Affiliation:
1. Institut FEMTO-ST, Departement LPMO, 32 Avenue de l'Observatoire, 25044 Besançon Cedex, France
Abstract
Several mathematical frameworks 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 that they are related to the Riemann zeta function and to incomplete Gauss sums, respectively.
Publisher
World Scientific Pub Co Pte Lt
Subject
Condensed Matter Physics,Statistical and Nonlinear Physics
Cited by
5 articles.
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