Huyghens, Bohr, Riemann and Galois: Phase-Locking
Mathematical Physics
2009-11-11 v1 math.MP
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.math-ph/0510044,
title = {Huyghens, Bohr, Riemann and Galois: Phase-Locking},
author = {Michel R. P. Planat},
journal= {arXiv preprint arXiv:math-ph/0510044},
year = {2009}
}
Comments
18 pages paper written in relation to the ICSSUR'05 conference held in Besancon, France to be published at a special issue of IJMPB