Reviews (1)

Best book on phonons since sliced bread
This book saved my physics career. A complete and comprehensive guide, yet enthralling as not many physics books are. A real must for all semiconductor physisists. Buy now, don't pay later. ... Read more

Book Description

Probably one of the most fashionable areas in the physical sciences today, 'Soft Condensed Matter' provides an excellent introduction to the topic, and includes colloids, polymers, liquid crystals, and amphiphiles. It is suitable for advanced undergraduate and beginning graduate students of physics, chemistry, materials science and chemical engineering. ... Read more

Reviews (1)

Excellent text for appreciating beauty of soft matter!
The chapters are written in straightforward language, conveying essential ideas and fundamentals in very readable manner. The book illustrates how one can convey complex ideas in simple words and yet capture all intricacies of the subject. The book is self contained introduction to colloids, polymers, liquid crystals, self-assembly, crystallization, glass transition, phase behavior and gelation. I have not encountered a better book that presents such a rich overview of these vastly different yet interrelated domain of condensed matter physics in less than 200 pages.

Since the book was written fairly recently, it presents a very modern understanding of described topics. The book by Chaikin and Lubensky (~700 pages) is the one written for anyone interested in meaty details, and equations in their full grandeur. Strobl's recent book on condensed matter is another excellent text and presents lots of physics in very well written graduate level text. But to taste and tempt into soft matter, Jones book definitely is the one to pick! ... Read more

Reviews (1)

A superb treatise for the theoretical physicist.
This book is indeed the 2nd volume of Theoretical Solid State Physics: Perfect Lattices in Equilibrium. As the subtitle specifies, this 2nd vol. refers to non-equilibrium and disordered systems. It is very complete. About the first 100 pages are dedicated to transport theory, Boltzmann equations and relations to density-matrix approach. Other long chapters are about optical properties and superconductivity; about 50 pages are dedicated to excitations; about 200 pages to the defects of solids. I particularly like this book because the authors make often use of self-consistent methods, like Thomas-Fermi one. The unique pity is that the system of units used in each section is not always clear. No mentions also of the most recent nanostructure objects and atomic-force microscopy. I nonetheless highly recommend it, especially to persons who yet have a knowledge of quantum mechanics. For a good and simpler introduction to solid state physics Kittel's book is probably better; about transport theory I'd recommend also the book by Ashcroft and Mermin. These three, I think, are a really must have. ... Read more

Book Description

Solid-state lasers have seen a fast and steady development and are the ubiquitous tool both for research and industrial applications. The author's monograph Solid-State Laser Engineering has become the most-used reference book in this area. The present graduate text on solid-state lasers takes advantage of this rich source by focusing on the needs at the graduate level and those who need an introduction. Numerous exercises with hints for solution, new text and updated material where needed make this text very accessible. ... Read more

Book Description

This unique publication summarizes fifty years of Russian research on shock compression of condensed matter using chemical and nuclear explosions. This research has important applications in physics, materials science and engineering. The book places the importance of Russian experiments in a global context. It then describes the experimental devices used, summarizing the results of experiments on pure metals, metal alloys and compounds, minerals, rocks, organic solids and liquids.The book emphasizes theoretical aspects, experimental problems, and data analysis. Since large scale underground nuclear tests have stopped, it will be some time before similar pressures can be generated by alternative means. This book will be of interest to condensed matter physicists, materials scientists, earth scientists and astrophysicists. ... Read more

Reviews (1)

A useful reference in type II superconductors
This book constitutes a standard reference for those who work in scientific and/or technological aspects of type II superconductors. It reviews in a quite condensed fashion a great deal of the present knowledge on the vortex state of type II superconductors, although it does not include the -intensively explored-mixed state of HTc materials. Quite "esoteric" subjects as the Corbino disk, or the influence of contacts in the noise spectra of type II superconductors are presented. Due to the extension of its scope within the field and its conciseness, it constitutes a nice reference book for those who work in type II superconductors. The only practical drawback is that units and notation are sometimes tricky. Other books in its same style, such as "Irreversible properties of type II superconductors" by Ullmaier (1975) might have the same usefulness, though. ... Read more

