An Introduction to Stochastic Processes in Physics

by Don S. Lemons

Overview

This book provides an accessible introduction to stochastic processes in physics and describes the basic mathematical tools of the trade: probability, random walks, and Wiener and Ornstein-Uhlenbeck processes. It includes end-of-chapter problems and emphasizes applications.

An Introduction to Stochastic Processes in Physics builds directly upon early-twentieth-century explanations of the "peculiar character in the motions of the particles of pollen in water" as described, in the early nineteenth century, by the biologist Robert Brown. Lemons has adopted Paul Langevin's 1908 approach of applying Newton's second law to a "Brownian particle on which the total force included a random component" to explain Brownian motion. This method builds on Newtonian dynamics and provides an accessible explanation to anyone approaching the subject for the first time. Students will find this book a useful aid to learning the unfamiliar mathematical aspects of stochastic processes while applying them to physical processes that he or she has already encountered.

Product Details

ISBN-13:	9780801868672
Publisher:	Johns Hopkins University Press
Publication date:	06/21/2002
Series:	Johns Hopkins Paperback
Pages:	128
Product dimensions:	5.50(w) x 8.50(h) x 0.39(d)
Age Range:	18 Years

About the Author

Don S. Lemons is a professor of physics at Bethel College and the author of Introduction to Stochastic Processes in Physics, also published by Johns Hopkins.

Table of Contents

Preface and Acknowledgments
Chapter 1. Random Variables
Chapter 2. Expected Values
Chapter 3. Random Steps
Chapter 4. Continuous Random Variables
Chapter 5. Normal Variable Theorems
Chapter 6. Einstein's Brownian Motion
Chapter 7. Ornstein-Uhlenbeck Processes
Chapter 8. Langevin's Brownian Motion
Chapter 9. Other Physical Processes
Chapter 10. Fluctuations without Dissipation
Appendix A. "On the Theory of Brownian Motion," by Paul Langevin, translated by Anthony Gythiel
Appendix B. Kinetic Equations
Answers to Problems
References
Index

What People are Saying About This

Gregory N. Derry

"This is a clear, well-written, and valuable book. It is both original and important because it ties together much disparate material scattered throughout the literature into a coherent and readable form."

K. Razi Naqvi

"This book will be much appreciated by those who wish to teach, without going into excessive and demanding mathematical details, a little more than can be covered by analysing a one-dimensional random walk on a lattice or solving the Langevin equation. The author covers a lot of ground in very few pages. The last chapter, entitled 'Fluctuations without Dissipation,' gives his admirably slim volume its own flavor. I will have no hesitation in recommending the book to my students."

From the Publisher

This is a clear, well-written, and valuable book. It is both original and important because it ties together much disparate material scattered throughout the literature into a coherent and readable form.
—Gregory N. Derry, Loyola College

This book will be much appreciated by those who wish to teach, without going into excessive and demanding mathematical details, a little more than can be covered by analysing a one-dimensional random walk on a lattice or solving the Langevin equation. The author covers a lot of ground in very few pages. The last chapter, entitled 'Fluctuations without Dissipation,' gives his admirably slim volume its own flavor. I will have no hesitation in recommending the book to my students.
—K. Razi Naqvi, Norwegian University of Science and Technology

This is a lucid, masterfully written introduction to an often difficult subject and a text which belongs on the bookshelf of every student of statistical physics. I have every confidence that the accessibility of the presentation and the insight offered within will make it a classic reference in the field.
—Dr. Brian J. Albright, Applied Physics Division, Los Alamos National Laboratory

Professor Lemons's book has reclaimed the field of stochastic processes for physics. For too long it has been taught as a highly mathematical subject devoid of its roots in the physical sciences. Professor Lemons's book shows how the subject grew historically from early fundamental problems in physics, and how the greater minds, like Einstein, used its methods to solve problems that are still important today. The book is not only a good introduction for students, but an excellent guide for the professional.
—William Peter, Advance Power Technologies, Inc.

Dr. Brian J. Albright

"This is a lucid, masterfully written introduction to an often difficult subject and a text which belongs on the bookshelf of every student of statistical physics. I have every confidence that the accessibility of the presentation and the insight offered within will make it a classic reference in the field."

William Peter

"Professor Lemons's book has reclaimed the field of stochastic processes for physics. For too long it has been taught as a highly mathematical subject devoid of its roots in the physical sciences. Professor Lemons's book shows how the subject grew historically from early fundamental problems in physics, and how the greater minds, like Einstein, used its methods to solve problems that are still important today. The book is not only a good introduction for students, but an excellent guide for the professional."

