Quantum Theory of the Electron Liquid
By addebook • Jul 19th, 2008 • Category: Engineer •
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Quantum Theory of the Electron Liquid
Quantum Theory of the Electron Liquid
By Gabriele Giuliani, Giovanni Vignale
Publisher: Cambridge University Press
Number Of Pages: 798
Publication Date: 2005-04-18
ISBN-10 / ASIN: 0521821126
ISBN-13 / EAN: 9780521821124
Binding: Hardcover
Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This book introduces the quantum theory of the electron liquid and the mathematical techniques that describe it. The electron liquid’s behavior is governed by the laws of quantum mechanics which prevail over the microscopic world of atoms and molecules.
Summary: New Bible
Rating: 5
A wonderful book: clearly a product of careful thought, and love. It is a timely “Pines and Nozieres” for the new generations. I find myself reading the first chapters over and over again, and always getting something new out of it. In spite of having read numerous accounts regarding subtle issues in density functional theory, I had never properly understood some of the important aspects (e.g. derivative discontinuities) until after reading their original presentation in chapter 7. I agree 100% with the review of R. Pepino, and would only like to add my praise for the lively writing style, which I find captivating: A pleasure to study, or even simply read. Its perfect mix of seriousness and passion, makes of The Quantum Theory of the Electron Liquid a major work that is both authoritative and engaging.
Summary: Wonderful!
Rating: 5
This is a kind of book rare to find nowadays. It seems to be the result of a long and careful investigation of the literature, of reflection, of deep physical understanding. It avoids hand-waving, “phenomenological”, jargon and fashionable types of arguments, in favor of well grounded, logical and mathematically solid arguments. It is the opposite of most we find today, that is, it is not a set of “lectures” quickly transformed into textbook; it is not the point of view of the authors, defended by phraseology; it is not a biased book. It is really a wonderful book, very well written, displaying love by the subject, strong curiosity and search for the truth.
Congratulations to the authors! May their book inspire other physicists to search truth instead of glory and fame. May their book inspire the young to avoid the fashion and easy way. May their book become a classic because it truly deserves.
Summary: An outstanding job
Rating: 5
Written with the student in mind, this book gives an excellent introduction to density functional theory, many-body quantum theory, and their application to the physical system now known as the electron liquid. Given the current interest in electron liquids, both from an applied and a theoretical standpoint, this book serves a need for those who want to educate themselves on the different techniques and strategies used to study the behavior of electron liquids, and general many-body systems. The authors of the book emphasize modern developments, and give many references for those readers who want to pursue the subject in even more detail. An understanding of both the physical and mathematical ideas in the book require concentrated effort, but anyone who has decided to read such a sizable book realizes that true insight into any subject only comes from such an effort. The authors understand this, and they do not hesitate to elaborate on sophisticated concepts when they arise. But they also interject informal and colloquial language in many places in the text. This serves to set the reader more at ease, and makes for even more enjoyable reading.
Readers (such as this reviewer) who have a background in high energy physics or relativistic quantum field theory will find many of the concepts used in these fields find application in the theory of electron liquids. In addition, many of the concepts used in high-energy physics, such as the idea of spontaneously broken symmetries, arose in condensed matter and many-body physics. The symbiosis of ideas between these different fields has been a fruitful one and this will no doubt continue in the years to come. An example of this is the Chern-Simons theory, which arose in the context of quantum chromodynamics as a theory of the strong interaction, and finds its way in this book in the discussion on the Laughlin theory of the fractional quantum Hall liquid. This theory, as the authors point out, is based on a careful choice of wave functions, and therefore cannot be viewed as systematic in its strategy in finding solutions. The Chern-Simons theory is brought in to provide a more systematic approach. It is a fascinating strategy, for using it one maps the problem of the two-dimensional electron liquid into an equivalent many-body problem of interacting composite particles. One can then use a mean-field approximation on the latter system. This approach is somewhat similar to the “duality” phenomena found in string theories (although the analogy is somewhat loose). The Chern-Simon theory also finds its place in purely mathematical contexts, such as topological quantum field theory and the theory of knots, and readers with a background in this area will see familiar constructions in the author’s discussions. The authors derive an expression for the electromagnetic response function for a system of composite particles that satisfies Kohn’s theorem, but point out that it does not have the correct scaling properties.
The authors give a thorough overview of density functional theory, with emphasis placed not only on the formalism but also on its utility in solving many-body problems. Readers growing up in the usual formalism of Hilbert spaces will need justification as to the power of density functional methods and how one can still calculate quantities of interest without really using the many-body wave function. And, anyone who has tried to perform numerical computations of quantum-mechanical quantities understands the need for algorithms that are manageable, i.e. that allow the computation of physical quantities in a reasonable time scale. The authors point out though that the Kohn-Sham equations, which result after the minimization of the energy as a functional of the electron density, can be solved computationally on a time scale that increases as a power of the number of electrons. This is to be contrasted with the computation of the solution of the N-electron Schrodinger equation, which depends exponentially on N. However, as in all problems in constrained optimization, there is no free lunch (this has been proven rigorously), and so there is always a penalty to be paid in any solution strategy. For the Kohn-Sham equations, one uses the `effective potential’ that is local in space, but has a nonlocal dependence on the density, allowing only an approximate description. Another penalty arises from using the determinantal wave function in the solution of the Kohn-Sham equations does not give a robust approximation to the true ground-state wave function. The last penalty arises because of the “universal” nature of density functional: it has the same form for all physical systems and so does not bring out the physical properties that are unique to a particular one. In addition to these issues, readers who insist on constructive approaches to mathematical proof will reject the proof of the Hohenberg-Kohn theorem, since it relies on proof by contradiction. In physical applications this is a minor issue of course, but in attempts to put density functional theory, indeed all of quantum field theory, on a constructive rigorous mathematical foundation, this issue is of importance. The authors (correctly) have no intention of respecting mathematical rigor, and state so explicitly. Instead they emphasize the physics behind the formalism and discuss the experimental evidence for it. Indeed, the book is full of examples of this evidence, and the appropriate references are given. Most of the discussion on the experimental situation is given in the context of the quantum Hall effect, which seems appropriate given that the authors have made original contributions to the understanding of this effect.
[DISCLOSURE: This reviewer knows the second author personally, but did not discuss this review with him. The opinions above are an honest assessment of the content of the book, and were not influenced, at least consciously, by any personal knowledge of the author.]
Summary: Great book!!
Rating: 5
This book is truly a valuable and unique resource for physicists and quantum chemists interested in the structure and dynamics of electronic systems, especially (but not solely) in the solid-state. It presents the standard theories, as well as very recent cutting-edge developments, for example, extensions of density functional theory to time-dependent phenomena and current-densities — all with elegant derivations and beautiful explanations. The authors have an extremely engaging writing style, which makes the book one of the most enjoyable physics books I have read. Many of the exercises at the end of each chapter are fascinating in themselves, instructive, and clearly explained.
I feel this book will prove to be a wonderful treasure for graduate students, postdocs, and professors.
Summary: Excellent
Rating: 5
This is the one of best overall book on the electronic theory of solids. It certainly covers all relevant aspect one could ever want to know about the topic and does a phenomenal job of clearly explaining and demonstrating the material. The best example is the chapter dedicated to the Fermi liquid with the very illuminating explanations of the theory of quasiparticles. This book is easy to read and its lecture does not require advanced mathematical knowledge. It is an excellent textbook and a very good start point for research problems. It is also remarkable the use of state of the art results and the elimination of several common misconceptions. I must say that the exercises are a good opportunity to better understand the material.
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