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The Quantum Dice: An Introduction to Stochastic Electrodynamics (Fundamental Theories of Physics)
Luis de la Peña , and
A.M. Cetto
Manufacturer: Springer
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ASIN: 0792338189 |
Book Description
In spite of the impressive predictive power and strong mathematical structure of quantum mechanics, the theory has always suffered from important conceptual problems. Some of these have never been solved. Motivated by this state of affairs, a number of physicists have worked together for over thirty years to develop
stochastic electrodynamics, a physical theory aimed at finding a conceptually satisfactory, realistic explanation of quantum phenomena.
This is the first book to present a comprehensive review of stochastic electrodynamics, from its origins to present-day developments. After a general introduction for the non-specialist, a critical discussion is presented of the main results of the theory as well as of the major problems encountered. A chapter on stochastic optics and some interesting consequences for local realism and the Bell inequalities is included. In the final chapters the authors propose and develop a new version of the theory that brings it in closer correspondence with quantum mechanics and sheds some light on the wave aspects of matter and the linkage with quantum electrodynamics.
Audience: The volume will be of interest to scholars and postgraduate students of theoretical and mathematical physics, foundations and philosophy of physics, and teachers of theoretical physics and quantum mechanics, electromagnetic theory, and statistical physics (stochastic processes).
Book Description
The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant.
C.W.Gardiner, Quantum Optics (Springer, Berlin 1991)
D.T. Gillespie, Markov Processes (Academic Press, San Diego 1992)
W.T. Coffey, Yu.P.Kalmykov, and J.T.Waldron, The Langevin Equation (2nd edition, World Scientific, 2004)
* Comprehensive coverage of fluctuations and stochastic methods for describing them
* A must for students and researchers in applied mathematics, physics and physical chemistry
Customer Reviews:
Best book on stochastic processes at this level.......2007-07-15
This is my favorite textbook. It is highly readable; everything is explained very clearly without being verbose, and it is very logically organized. One of the book's best features is the author's commentary on the inappropriate uses of particular approaches or the care needed in working particular problems correctly. These insightful sections are clearly the result of a true mastery of the subject and make easier the use of the book for self-study, in which access to such commentary (from a lecturer) is typically not available.
Although it doesn't read like it, this book is actually quite dense with information. It is not uncommon for me to come across a difficult problem in my work, only to find it solved in here. There are many exercises, all of which are interesting and add to the presentation in each chapter.
I do not have any complaints about this book, and I can not recommend any other book more highly than this for anyone interested in learning more about stochastic processes. Even as a first book on the subject, for readers with sufficient mathematical sophistication I can not think of a better book.
A final note: the changes to the third edition are apparently mostly in the chapter on quantum mechanics. You might consider trying to find a bargain on the second edition if such changes are not important to you!
A rare find .......2007-05-20
Before I knew of this book, I used to refer to Chandrasekhar's paper on stochastic processes. This book is very physical and tries to avoid unnecessary dry mathematical rigour (replacing it with clear physical insights) Also the physical problems considered in the book to elucidate the mathematical framework vary from fundamental physics to applications. The exercises are essential but otherwise also the book is a smooth reader. The sections on master equation, Focker plank equation and fluctuation dissipation are my favourites.
I used to work in systems biology and now I have changed my focus to biophysics and the book is useful to me still. I was so desperate to get the book that I had to buy it second hand at the price of first hand. I do not regret about that at all.
Regards
Purushottam
JHU Chemical Engineering,
Grad student
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Quantum-Classical Correspondence: Dynamical Quantization and the Classical Limit (The Frontiers Collection)
A.O. Bolivar
Manufacturer: Springer
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ASIN: 3540201467 |
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At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics.
Quantum-Classical Correspondence elucidates the problem by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.
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Stochastic Processes in Quantum Physics (Monographs in Mathematics)
Masao Nagasawa
Manufacturer: Birkhäuser Basel
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ASIN: 3764362081 |
Book Description
"Stochastic Processes in Quantum Physics" addresses the question 'What is the mathematics needed for describing the movement of quantum particles', and shows that it is the theory of stochastic (in particular Markov) processes and that a relativistic quantum particle has pure-jump sample paths while sample paths of a non-relativistic quantum particle are continuous. Together with known techniques, some new stochastic methods are applied in solving the equation of motion and the equation of dynamics of relativistic quantum particles. The problem of the origin of universes is discussed as an application of the theory. The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level, and some selected chapters can be used as (sub-)textbooks for advanced courses on stochastic processes, quantum theory and theoretical chemistry.
