Topics and Methods in Condensed Matter Theory - From Basic Quantum Mechanics to the Frontiers of Research

This book provides material for courses in theoretical physics for undergraduate and graduate students specializing in condensed matter, including experimentalists who want a thorough theoretical background; the advanced part should be of interest to research workers too. A good first course in quantum mechanics is assumed. Here a variety of many-body phenomena in condensed matter are discussed, with special attention paid to the understanding of strong correlation effects. This requires a variety of theoretical tools (diagram expansions, groups, recursion methods and more). The text, which arose naturally from teaching, is eminently readable and the mathematical treatments are explained in enough detail to be followed easily. Proofs of all the relevant theorems are provided, but the main emphasis is always on the physical meaning or applicability of the results. Many examples are provided for illustration and also serve as worked problems.
 

List of contents

I-Introductory Many-Body Physics.- Basic Many-Body Quantum Mechanics.- Adiabatic Switching and Time-Ordered series.- Atomic Shells and Multiplets.- Green's Functions as Thought Experiments.- Hopping Electron Models: an Appetizer.- Many-body Effects in Electron Spectroscopies.- Symmetry in Quantum Physics.- Group Representations for Physicists.- Simpler Uses of Group Theory.- Product of Representations and Further Physical Applications.- More on Green Function Techniques.- Equations of Motion and Further Developments.- Feynman Diagrams for Condensed Matter Physics.- Many-Body Effects and Further Theory.- Non-Equilibrium Theory.- Non-Perturbative Approaches and Applications.- Some Recursion Techniques with Applications.- Aspects of Nonlinear Optics and Many-Photon Effects.- Selected Exact Results in Many-Body Problems.- Quantum Phases.- Pairing from repulsive interactions.- Algebraic Methods.- Appendices.- Appendix 1: Zero-point Energy in a Pillbox.- Appendix II-Character Tables.- Proof of the Wigner-Eckart Theorem.

About the author

Professor Michele Cini is a full professor of solid state theory at the Department of Physics , University of Roma Tor Vergata. Born in Pisa in 1946, he graduated there in 1969. He is the author of about 100 theoretical research papers dealing with electron spectroscopies, nonlinear optics, recursion methods, electronic transport, antiferromagnetism and superconductivity.

Summary

This book provides course material in theoretical physics intended for undergraduate and graduate students specializing in condensed matter, including experimentalists who want a good theoretical background. The book arose naturally from teaching activity, offering readable and mathematical treatments explained in sufficient detail to be followed easily. Proofs of all the relevant theorems are provided, but the main emphasis is always on the physical meaning and applicability of the results. Many examples are provided for illustration; these also serve as worked problems.
Other related topics discussed in the book are atomic physics, relativistic quantum mechanics, elementary QED, electron spectroscopy, nonlinear optics, and various aspects of the many-body problem. Methods such as group representation theory, Green’s functions, the Keldysh formalism and recursion techniques were also imparted. As prerequisite, a good first course in quantum mechanics is assumed.

Additional text

From the reviews:

"Cini has prepared an advanced book in a specialized area of quantum physics … . The author has divided the book into five broad topics: many-body physics, symmetry in quantum physics, Green’s function techniques, nonperturbative applications, and exact results in many-body problems. … There are problems at the end of each chapter with solutions. … There are some diagrams to explicate the text and a good index. … Graduate students through professionals." (N. Sadanand, CHOICE, Vol. 45 (7), 2008)
"This text is aimed at students specialising in condensed matter theory and is structured as an introductory course to the topic. … this text discusses some exact results that can be obtained pertaining to quantum phases and repulsive interactions. Ultimately this book provides an interesting introduction to an area of active research." (M. Foreman, Contemporary Physics, Vol. 50 (2), March-April, 2009)
"This book treats various theoretical topics in condensed matter physics … . This book is aimed mainly at condensed matter physicists who are working in the area of atomic and solid state physics, and who are looking for some systematic methods and numerical algorithms. It can also be of interest for undergraduate students … in quantum physics, operational computation and algebra." (Jean-Yves Fortin, Mathematical Reviews, Issue 2009 c)
"The present book is devoted to condensed matter physics, which includes theoretical background of the theory and their use in applications, i.e. in experiments. … the book is well written, readable and the mathematical treatments are explained in enough detail. Proofs of all the relevant theorems are given. There are a lot of illustrative examples, and relevant problems. … the book provides material for courses in theoretical physics, and it is recommended for undergraduate and graduate students specializing in condensed matter physics." (Farruh Mukhamedov,Zentralblatt MATH, Vol. 1146, 2008)

Report

From the reviews:

"Cini has prepared an advanced book in a specialized area of quantum physics ... . The author has divided the book into five broad topics: many-body physics, symmetry in quantum physics, Green's function techniques, nonperturbative applications, and exact results in many-body problems. ... There are problems at the end of each chapter with solutions. ... There are some diagrams to explicate the text and a good index. ... Graduate students through professionals." (N. Sadanand, CHOICE, Vol. 45 (7), 2008)
"This text is aimed at students specialising in condensed matter theory and is structured as an introductory course to the topic. ... this text discusses some exact results that can be obtained pertaining to quantum phases and repulsive interactions. Ultimately this book provides an interesting introduction to an area of active research." (M. Foreman, Contemporary Physics, Vol. 50 (2), March-April, 2009)
"This book treats various theoretical topics in condensed matter physics ... . This book is aimed mainly at condensed matter physicists who are working in the area of atomic and solid state physics, and who are looking for some systematic methods and numerical algorithms. It can also be of interest for undergraduate students ... in quantum physics, operational computation and algebra." (Jean-Yves Fortin, Mathematical Reviews, Issue 2009 c)
"The present book is devoted to condensed matter physics, which includes theoretical background of the theory and their use in applications, i.e. in experiments. ... the book is well written, readable and the mathematical treatments are explained in enough detail. Proofs of all the relevant theorems are given. There are a lot of illustrative examples, and relevant problems. ... the book provides material for courses in theoretical physics, and it is recommended for undergraduate and graduate students specializing in condensed matter physics." (Farruh Mukhamedov,Zentralblatt MATH, Vol. 1146, 2008)

Product details

• Authors: Michele Cini
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 06.10.2010
• EAN: 9783642089640
• ISBN: 978-3-642-08964-0
• No. of pages: 443
• Dimensions: 155 mm x 25 mm x 235 mm
• Weight: 698 g
• Illustrations: XX, 443 p. 73 illus.
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Atomic physics, nuclear physics; B, ups, Theory, Solid State Physics, Condensed Matter Physics, Condensed matter, Physics and Astronomy