Ebook: The Fokker-Planck Equation: Methods of Solutions and Applications (Springer Series in Synergetics)

This book with Chapt. 12 on Statistical Properties of Laser Light is an example where the wish for general schemes creates selfmomentum that defeats the objective to describe real physics. The difficulties become serious when authors engage deeply in mathematical tools, here the Fokker-Planck equation, and impose methods onto systems for convenience, or to demonstrate an application - while compromising much on actual physics and the foundations. As a consequence, the missing integrity leaves readers behind in big uncertainty if obtained (formal) results represent, or do no longer represent (laser) physics.

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."