rational numbers, the other on the elements of a Galois field. In both cases we analyse in detail the phase properties and find them related respectively to the Riemann zeta function and to incomplete Gauss sums.

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