Invitation to the "Spooky" Quantum Phase-Locking Effect and its Link to 1/F Fluctuations

An overview of the concept of phase-locking at the non linear, geometric and quantum level is attempted, in relation to finite resolution measurements in a communication receiver and its 1/f noise. Sine functions, automorphic functions and cyclotomic arithmetic are respectively used as the relevant trigonometric tools. The common point of the three topics is found to be the Mangoldt function of prime number theory as the generator of low frequency noise in the coupling coefficient, the scattering coefficient and in quantum critical statistical states. Huyghens coupled pendulums, the Adler equation, the Arnold map, continued fraction expansions, discrete Mobius transformations, Ford circles, coherent and squeezed phase states, Ramanujan sums, the Riemann zeta function and Bost and Connes KMS states are some but a few concepts which are used synchronously in the paper.