An Introduction to Stochastic Processes in Physics (Johns Hopkins Paperback) by Don S. Lemons (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review 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 PhysicsThe 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 PhysicsSelf-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 ReviewsThis 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 CollegeThis 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 TechnologyThis 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 LaboratoryProfessor 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. Review 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 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is an intersting and worthwhile introduction to stochastic processes that expresses the main ideas in a language familiar to physicists. The book “does exactly what it says on the tin” using fairly basic undergraduate mathematics. The introductry chapters are too long – many of the basic results here are very rudimentary and this takes away from the book. It’s chapter 6 before we hit random process properly, defining the Weiner process as a random variable in terms of difference or increment that is normally distributed. In subsequent chapters he covers stochastic differential equations that are important in physics; Ornstein-Ulenbeck etc. Lemons shows us how to integrate these stochastic differential equations using basic mathematical and statistical tools. In this the book is excellent. So, having read the book one will have a familiarity with the elements of continuous time processes but that’s all.I’m not a physicist but on the applied mathematics side the important points are, in my humble opinion, a) the problem of integration of a random curve (i.e. rocket science) – why does ordinary integration not work? and b) what are the constants of motion (e.g. conservation of mass) that are preserved. In a) the question is waved away a bit – the fact that Reimann sums don’t actually “sum” means that a new integrator is necessary (e.g. Ito calculus) – a couple of chapters dealing with this would be better than the long intro. For b) martingales are the key as they conserve expectation. This is a language familiar to physics and interpreting this important probability concept into physically meaningful problems would be a great help and steping stone to a deeper understanding of random process.

⭐This book is a perfect introduction to Stochastic Process for Physicists.However it is only an introduction.Our friends Economists are much ahead of us Physicists in the use of stochastic process . So for example the book do not explain ITO calculus and therefore the reader never knows that the stochastic differential equation is just symbolic. That the integrals involving paths do not exist and have to be interpreted like ITO or Stratonovich. I recomend another book like the one by Thomas Mikoshch or the one by Fima Klebaner for further studies

⭐Great book for an introduction for the subject. I wish Lemons wrote a second, more advanced text.

⭐This is extremely well written and accessible to those interested in being introduced to the subject. Even those with more knowledge of the subject will likely find insightful views and explanations. It is a quick read as well.

⭐I received this book right when I was told I would, and it was perfect! I ordered it for a professor, so I didn’t read it myself, but he is happy with it!

⭐It is a pity that Ito Calculus is never taught in the physics curriculum (graduate or undergraduate), and learning it properly requires more advanced mathematics. This book won’t overcome this deficit, however, it’ll give the physicist an excellent intro to stochastic processes and practical (ready-to-use) methods for solving stochastic differential equations. I am amazed at how easy it is to read this book, and how clever and concise the presentation is. Definitely worth 5 stars for these 128 pages of text. Well worth the price tag. Get the hardcover if you want the book to last because you may refer to it again and again. It’s a shame it took so long for a book of the sort to be made available.

⭐This very short and to the point text is incredible. If you are an undergraduate or graduate student in physics (I am a grad student)this work is an extremely useful basic overview/review of this topic. I would say it is essential. I wish I would have gotten and read this text completely in undergrad.

⭐This book is awesome! I am a chemist and I always felt that something was missing in my understanding of the transition from the deterministic to the probabilistic description of physical reality. I always felt that I was not really getting it (e.g. the fluctuation-dissipation theorem). I always felt unprepared for modern statiscal mechanics. This book is definitely filling the gap.

⭐Buena introducción a los procesos estocásticos en física.

⭐

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