Book Description
This book offers a systematic and comprehensive exposition of the quantum stochastic methods that have been developed in the field of quantum optics. It includes new treatments of photodetection, quantum amplifier theory, non-Markovian quantum stochastic processes, quantum input--output theory, and positive P-representations. It is the first book in which quantum noise is described by a mathematically complete theory in a form that is also suited to practical applications. Special attention is paid to non-classical effects, such as squeezing and antibunching. Chapters added to the previous edition, on the stochastic Schrödinger equation, and on cascaded quantum systems, and now supplemented, in the third edition by a chapter on recent developments in various pertinent fields such as laser cooling, Bose-Einstein condensation, quantum feedback and quantum information.
Book Description
This volume explains the fundamental concepts and theoretical techniques used to understand the properties of quantum systems used to understand the properties of quantum systems having large numbers of degrees of freedom. A number of complimentary approaches are developed, including perturbation theory; nonpurturbative approximations based on functional integrals; general arguments based on order parameters; symmetry, and Fermi liquid theory; and stochastic methods. Each approach provides its own insights and quantitative capabilities, and in conjunction provide a powerful framework for understanding a wide variety of physical systems. Written at a level for graduate students with no prior background in manybody theory, this classic text is intended for physicists in solid state physics, field theory, atomic physics, condensed matter physics, quantum chemistry, and nuclear physics.
Customer Reviews:
Clear, precise, and modern.......2002-09-11
A great physics book for field theory applied to condensed
matter and sometimes nuclear physics problems. The authors
are EXTREMELY careful mathematically and really don't skip
any steps or shove stuff under the rug; in fact, the first
chapter is just all math about how to do integrals and path
integrals and field integrals and deal with Grassman numbers.
A bit unusual for a physics book, but that's their style.
The rest of the book deals with the usual and other material:
zero-temperature Green's functions and perturbation theory
(for energy, Green's function, etc.) The treatment is detailed
and relatively exhaustive. Then there is the same for finite-
temperature. The earlier sections on linear response are
concise and one of the best treatments of the subject I have
seen leading directly to the fluctuation dissipation expression
(after this book I realized this vaunted "fluctuation-dissipation" that no one can explain is just
a straightforward thing about commutators and pert. theory).
The book also has other good stuff: a chapter on mean field theory, Landau-Ginzburg theory, order parameters, and a nice
discussion about spontaneous symmetry breaking that helps
clarify a bunch of stuff. Then there is a whole chapter on
further aspects of one-particle Green's functions (Dyson
equation, solving for poles, quasiparticles, satellites, etc.)
that is pretty good and gets the physical point across. There
is also a chapter on statistical (monte carlo, numerical, etc.)
methods for doing quantum many body problems. While some of
the methods are not the most up to date or modern, the basics
are all there (Monte Carlo, Hubbard-Strataonvich (spelling?),
inverting matrices via Monte Carlo, some stuff about lattice
systems, Langevin equation simulation for Monte Carlo, updating
problems, etc.) There is also a chapter on more advanced
functional integration stuff. Also there is a nice description
of the loop expansion and whatnot.
The book is very well written, has no errors as far as I can
tell, and is exhaustive on what it treats. The problems at
the end of the first few chapters deal with physics problems
and help build intuition whereas the texts in these chapters
are more formal. The book could use some more physical insights
sprinkled throughout, but that is not too much of a drawback.
The book is based on functional integration (Feynman integral)
methods for field theory: this is the modern way folks do it
and it is a powerful way of doing field theory both to
derive results, connect results, do expansions and what not,
and also for certain kinds of monte carl computations. So
having read this, the reader is up to date on a pretty modern
view of field theory in condensed matter (and somewhat on
nuclear physics).
Highly recommended unless you can't stand precise and long
mathematical treatments. My only misgiving is that sometimes
I wish the authors provided more physical insights for certain
concepts and gave some examples rather than "just the math";
but they do this in other parts of the book, so perhaps
my complaint, which is not that serious, is more about the
uneven way this is done. Nevertheless, this is 5/5 and a book
you will read many times and learn from many times.
An important book for beginner cond-mat physicists and more........2000-04-10
A very good introduction to the many particle systems, includes all from the basics of coherent states to very complex parts of theory.
