The Fokker-Planck Equation: Methods of Solution and Applications (Springer Series in Synergetics) (英語) ペーパーバック – 2013/10/4
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This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.
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The caveat in this review is the following: the printing and binding quality of the book being sold really suck. I mean, really. It comes with flimsy covers (of magazine-like quality) filmed with chep plastic that is going to detach soon, and the binding will crack for sure as the book starts to get used.
This Chinese quality standard comes from the fact that this kind of book is not printed in the usual sense anymore. It is produced "on demand:" when a customer orders it, it is printed (it seems that on a regular, $99 deskjet printer) and then bound by Amazon (by a third-party, of course) on agreement with Springer.
More and more, after having been scammed a few times by now (see my other review on Ma's "Statistical Mechanics" book), I will not buy technical books on paperback on Amazon anymore (except by Dover).
I recommend reading this book along with Gardiner's book (Handbook of Stochastic Methods) to anyone who wants to learn about stochastic dynamics seriously.
The approach in the book to "treat the electrical field classically, i.e., neglect its operator character[istic], provided that a proper classical noise source is added [with a] strength ... so that it leads to the correct spontaneous emission rate" remains an ad hoc attempt ("semiclassical") without systematic investigation of the involved approximations and their validity that depends upon the scope of the intended laser investigation. A test for evidence would have been to indicate how higher approximations should be obtained and how they affect the results obtained from the "simple laser model".
Chapt. 12 starts from macroscopic considerations, i.e., an equation for the (complex) amplitude "b" of the field: db/dt = beta*d*b - beta*|b|^2 * b (on the right side the first and second parts represent the pumping and (nonlinear) collision effects, respectively). To introduce fluctuations of the field, a formal Langevin term n(t) is then added heuristically, which implies the "simple laser model". However, the delta-correlated Gaussian noise n(t) does not represent the real interactions; there is no true justification for simply adding this term. Finding a correct description of laser fluctuations requires studying the real physical mechanisms. One important source is the fluctuation in the pumping light itself. Therefore, the associated term ("beta*d") represents actually a random fluctuation. Consequently, we face a problem and a stochastic differential equation very much different from the artificial application of the Langevin equation, or the equivalent Fokker-Planck equation. Regrettably, the book does not attempt corresponding answers although crucial for integrity that would be a responsibility of the author, not the reader.
The book is not reader-friendly due to its difficult style of writing, apparently without a professional editing for clarity through better grammar. - The list of References is shockingly outdated (w/o exception all entries are older than 20 years). Note, the shown year of publication (1996) refers to a re-print, not to any revision of the 2nd edition which had been published years before, in 1989. It is very misleading, when the Synopsis to this book claims: "A supplement is included, containing a short review of new [!] material together with some recent [!] references."
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