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The Luttinger Model is the only model of many-fermion physics with legitimate claims to be both exactly and completely solvable. In several respects it plays the same role in many-body theory as does the 2D Ising model in statistical physics. Interest in the Luttinger model has increased steadily ever since its introduction half a century ago. The present volume starts with reprints of the seminal papers in which it was originally introduced and solved, and continues with several contributions setting out the landscape of the principal advances of the last fifty years and of prominent new directions.
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 provides an in-depth introduction to the physics of the interacting electron liquid in a broad variety of systems, including metals, semiconductors, artificial nano-structures, atoms and molecules. One, two and three dimensional systems are treated separately and in parallel. Different phases of the electron liquid, from the Landau Fermi liquid to the Wigner crystal, from the Luttinger liquid to the quantum Hall liquid are extensively discussed. Both static and time-dependent density functional theory are presented in detail. Although the emphasis is on the development of the basic physical ideas and on a critical discussion of the most useful approximations, the formal derivation of the results is highly detailed and based on the simplest, most direct methods.
In the slightly more than thirty years since its formulation, the Hubbard model has become a central component of modern many-body physics. It provides a paradigm for strongly correlated, interacting electronic systems and offers insights not only into the general underlying mathematical structure of many-body systems but also into the experimental behavior of many novel electronic materials. In condensed matter physics, the Hubbard model represents the simplest theoret ical framework for describing interacting electrons in a crystal lattice. Containing only two explicit parameters - the ratio ("Ujt") between the Coulomb repulsion and the kinetic energy of the electrons, and the filling (p) of the available electronic band - and one implicit parameter - the structure of the underlying lattice - it appears nonetheless capable of capturing behavior ranging from metallic to insulating and from magnetism to superconductivity. Introduced originally as a model of magnetism of transition met als, the Hubbard model has seen a spectacular recent renaissance in connection with possible applications to high-Tc superconductivity, for which particular emphasis has been placed on the phase diagram of the two-dimensional variant of the model. In mathematical physics, the Hubbard model has also had an essential role. The solution by Lieb and Wu of the one-dimensional Hubbard model by Bethe Ansatz provided the stimulus for a broad and continuing effort to study "solvable" many-body models. In higher dimensions, there have been important but isolated exact results (e. g. , N agoaka's Theorem).
Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.
Systems of strongly correlated electrons are at the heart of recent developments in condensed matter theory. They have applications to phenomena like high-c superconductivity and the fractional quantum hall effect. Analytical solutions to such models, though mainly limited to one spatial dimension, provide a complete and unambiguous picture of the dynamics involved. This volume is devoted to such solutions obtained using the Bethe Ansatz, and concentrates on the most important of such models, the Hubbard model. The reprints are complemented by reviews at the start of each chapter and an extensive bibliography.
This introductory, reference handbook summarizes the terms and definitions, most important phenomena, and regulations discovered in the physics, chemistry, technology, and application of nanostructures. These nanostructures are typically inorganic and organic structures at the atomic scale. Fast progressing nanoelectronics and optoelectronics, molecular electronics and spintronics, nanotechnology and quantum processing of information, are of strategic importance for the information society of the 21st century. The short form of information taken from textbooks, special encyclopedias, recent original books and papers provides fast support in understanding "old" and new terms of nanoscience and technology widely used in scientific literature on recent developments. Such support is indeed important when one reads a scientific paper presenting new results in nanoscience. A representative collection of fundamental terms and definitions from quantum physics, and quantum chemistry, special mathematics, organic and inorganic chemistry, solid state physics, material science and technology accompanies recommended second sources (books, reviews, websites) for an extended study of a subject. Each entry interprets the term or definition under consideration and briefly presents main features of the phenomena behind it. Additional information in the form of notes ("First described in: ", "Recognition: ", "More details in: ") supplements entries and gives a historical retrospective of the subject with reference to further sources. Ideal for answering questions related to unknown terms and definitions of undergraduate and Ph.D. students studying the physics of low-dimensional structures, nanoelectronics, nanotechnology. The handbook provides fast support, when one likes to know or to remind the essence of a scientific term, especially when it contains a personal name in its title, like in terms "Anderson localization", "Aharonov-Bohm effect", "Bose-Einstein condensate", e.t.c More than 1000 entries, from a few sentences to a page in length.
Advances through carefully conducted quantitative work on well designed, high quality materials characterize the present state of high-temperature superconductivity research. The contributions to this volume present a theoretical and experimental overview of electronic structure and physical properties, including anisotropic features, of high-temperative materials, with a focus on cuprates. In order to enhance the understanding of the mechanisms of superconductivity at high temperatures, this volume is divided into theoretical and experimental parts. The contributions to the two parts correspond to each other, giving readers involved in either area of research activity a reference to findingsof the other. On the other hand, this book gives young physicists high-level information on the present state of research, enhanced by tutorial contributions of leading physicists in the field.
The fractional quantum Hall effect has opened up a new paradigm in the study of strongly correlated electrons and it has been shown that new concepts, such as fractional statistics, anyon, chiral Luttinger liquid and composite particles, are realized in two-dimensional electron systems. This book explains the quantum Hall effects together with these new concepts starting from elementary quantum mechanics.
The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.
The book reflects scientific developments in the physics of metallic compound based nanodevices presented at the NATO-sponsored Workshop on nanophysics held in Russia in the summer of 2003. The program tackles the most appealing problems. It brings together specialists and provides an opportunity for young researchers from the partner countries to interact with them and get actively involved in the most attractive and promising interdisciplinary area of contemporary condensed matter physics.