Book Description
Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
Customer Reviews:
Uninspired!.......2006-05-02
Chaichian and Demichev (Vol-I) present a sampling of topics on the mathematical aspects of path integration. There is a second volume which then covers heavier topics (so to speak) such as gravity and quantum field theory. The comments here apply ONLY to the first volume.
For the regular-Joe physicist (such as myself) who actually use path integrals in the "real world", there exists a perpetual inferiority complex about just how much of what we do (and that applies to almost all of mathematical physics) is "rigorously justified". At the same time, all the humdrum axioms and lemmas and proofs and gobbledygook notation is bearable to this group for maybe..what... two-three minutes, maybe?
So, when I first learned that these authors were going to treat this topic with an audience from earth in mind, I was pretty excited.
I was also very interested in the fact that they actually devote the first half of the presentation to the application of path-integrals to the topics of random movement which is of interest to (myself and) most applications outside of the academia. The second half of the book is devoted to the applications to non-relativistic quantum mechanics.
Having frustratedly given up on a multitude of articles on the topic of mathematical aspects of path integration after the first few paragraphs, I, nonetheless, had the nagging feeling about just how deep can they go and still keep the presentation interesting to a physicist? The larger question is: just who the intended audience is? After all, the snobby "rigor" types won't even consider a tutorial format as legitimate, and those who just don't care about the rigor of the underlying mathematics, well, just don't care.
In addition to those like myself who are anxious to know just enough about the rigor, it turns out, there is a fourth group: those who have sadly never heard about path integrals and want to learn just enough for intelligent conversation. I now believe that this book is (or at least, should be) intended for the latter group. Indeed, the preface itself says (p. ix par.5) "The book is intended for those who are familiar with the basic facts from classical and quantum mechanics". Alas it does not say exactly what these audience should expect to get out of this presentation. The preface does say (ibid. par.2) "This book expounds the fundamentals of path integrals...and their numerous applications in... physics". At that early juncture, one would wonder, just how do they intend to deliver on such a ambitious claim in only 320 pages; and it turns out that they don't.
I skimmed the first half with excitement, since the treatment of the stochastic movement by path integrals, is never properly collected in any one place that I've seen (with the qualified exception of a small book by Wiegel-1986). The coverage is fairly broad but never deep. Each short section touches on the main ideas and outlines the computation. This is not necessarily a bad thing in order to inexorably cover maximum ground. What I especially liked were all the worked example problems which would serve the basis for some form of deeper understanding. If it weren't for these, methinks, the novice reader would hardly retain any of the material presented in (what is, at best) an outline fashion.
The biggest disappointment in the section on stochastic movement was the implicit assumption of movement in dense media (hence the ubiquitous Wiener measure) in _all_ computations. I would have liked to see a mention of the fact that it is NOT always true that the variance of displacement is proportional to the first power of time-interval. This misconception is one that has misled the financial industry for nearly a century. I would have liked to see Feynman's approach to stochastic movement (a la Ch.12 Feynman&Hibbs) which elegantly shows a case where the variance goes like the cube of time-interval. Even in cases where the variance is linear in time, it only becomes thus, for times much longer than the interval between scatterings. Even in section 1.2.9 where the calculation starts free of the Wiener measure, the authors are anxious to go the large N regime where the path-integral once-again contains the Wiener measure.
Back to general observations on the book: I found the presentation felt much like the samples of music tracks for CD's for sale on Amazon: a few bars and just as it is getting enticing, it's off to another topic. That's not so bad per se; what makes it frustrating is that the authors do not say where to get the full version. This, despite the fact that the sections seem like they have been cut and pasted (and often abridged) from other sources. Indeed that jibes with the fact that these pages were once the authors' lecture notes. I too would prepare lecture just that way, but there is a long way from printing lecture notes to writing a book, much less a treatise as claimed in par.2 of the preface. If it is true that the sections were paraphrased or lifted from various sources, why not just give those sources and let the reader pursue the topic further? That alone would have made this book worthwhile as a compilation. For this shortcoming I fault the editor at IOP as much as the authors; It is the editor's responsibility to ensure that a book is more than just a fancy print-out of notes by the typical physics-types who by far don't know clear writing from a brick. But I'm really sorry to say that it gets worse.
The business of the missing citations started out as merely annoying. Until I noticed that certain cut-and-pastes are literal lifting of material from one of the sources on the topic I am familiar with. The book by Kleinert contains nearly everything any physicist needs to know about path integrals. It seems that these authors agree, alas, a little too well!!