Book Description

This reader-friendly introduction to the theory that underlies the many fascinating properties of solids assumes only an elementary knowledge of quantum mechanics. Taylor and Heinonen describe the methods for performing calculations and making predictions of some of the many complex phenomena that occur in solids and quantum liquids. Their book, aimed at advanced undergraduates and beginning graduate students, leads the reader from the fundamental behavior of electrons and atoms in solids to the most recently explored manifestations of the quantum nature of condensed matter. ... Read more

Reviews (2)

An OK book
Since the first edition of Ashcroft/Mermin 's Solid State Physics, the Condensed Matter Physics has been expanded a lot in all directions. Things like high Tc Superconductivity and Quantum Hall Effect were not even discovered in the 1970s. And even in this age, not many textbooks touched the areas that actually most researchers in Condensed Matter Physics are currently working on.
This book is a good try for putting all the new topics as well as the classical ones together in one textbook. But after reading it, I am afraid the book spreaded too much while most topics are not described very clearly in this small book.
My feeling is, looking at the content only, you'll find this a great book --- almost everything interesting has been included! But if you really try to learn some topics --- especially the "advanced ones" --- you'll find many chaptors just give rough ideas or descriptions and finally it turns out not that helpful.
But of course this is not a bad book in general. If you are not in the research of COndensed Matter Physics, browsing this book can give you an nice overview of the current Condensed Matter Physics.

It is an excellent book.
Unfortunately it and its predecessor A Quantum Approach to Solid State are not very well-known yet. In conrast to many 'standard' Condensed Matter texts (like Ascroft & Mermin, Kittel, Marder, etc.) the authors do not attempt to cover all of the huge field. Instead they concentrate on the Quantum side of things which is reflected in the title (for example, no Soft Condensed Matter topics and purely classical results are included). This allows them to discuss several different approaches to the same question. To start they give you an appetizer which includes phonons, some magnetism and a short overview of what's to come. The arguments are intuitive at first and thus easy to understand Then they successfully bring more and more depth to the questions. This helps you to keep in mind the goal they are trying to achieve without getting lost in the forest of details. Quite often you can also use their derivation as a way to remember the result without memorizing it. You get a feel for what's to come and what is in need of patching (here is an example: they discuss Landau levels in a magnetic field by saying that a cirle looks like an oscillator from a side so the orbits should be quantized in the same way and then apply the same formula; this is an easy way to remember it but it is certainly not rigorous!). The book ends with a good discussion of the Quantum Hall effect and effect Kondo and thus cannot be called elementary. No shortcuts are taken so the presentation is smooth and easy to follow till the very end. The book was an enlightment when I first saw it!
On the minus side Taylor and Heinonen seem to be fond of indeces so some familiar expressions may look unexpectedly complicated and not immediately recognizable. An arguable drawback of the simplicity is that I adopt and 'privatize' their ideas so quickly that the second reading (the hunt for the missed points) is not that much fun (keeps me in a state of trying to figure out what was that that I was finding so difficult). Due to its limited content you will need to supplement this text with others which are more complete.
I hope that this short review helps spread the word about another good introduction to the complicated field of CMP. ... Read more

Book Description

Basic Solid State Chemistry, Second Edition is a thorough revision of this best selling introductory text. This new edition provides the reader with an up to date account of the essential topics in this exciting and developing area. Whilst the structure of the first edition has been retained, introducing topics in a logical and coherent way, the text has been revised to include latest developments and concepts. There is a new chapter on Synthetic Methods covering solid state, precursor, chemie douce, intercalation, gas phase (MOCVD, vapour phase transport), hydrothermal and other methods. In addition there is new material on fullerenes, spinels and applications of phase diagrams. The coverage of solid solutions has been expanded and many of the diagrams have been considerably improved, as have the examples and problems. ... Read more

Reviews (1)

excellent source of crystal chemistry material
Professor West's magnum opus:

This book was the bible in the inorganic chemistry department of the University of Aberdeen, Scotland, where Prof. West taught during my undergraduate years.

