Date: Mon, 6 Nov 2006
From: "ADLUNG, Sonke"
Subject: Classical and Quantum Chaos, Reports 1 & 2
I am attaching the reports we solicited on your book project. As you will
see, the bottom line is clearly positive, and the referees are encouraging
us to move ahead. Please let me know your reactions to the reports
-------------------------------------- Report 1
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The authors have prepared a graduate-level textbook that aims to bridge
the gap between the mathematical and physical approaches to nonlinear
dynamical systems. The book is not intended to be an introduction to
nonlinear dynamics. The authors in fact note that the readers need to
have a modest background in the field, as might be provided by a number of
standard books, to benefit from their treatment. Thus, the audience for
the book will be limited to advanced graduate students in mathematics or
the physical sciences (and perhaps experienced researchers in nonlinear
dynamics) who wish to have a solid grounding in the methods of
periodic-orbit (cycle) analysis.
The authors are themselves experienced researchers in nonlinear dynamics
and bring an authoritative perspective and tone to the project. For
example, the sample first chapter reads like a (serious) conversation with
a colleague who is willing to point out the difficulties as well as the
power of the analysis. The treatment seems to be particularly up-to-date
with the inclusion of a discussion of important computational techniques
that are required to make use of the analytic developments. Although the
foundations of periodic-orbit analysis have been known for many years, it
is only recently that advances in both the analytic and computational
techniques have made the application of these ideas possible for a wide
range of interesting systems. Hence, I believe that the book makes an
important and timely contribution to the literature of nonlinear dynamics.
A distinctive feature of the book is its thorough treatment of quantum
chaos in terms of periodic-orbit analysis. This area of study illuminates
the boundary between the macroscopic and microscopic (quantum) worlds,
helping to clarify concepts on both sides of the boundary. In addition,
quantum chaos may turn out to be important in understanding both the
potential and the problems with so-called quantum computers.
I noticed one minor inconsistency: On page 9, the authors lay out the
common strategy for analyzing dynamical systems in three stages: I.
diagnose, II. count, III. measure. However, on page 26, the stages are
given as 1) count, 2) weigh, 3) add up.
The writing is generally well done and interesting. However, I did find a
few minor typographical errors, indicating that the authors need to do a
careful proofreading of the manuscript.
Page 9, line 4, should read "it, it is not...."
Page 12, 4 lines from bottom "system" should be "systems"
Page 14, middle of the page "tolinear" should be "to linear"
Page 19, middle of the page "that falls of the edge" should be "that
falls off the edge"
Page 22, 6 lines after Eq. (1.15), "retaced" should be "retraced"
Page 25, line 6, should be "the theory of dynamical zeta ..."
-------------------------------------- Report 2
-----------------------------------------
This is a very interesting and ambitious project by a respected and
well-known researcher and his collaborators in the field for which the
book is written. A version of the text has been on-line for a number of
years, and I gather it has been used by the author for a graduate-level
course covering these topics at Georgia Tech and in Europe. This is not a
book for a first course in chaos or for the faint of heart, since it
covers a wide range of topics with a high level of mathematical
sophistication. I have no doubt that in the hands of the author, the
course for which it was written is highly successful. It is less clear
the extent to which it has been or would be adopted by others since
courses on these topics tend to be somewhat individualized to the
interests and abilities of the instructor, and there are competing texts
at various levels and with different emphasis. The subject matter is of
considerable current interest, although some of the chaos hype and
consequent student interest has subsided over the past decade or so.
The book attempts to cover some rather difficult topics using relatively
high-level mathematics. The writing is clear and informal, sometimes
sounding more like a lecture than a written treatise. Quotations and
humor are sprinkled throughout. These techniques should help relieve the
fear that the reader might otherwise have in plowing through the material.
The topics covered include the major formal principles of nonlinear
dynamical systems theory, but without many of the applications that might
interest students and researchers. For example, there is relatively
little on fractals, detecting chaos in experimental data, chaos control,
spatiotemporal chaos, self-organization, high-dimensional and complex
systems, and numerical methods. On the other hand, there is relatively
much on quantum chaos that is largely lacking in other texts.
I think this is a book that many researchers and upper-level students
would like to own and that would be purchased by university libraries. How
widely it will be adopted as a course text has to be seen. The subject is
good and of considerable current interest, the level is high, the choice
of topics may or may not coincide with the desires of other instructors,
and there are some competing texts.
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