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This book sets out modern methods of computing properties of materials, including essential theoretical background, computational approaches, practical guidelines and instructive applications.
In the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner ant magnets, and superconductors. It is in essence a weak coupling expan sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics.
The exciting field of nanostructured materials offers many challenging perspectives for fundamental research and technological applications. The combination of quantum mechanics, interaction, phase coherence, and magnetism are important for understanding many physical phenomena in these systems. This book provides an overview of many aspects of interacting electrons in nanostructures, including such interesting topics as quantum dots, quantum wires, molecular electronics, dephasing, spintronics, and nanomechanics. The content reflects the current research in this area and is written by leading experts in the field.
Proceedings of the NATO Advanced Research Workshop, held in St. Petersburg, Russia, 13-16 June 2002
This book is the third of a three-volume series written by the same author. It aims to deliver a comprehensive and self-contained account of the fundamentals of the physics of solids. In the presentation of the properties and experimentally observed phenomena together with the basic concepts and theoretical methods, it goes far beyond most classic texts. The essential features of various experimental techniques are also explained. This volume is devoted mostly to the discussion of the effects of electron—electron interaction beyond the one-electron approximation. The density-functional theory is introduced to account for correlation effects. The response to external perturbations is discussed in the framework of linear response theory. Landau’s Fermi-liquid theory is followed by the theory of Luttinger liquids. The subsequent chapters are devoted to electronic phases with broken symmetry: to itinerant magnetism, to spin- and charge-density waves and their realizations in quasi-one-dimensional materials, as well as to the microscopic theory of superconductivity. An overview is given of the physics of strongly correlated systems. The last chapter covers selected problems in the physics of disordered systems.
This book surveys advances in the study of electron behavior in systems without periodicity--one of the most fascinating areas in solid state physics. The first half of the book covers impurity bands in three dimensions, focusing on the regime in which the electrons are spatially localized, so that an interesting interplay of localization and interaction arises. The second part of the book covers the outstanding features of two-dimensional electron systems, explaining the remarkable effects of magnetic fields, including the normal and fractional quantum Hall effect. As a whole, the book draws together findings from an enormous amount of research into the electronic properties of disordered systems, while the separate chapters may be read as self-contained units.

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