He was/is a very likeable man, always helpful to his undergraduate and postdoctoral students, and the presentation is user-friendly and clear. The department is world-class, and again, it is hard to outdo this book for clarity and scope of inorganic/crystal chemistry.

Topics: crystal structure, crystallography, phase diagrams, electrical properties, magnetic/optical properties, etc... ... Read more

Book Description

Chemical reactions at surfaces do not follow the same reaction dynamics as atoms in the gas phase. The changes from "ideal" interactions depend on the electronic structure and the spatial and geometric shape of the surface. The dynamics of chemical reactions at surfaces have all the complexity of gas-phase molecules reaction dynamics, plus those associated with the additional phenomena due to the presence of a solid surface. ... Read more

Book Description

Silicon, the basic material for a multibillion-dollar industry, is the most widely researched and applied semiconductor, and its surfaces are the most thoroughly studied of all semiconductor surfaces. Silicon Surfaces and Formation of Interfaces may be used as an introduction to graduate-level physics and chemical physics. Moreover, it gives a specialized and comprehensive description of the most common faces of silicon crystals as well as their interaction with adsorbates and overlayers. This knowledge is presented in a systematic and easy-to-follow way. Discussion of each system is preceded by a brief overview which categorizes the features and physical mechanisms before the details are presented. The literature is easily available, and the references are numerous and organized in tables, allowing a search without the need to browse through the text.

Though this volume focuses on a scientific understanding of physics on the atomistic and mesoscopic levels, it also highlights existing and potential links between basic research in surface science and applications in the silicon industry. It will be valuable to anyone writing a paper, thesis, or proposal in the field of silicon surfaces. ... Read more

Book Description

The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars A. C. Phillips Solid State Physics, Second Edition is aimed at students taking a first course in this subject, although it will also be of interest to professional physicists and electronic engineers requiring a grasp of the fundamentals of this important area of physics. Basic concepts are introduced in an easily accessible context: for example, wave propagation in crystals is introduced using one-and two-dimensional geometries. Only when these basic ideas are familiar are generalisations to three dimensions and the elegant framework of the reciprocal lattice made. Extensively rewritten, the Second Edition now includes new and expanded coverage of semiconductor devices, the quantum Hall effect, quasicrystals, high temperature superconductors and techniques for the study of the surfaces of solids. A chapter on dielectrics and ferroelectrics has also been added. Solid State Physics, Second Edition features:

• A carefully written and structured text to help students fully understand this exciting subject.
• A flow diagram allowing topics to be studied in different orders or omitted altogether.
• Optional "starred" and highlighted sections containing more advanced and specialised material for the more ambitious reader.
• Carefully selected problems at the end of each chapter designed to assist learning. Solutions are provided at the end of the book.

Reviews (3)

Not satisfactory
I used this book in an Introducion to Solid State Physics course, and although I found subjects were well-described and complete, the text was hard to comprehense and quite poorly written.

My professor explained that there are few books that teach Solid State Physics on this level, and that of those books this one may be the best there is. I found it hard to learn from, even though the quality of the information in this book is high.

a different, but worthwhile, approach ¿ try before buying
When Professor Hall lectured Solid State Physics on an undergraduate course at Manchester he deviated from the approach taken in the book, which surprised me somewhat. I'll come back to this later.

The book is very sound if somewhat idiosyncratic. In particular, I found that Hook and Hall used explanatory devices quite different to those followed by my other lecturers, and by most other textbooks. This could be a good or a bad thing, depending on your mental aptitude and/or fondness for their exposition.

I suspect the reason Hall used a different approach in lectures was to tie in with the way we learnt related subject material at Manchester (solid state being just one of three or four compulsory 2nd year courses dealing with atomic and sub-atomic matter).

This is not to say that anything in the book is misleading. It's very well-written and comprehensive, and if this is a subject that you want to learn more about than you can in general texts, I can recommend it as it helped me on several occasions. Perhaps spend half an hour with it in the library or bookshop before buying.