Editorial Reviews

Students will love this book. It tells them without fuss how to do simple and useful numerical calculations, with just enough background to understand what they are doing . . . a refreshingly brief and unconvoluted work.
—Vinay Ambegaokar, American Journal of Physics

The book is very clearly set out and very easy to read. Undergraduate students and those wishing to learn about stochastic processes for the first time would enjoy the clear pedagogic presentation.
—B.I. Henry, The Physicist

[An Introduction to Stochastic Processes in Physics] presents fundamental ideas with admirable clarity and concision. The author presents in about 100 pages enough material for the student to appreciate the very different natures of stochastic and sure processes and to solve simple but important problems involving noise. Any physicist wondering what noise is about would be well advised to pack Lemons' books for their next train journey.
—S.M. Barnett, Contemporary Physics

Self-contained and provides adequate insight into stochastic processes in physics. It is quite readable and will be useful to students interested in learning about stochastic processes and their relevance in understanding the physical phenomena. It also provides teachers a good approach to communicate the essence of the subject to students.
—Suresh V. Lawande, Mathematical Reviews

From the Publisher

Self-contained and provides adequate insight into stochastic processes in physics. It is quite readable and will be useful to students interested in learning about stochastic processes and their relevance in understanding the physical phenomena. It also provides teachers a good approach to communicate the essence of the subject to students.

Mathematical Reviews - Suresh V. Lawande

Students will love this book. It tells them without fuss how to do simple and useful numerical calculations, with just enough background to understand what they are doing . . . a refreshingly brief and unconvoluted work.

American Journal of Physics - Vinay Ambegaokar

[ An Introduction to Stochastic Processes in Physics] presents fundamental ideas with admirable clarity and concision. The author presents in about 100 pages enough material for the student to appreciate the very different natures of stochastic and sure processes and to solve simple but important problems involving noise. Any physicist wondering what noise is about would be well advised to pack Lemons' books for their next train journey.

Contemporary Physics - Professor S.M. Barnett

Self-contained and provides adequate insight into stochastic processes in physics. It is quite readable and will be useful to students interested in learning about stochastic processes and their relevance in understanding the physical phenomena. It also provides teachers a good approach to communicate the essence of the subject to students.

— Suresh V. Lawande

Mathematical Reviews

The book is very clearly set out and very easy to read. Undergraduate students and those wishing to learn about stochastic processes for the first time would enjoy the clear pedagogic presentation.

— B.I. Henry

The Physicist

Students will love this book. It tells them without fuss how to do simple and useful numerical calculations, with just enough background to understand what they are doing... a refreshingly brief and unconvoluted work.

— Vinay Ambegaokar

American Journal of Physics

"[An Introduction to Stochastic Processes in Physics] presents fundamental ideas with admirable clarity and concision. The author presents in about 100 pages enough material for the student to appreciate the very different natures of stochastic and sure processes and to solve simple but important problems involving noise. Any physicist wondering what noise is about would be well advised to pack Lemons' books for their next train journey."

Contemporary Physics - S.M. Barnett

"The book is very clearly set out and very easy to read. Undergraduate students and those wishing to learn about stochastic processes for the first time would enjoy the clear pedagogic presentation."

The Physicist - B.I. Henry

This is a clear,well-written,and valuable book. It is both original and important because it ties together much disparate material scattered throughout the literature into a coherent and readable form.

Gregory N. Derry

This book will be much appreciated by those who wish to teach,without going into excessive and demanding mathematical details,a little more than can be covered by analysing a one-dimensional random walk on a lattice or solving the Langevin equation. The author covers a lot of ground in very few pages. The last chapter,entitled 'Fluctuations without Dissipation,' gives his admirably slim volume its own flavor. I will have no hesitation in recommending the book to my students.

K. Razi Naqvi

This is a lucid,masterfully written introduction to an often difficult subject and a text which belongs on the bookshelf of every student of statistical physics. I have every confidence that the accessibility of the presentation and the insight offered within will make it a classic reference in the field.

Brian J. Albright

Professor Lemons's book has reclaimed the field of stochastic processes for physics. For too long it has been taught as a highly mathematical subject devoid of its roots in the physical sciences. Professor Lemons's book shows how the subject grew historically from early fundamental problems in physics,and how the greater minds,like Einstein,used its methods to solve problems that are still important today. The book is not only a good introduction for students,but an excellent guide for the professional.

William Peter

A textbook for physics and engineering students that recasts foundational problems in classical physics into the language of random variables. It develops the concepts of statistical independence, expected values, the algebra of normal variables, the central limit theorem, and Wiener and Ornstein-Uhlenbeck processes. Answers are provided for some problems. Annotation c. Book News, Inc., Portland, OR (booknews.com)