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.
|Publisher:||Johns Hopkins University Press|
|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 in Kansas and consults at Los Alamos National Laboratory.
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
What People are Saying About This
"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."
"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."
"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."
"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."