I could not find a better text on solid state at this level when I took my degree in 1995 (IIRC the first edition of Hook-Hall was 1970's, the second early 90's), but that situation may have changed by now.

I didn't learn a single thing.
I had this textbook for one of my fourth year undergrad courses. It seemed that Hook & Hall know what they are talking about, but they certainly couldn't explain it to me. Perhaps this text may be useful for graduate studies or as a reference, but I could not recommend it for an introductory course to solid state physics. ... Read more

Book Description

This is a long-needed general introduction to the physics and chemistry of the liquid-vapor phase transition of metals. Physicists and physical chemists have made great strides understanding the basic principles involved, and engineers have discovered a wide variety of new uses for fluid metals. Yet there has been no book that brings together the latest ideas and findings in the field or that bridges the conceptual gap between the condensed-matter physics relevant to a dense metallic liquid and the molecular chemistry relevant to a dilute atomic vapor. Friedrich Hensel and William Warren seek to change that here. They draw on cutting-edge research and data from carefully selected fluid-metal systems as they strive to develop a rigorous theoretical approach to predict the thermodynamic behavior of fluid metals over the entire liquid-vapor range.

This book will appeal to theoreticians interested in metal-nonmetal transitions or continuous phase transitions in general. It will also be of great value to those who need to understand the practical applications of fluid metals, for example, as a high-temperature working fluid or as a key component of semiconductor manufacturing. ... Read more

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. ... Read more

Reviews (3)

Clear, precise, and modern
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.

The only book touches the path integral method in many-body
Among the available textbooks of many-body theory, like Mahan's, AGD's ..., this is the "only" one which touches the path-integral method. Based on the coherent state representation, the author systematically introduced the Green's Function formalism at finite and zero temperatures. Applications to phase transitions, Landau Fermi Liquid and Stochastic processes are also discussed. Overall, it's a good introduction textbook, also ideal for self-study. Its exercises are more noteworthy for lots of beatiful physics. Yet, it didn't cover topics like spin path integrals, non-linear sigma model ...., which are more interesting in frontier research.

An important book for beginner cond-mat physicists and more.
A very good introduction to the many particle systems, includes all from the basics of coherent states to very complex parts of theory. ... Read more

Book Description

Quantum computing promises to solve problems which are intractable on digital computers. Highly parallel quantum algorithms can decrease the computational time for some problems by many orders of magnitude. This important book explains how quantum computers can do these amazing things. Several algorithms are illustrated: the discrete Fourier transform, Shor's algorithm for prime factorization; algorithms for quantum logic gates; physical implementations of quantum logic gates in ion traps and in spin chains; the simplest schemes for quantum error correction; correction of errors caused by imperfect resonant pulses; correction of errors caused by the nonresonant actions of a pulse; and numerical simulations of dynamical behavior of the quantum Control-Not gate. An overview of some basic elements of computer science is presented, including the Turing machine, Boolean algebra, and logic gates. The required quantum ideas are explained. ... Read more

Reviews (1)

Textbook-boring.
This Introduction to Quantum Computers reads like a textbook on a subject that does have material to it, but nothing that demands a textbook. At this stage in the game of Quantum Computing, the material that has beendiscovered is more than enough interesting fodder for a book, but atextbook-boring approach is not something that is going to make this booksell. There are probably not many Quantum Computing classes in colleges,and unless the book is made for people directly working in the field (it'snot), there isn't enough interesting information to keep the reader awake. ... Read more

Book Description

This book presents a self-contained account of the exact solution of the Hubbard model in one dimension. The description of solids at a microscopic level is complex, involving the interaction of a huge number of its constituents. It is impossible to solve the corresponding many-body problems, although insight can be gained from analysis of simplified models. An important example is the Hubbard model, which describes interacting electrons in narrow energy bands and which has been applied to a diverse range of problems. ... Read more

