Noise, Oscillators and Algebraic Randomness: From Noise in Communication Systems of Number Theory Lectures of a School Held in Chapelle des Bois, France, April 5–10, 1999

Michel Planat (auth.), Michel Planat (eds.)3540675728, 9783540675723

Noise is ubiquitous in nature and in man-made systems. Noise in oscillators perturbs high-technology devices such as time standards or digital communication systems. The understanding of its algebraic structure is thus of vital importance. The book addresses both the measurement methods and the understanding of quantum, 1/f and phase noise in systems such as electronic amplifiers, oscillators and receivers, trapped ions, cosmic ray showers and in commercial applications. A strong link between 1/f noise and number theory is emphasized. The twenty papers in the book are comprehensive versions of talks presented at a School in Chapelle des Bois (Jura, France) held from April 6 to 10, 1999 by engineers, physisicts and mathematicians.

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Table of contents :
Introduction….Pages 1-5
Mathemagics….Pages 6-67
Thermal and Quantum Noise in Active Systems….Pages 71-83
Dipole at ν = 1….Pages 84-106
Stored Ion Manipulation Dynamics of Ion Cloud and Quantum Jumps with Single Ions….Pages 107-124
1/ f Fluctuations in Cosmic Ray Extensive Air Showers….Pages 125-136
Stochastic Resonance and the Benefit of Noise in Nonlinear Systems….Pages 137-155
Time is Money….Pages 156-171
Oscillators and the Characterization of Frequency Stability: an Introduction….Pages 175-188
Phase Noise Metrology….Pages 189-215
Phonon Fine Structure in the 1/ f Noise of Metals, Semiconductors and Semiconductor Devices….Pages 216-231
The General Nature of Fundamental 1/ f Noise in Oscillators and in the High Technology Domain….Pages 232-264
1/ f Frequency Noise in a Communication Receiver and the Riemann Hypothesis….Pages 265-287
Detection of Chaos in the Noise of Electronic Oscillators by Time Series Analysis Methods….Pages 288-304
Geometry and Dynamics of Numbers Under Finite Resolution….Pages 305-323
Diophantine Conditions and Real or Complex Brjuno Functions….Pages 324-342
Algebraic and Analytic Randomness….Pages 345-356
From Symbolic Dynamics to a Digital Approach: Chaos and Transcendence….Pages 357-371
Algebraic Dynamics and Transcendental Numbers….Pages 372-378
Dynamics of Some Contracting Linear Functions Modulo 1….Pages 379-387
On the Modular Function and Its Importance for Arithmetic….Pages 388-397
On Generalized Markoff Equations and Their Interpretation….Pages 398-417