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Noise, Oscillators and Algebraic Randomness

From Noise in Communication Systems to Number Theory

  • Conference proceedings
  • © 2000

Overview

Editors:
  1. Michel Planat

    1. Laboratoire de Physique et Merologie, des Oscillateurs du CNRS, Besançon Cedex, France

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  • The book is an original attempt to connect the noise in experimental physics (electronic oscillators, receivers...) to arithmetic
  • Several forms of noise are covered: classical and quantum noise, phase noise, 1/f noise
  • Concrete applications of analytical number theory are also provided
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics (LNP, volume 550)

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Table of contents (22 papers)

  1. Front Matter

    Pages I-VIII
    Download chapter PDF

  2. Introduction

    • Michel Planat
    Pages 1-5

  3. Mathemagics

    • Pierre Cartier
    Pages 6-67

  4. Thermal and Quantum Noise in Active Systems

    • Jean-Michel Courty, Francesca Grassia, Serge Reynaud
    Pages 71-83

  5. Dipole at ν = 1

    • V. Pasquier
    Pages 84-106

  6. Stored Ion Manipulation Dynamics of Ion Cloud and Quantum Jumps with Single Ions

    • Fernande Vedel
    Pages 107-124

  7. 1/f Fluctuations in Cosmic Ray Extensive Air Showers

    • E. Faleiro, J.M.G. GĂ³mez
    Pages 125-136

  8. Stochastic Resonance and the Benefit of Noise in Nonlinear Systems

    • François Chapeau-Blondeau
    Pages 137-155

  9. Time is Money

    • Marcel Ausloos, Nicolas Vandewalle, Kristinka Ivanova
    Pages 156-171

  10. Oscillators and the Characterization of Frequency Stability: an Introduction

    • Vincent Giordano, Enrico Rubiola
    Pages 175-188

  11. Phase Noise Metrology

    • Enrico Rubiola, Vincent Giordano
    Pages 189-215

  12. Phonon Fine Structure in the 1/f Noise of Metals, Semiconductors and Semiconductor Devices

    • Mihai N. Mihaila
    Pages 216-231

  13. The General Nature of Fundamental 1/f Noise in Oscillators and in the High Technology Domain

    • Peter H. Handel
    Pages 232-264

  14. 1/f Frequency Noise in a Communication Receiver and the Riemann Hypothesis

    • Michel Planat
    Pages 265-287

  15. Detection of Chaos in the Noise of Electronic Oscillators by Time Series Analysis Methods

    • C. Eckert, M. Planat
    Pages 288-304

  16. Geometry and Dynamics of Numbers Under Finite Resolution

    • Jacky Cresson, Jean-Nicolas DĂ©nariĂ©
    Pages 305-323

  17. Diophantine Conditions and Real or Complex Brjuno Functions

    • Pierre Moussa, Stefano Marmi
    Pages 324-342

  18. Algebraic and Analytic Randomness

    • Jean-Paul Allouche
    Pages 345-356

  19. From Symbolic Dynamics to a Digital Approach: Chaos and Transcendence

    • K. Karamanos
    Pages 357-371

  20. Algebraic Dynamics and Transcendental Numbers

    • Michel Waldschmidt
    Pages 372-378
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Keywords

About this book

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.

Editors and Affiliations

  • Laboratoire de Physique et Merologie, des Oscillateurs du CNRS, Besançon Cedex, France

    Michel Planat

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