Book Description

This text provides an introduction, at the level of an advanced student in engineering or physics, to the field of nanomechanics and nanomechanical devices. It provides a unified discussion of solid mechanics, transducer applications, and sources of noise and nonlinearity in such devices. Demonstrated applications of these devices, as well as an introduction to fabrication techniques, are also discussed. The text concludes with an overview of future technologies, including the potential use of carbon nanotubes and other molecular assemblies. ... Read more

Reviews (1)

Very useful and readable
This is a terrific introduction to the subject. It's lucid, covers all aspects in a consise manner and is very readable. I like this book, because it is a good marriage of readability as well as some mathematical rigor. Useful for students with backgrounds in many fields!

Has a section on nanostructures that is terrific in that it covers many of the recent structures that have been fabricated and used to verify physical laws.

Definitely a book worth buying. ... Read more

Book Description

Graphite intercalation compounds are a new class of electronic materials that are classified as graphite-based host guest systems. They have specific structural features based on the alternating stacking of graphite and guest intercalate sheets. The electronic structures show two-dimensional metallic properties with a large variety of features including superconductivity. They are also interesting from the point of two-dimensional magnetic systems. This book presents the synthesis, crystal structures, phase transitions, lattice dynamics, electronic structures, electron transport properties, magnetic properties, surface phenomena, and applications of graphite intercalation compounds.The applications covered include batteries, highly conductive graphite fibers, exfoliated graphite and intercalated fullerenes and nanotubes. ... Read more

Book Description

Electron Correlations in Molecules and Solids bridges the gap between quantum chemistry and solid-state theory. In the first half of the text new concepts are developed for treating many-body and correlation effects, combining standard quantum chemical methods with projection techniques, Greens-function methods and Monte-Carlo techniques. The second half deals with applications of the theory to molecules, semiconductors, transition metals, heavy-fermion systems, and the new high-Tc superconducting materials. ... Read more

Reviews (2)

Think!
Think! before writing a review and confusing people about cumulants, as the previous reviewer does.

Cumulants are widely used in physics and more recently also in theoretical chemistry. Their algebra is very simple, although a bit unfamiliar. Obviously, the "reviewer" Alan Mason from Round Rock, Texas has not understood that algebra. Take his first example: he is certainly right that with his choice of A one finds ¹ c. It is also true, (not pointed out by him) that c¹ <1opA>c=0 where 1op is the unit operator. But so what! These are well known consequences of the cumulant algebra but they do not imply that any of the equations in the book are wrong. Certainly, they are not. Mason should try to familiarize himself with the Grassmann algebra which is also not a standard one. He should be even more startled. But he would fail by concluding from his surprises that "This kinghas no clothes".

This emperor has no clothes
Professor Fulde's primary purpose in this advanced monograph, as stated in the preface, is to provide a unified treatment of electron correlations in molecules and in "solids"; by the latter, he means materials suchas metals in which the electrons are not well localized. The basic idea isthat since the electron correlation hole is a local object, it should bepossible to develop a theory that applies equally well to electroncorrelations in both cases.

First, let us say what is meant by electroncorrelation.One starts with a Hamiltonian H that describes an atomicsystem, say, with n electrons; H acts on a Hilbert space S.Pick afinite-dimensional subspace S_0 and apply a variational principle tominimize the expectation E = <\Phi, H \Phi> over all wavefunctions\Phi expressible as a single Slater determinant of n single-electronwavefunctions \phi_i, 1 <= i <= n.The latter can be any normalizedvector in S_0; we form the Slater determinant and minimize E over all suchchoices of the \phi_i. This leads to the Hartree--Fock equations (2.3.13). In the limit as S_0 increases to all of S, E will decrease to a valueE_{HF} called the Hartree--Fock limit.It will be greater than the trueground-state energy E_0, because the true ground-state wavefunction is aconvergent sum of Slater determinants, not a single determinant. Thedifference E_{HF} - E_0 has an interesting physical interpretation thatjustifies calling it the electron correlation energy.This follows fromexamining the Coulomb term in the one-particle Fock equations (2.3.13) --each electron is treated as though it interacted with the average chargedistribution of the remaining electrons, whereas in fact it interacts withthe actual distribution.The effect of this is to overestimate the groundstate energy by allowing electrons to come too close, closer than the trueCoulomb force would allow.Thus, if we haven't left out necessary terms inthe Hamiltonian (such as spin-orbit coupling, relativistic effects forheavy transition metals, etc.), it is natural to attribute the differenceE_{HF} - E_0 to this "electron correlation" effect. Thecorrelation suppresses the likelihood of other electrons being close to agiven oneas compared to what the HF equations would predict, hence theterm "correlation hole"and its local nature.

