Huyghens, Bohr, Riemann and Galois: Phase-Locking

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.

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

References in corpus (2)

• Mutually Unbiased Bases and Finite Projective Planes
• Mutually unbiased phase states, phase uncertainties, and Gauss sums

Cited by in corpus (5)

• Ramanujan sums analysis of long-period sequences and 1/f noise
• Qudits of composite dimension, mutually unbiased bases and projective ring geometry
• Introduction to a Quantum Theory over a Galois Field
• Riemann hypothesis and Quantum Mechanics
• Quantum Fourier transform and tomographic Renyi entropic inequalities