MacDonald D.K.C. Noise and Fluctuations: An Introduction

John Wiley & Sons, Inc., NY, London, 2006. – 121 p. – ISBN: 0486450295An understanding of fluctuations and their role is both useful and fundamental to the study of physics. This concise study of random processes offers graduate students and research physicists a survey that encompasses both the relationship of Brownian Movement with statistical mechanics and the problem of irreversible processes. It outlines the basics of the physics involved, without the strictures of mathematical rigor.
The three-part treatment starts with a general survey of Brownian Movement, including electrical Brownian Movement and "shot-noise," Part two explores correlation, frequency spectrum, and distribution function, with particular focus on application to Brownian Movement. The final section examines noise in electric currents, including noise in vacuum tubes and a random rectangular current. Frequent footnotes amplify the text, along with an extensive selection of Appendixes.General surveyBrownian Movement
Electrical Brownian Movement and "shot-noise"
The observed noise: time-dependence and frequency response
Concluding Summary
Correlation, frequency spectrum, and distribution function
Statistically stationary variables
The autocorrelation function and the Wiener- Khintchine theorem
Application to Brownian Movement
A traffic problem
A related electron-beam noise problem
The distribution function and the approach to equilibrium
Irreversibility and the "microscopic" forceNoise in electric currents
Noise in vacuum tubes
A random rectangular current
Appendices
The mean and fluctuations of a Bernoulli distribution
Alternative derivation of Einstein's Brownian Movement equation
Proof of Campbell's theorem
The autocorrelation function for a random rectangular current, and the Poisson distribution