Electroncorrelation effects are of supreme importance in chemistry, becausealthough generally small compared to the self-consistent field energiesE_{SCF}, when chemical bonding occurs the difference in the correlationenergy corrections is typically not small compared to the difference in theE_{SCF}. Furthermore, the correlation effects are expected to beexquisitely sensitive to the geometry of the orbitals, so we have afascinating problem lying at the heart of chemistry.

The first fourchapters give a rapid, somewhat demanding, and authoritative overview ofthe basic

approximation schemes (the one described above is called theindependent electron approximation). The important topics, includingdensity functional theory, are treated.

After this promising start, inChap. 5 Prof. Fulde takes up the main business of the book -- developing ageneral scheme for constructing localized basis functions optimized so asto account for electron correlation.If he had succeeded in this, it wouldbe a major contribution to the subject.But alas, I have to report thatdue to a disastrous mathematical oversight, his results are invalid.Thesmoking gun is Eq. (5.1.20); this does NOT give a well- defined innerproduct because it is not bilinear and cannot be made so in a consistent,well-defined way.The root of the trouble is the cumulant formula(5.1.15).Let's call the A_i there "atoms" (with respect tocumulant formation).The problem is Fulde's tacit assumption that if theoperator Op is a sum of monomials in the A_i then

<\Phi_0|Op|\Phi_0>^c can be defined as the corresponding sum ofthe cumulants of the individual monomials.But what if this expression asa sum of monomials isn't unique? If we write Op in a different way, doesthe prescription give the same result? The answer is no! Cumulant formation does not respect the ordinary rules of algebra; in particular,one cannot substitute.(I give two examples below.)But in (5.1.20), Aand B can be expressed in many different ways as a sum of monomials in thecumulant atoms (here H_1 and possibly H_0). Without a well-defined --bilinear, positive-semidefinite -- inner product, the entire treatmentcollapses.This seems to explain the otherwise puzzling lack of referencesin the literature to the work of Fulde's school; for example, there are none in Vol. 93 in the Advances in Chem. Phys. series (Prigogine, Riceeds.), entitled New Methods in Computational Quantum Mechanics, nor in manyother places I have looked.

Here are my examples. A is an atom forcumulant formation, and I use only the formulas^c = and ^c = - ^2.

1) Let A be thetwo-by-two matrix with 0, 0 in the first column and 1, 0 in the second;with the standard unit vectors e_1 and e_2, we have A e_1=0, A e_2=e_1, andA^2 = 0. Set e = (e_1 + e_2)/sqrt(2) and define the expectation by E(Op) =. Then 0 = <0>^c is not equal to ^c =-^2=0-(1/2)^2=-1/4.Here we have expressed zero in twodifferent ways: as the scalar 0 and as the operator A^2, and have gotten different results.

2) Take A = diag(x, y) with x and y real roots of apolynomial \Sum_0^n c_k w^kwith scalar coefficients c_k. Set E(Op) =. Then 0 = \Sum_0^n c_k A^k as an operator, but \Sum_0^nc_k ^c does not equal zero.Take, e.g., n=2, x=2, y=3; theysatisfy w^2-5w+6=0.We have \Sum_0^2 c_k ^c =6<1>^c -5^c + 1^c = 6 - 5 x 2 +-^2 =6-10+4-4=-4.

So, let readers of this book be warned! ... Read more