For example start with the _close_ similarity of equations 2.268, 2.269, and 2.270 (p.165) compared to those of 2.153, 2.154, and 2.155 of Kleinert (3rd ed. section 2.3.2. as of Apr-28-06). While the sequence is only "nearly" identical and the text is paraphrased, the "auxiliary frequency" trick introduced immediately following these equations (unnumbered on top of p. 166 vs. 2.156 Kleinert Apr-28-06 p.113) is identical even in the text preceding it. Since this trick is not found anywhere else in the literature (that I've seen), it stands to good reason for the authors to cite Kleinert. The near identical sequence of calculations continues through 2.2.74 completing the cloning of the section from Kleinert.
There are more examples: pages 168 and 169 of the book seem copied of Kleinert section 2.4 and 2.4.1 on the Gelfand-Yaglom method, without proper citation.
Then there is the nearly identical sequence, in the book's section 2.4.1 starting with eqn 2.4.15 compared to Kleinert's section 6.3 eqn 6.51, and the figure 2.3 compared to Kleinert Fig 6.3.
Conversely, on pg 269 in the discussion on the Coulomb potential in 3D, the authors choose not to follow Kleinert, and to solve the path-integral using a "midpoint prescription". But then it begs the question: why not use some other choice: a post-point or pre-point. The best advice would have been to follow Kleinert's (ch.13) non-holonomic mapping technique. But that's just my preference.
I imagine that similar "issues" relative to other published sources (with which I'm not familiar ) may well exit, as I had first surmised any lecture notes would contain. The problem is that proper citations are missing particularly in cases where novel methods or results have been copied or paraphrased, firstly as proper practice of publication, and secondly, for the sake of the reader should s/he wish to pursue the topic in more detail.
The second half (as in the first half) proceeds in the same outline-esque, fast pace through major topics. As already alluded, this style's merits depend subjectively on the needs and the tastes of the reader.
The first half of the book, being devoted to random movement (Wiener's idea) contains good tutorials on how to move between the path integral approach and the traditional differential-eqn approach to stochastic movement. I can't help but think that the students and applicators of path integral never seem to get quite past the psychological need to show that what they are doing is legit, and really the same as the more traditional differential-eqn approach. The first half of the book serves this particular need well, at least in the cases of the problems typically discussed in standard texts such as the diffusion equation and slightly more complex variations thereof.
Let me cut to the chase here. To learn about path-integrals (for a physicist's purposes) one need only to own two books, the original lecture notes by Feynman (as written and edited by Hibbs) and the Kleinert's 3rd edition, as follow-on. Alas, the former is now out of print (a crime if you ask me), but I have been badgering Dover's editors to reprint it. It also contains many errors and typos; you can get a list of the corrections from me by email (write mathematicus at yahu). Kleinert's book is continually being expanded and corrected by him. He's been known to share individual chapters with other physicists in electronic format, look for him in Berlin.
Finally, when deciding to write a book on a topic where so many distinguished texts exist, the new author should ask himself what is it that I am going to say, or what new point of view am I going to present that is new or different from the existing body of literature. It seems plain that neither the authors nor the editor asked this question before generating the book in its present form. At the present price I am hard pressed to recommend it.
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An Introduction to Quantum Stochastic Calculus (Monographs in Mathematics)
K.R. Parthasarathy
Manufacturer: Birkhäuser Basel
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ASIN: 3764326972 |
Book Description
"Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly
"This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews
An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features:
The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle.
Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields.
Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions.
The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.
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Quantum Fluctuations (Princeton Series in Physics)
Edward Nelson
Manufacturer: Princeton University Press
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ASIN: 0691083797 |
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Quantum Optics: Including Noise Reduction, Trapped Ions, Quantum Trajectories, and Decoherence (Advanced Texts in Physics)
Miguel Orszag
Manufacturer: Springer
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ASIN: 3540650083 |
Book Description
Quantum Optics gives a very broad coverage of basic laser-related phenomena that allow scientists and engineers to carry out research in quantum optics and laser physics. It covers the quantization of the electromagnetic field, quantum theory of coherence, atom-field interaction models, resonance fluorescence, quantum theory of damping, laser theory using both the master equation and the Langevin approach, the correlated-emission laser, input-output theory with application in nonlinear optics, quantum trajectories, atom optics, quantum non-demolition measurements and generation of non-classical vibrational states of ions in a Paul trap. These topics are presented in a unified and didactic manner. The presentation of the book is clear and pedagogical; it balances the theoretical aspects of the optical phenomena with recent relevant experiments.
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