Luttinger Model
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Quantum Theory Of The Electron Liquid
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Author : Gabriele Giuliani
language : en
Publisher: Cambridge University Press
Release Date : 2008-06-19
Quantum Theory Of The Electron Liquid written by Gabriele Giuliani and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-19 with Science categories.
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.
Luttinger Model
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Author : Vieri Mastropietro
language : en
Publisher: World Scientific
Release Date : 2014
Luttinger Model written by Vieri Mastropietro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Science categories.
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.
Exactly Solvable Models Of Strongly Correlated Electrons
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Author : Vladimir E. Korepin
language : en
Publisher: World Scientific
Release Date : 1994
Exactly Solvable Models Of Strongly Correlated Electrons written by Vladimir E. Korepin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Technology & Engineering categories.
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.
The Hubbard Model
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Author : Dionys Baeriswyl
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
The Hubbard Model written by Dionys Baeriswyl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
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).
Geometric Analysis And Applications To Quantum Field Theory
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Author : Peter Bouwknegt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Analysis And Applications To Quantum Field Theory written by Peter Bouwknegt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.
Models Of Quantum Matter
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Author : Hans-Peter Eckle
language : en
Publisher:
Release Date : 2019
Models Of Quantum Matter written by Hans-Peter Eckle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Science categories.
The book introduces tools with which models of quantum matter are built. The most important technique, the Bethe ansatz, is developed in detail to perform exact calculations of the physical properties of quantum matter.
Many Body Problem The An Encyclopedia Of Exactly Solved Models In One Dimension 3rd Printing With Revisions And Corrections
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Author : Daniel C Mattis
language : en
Publisher: World Scientific
Release Date : 1993-03-15
Many Body Problem The An Encyclopedia Of Exactly Solved Models In One Dimension 3rd Printing With Revisions And Corrections written by Daniel C Mattis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-15 with Science categories.
This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once had to be omitted owing to lack of space — such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain, or Bethe's original paper on the Bethe ansatz — can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developments: the exact solution of the Hubbard model, the concept of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, solitions and the approach to thermodynamic equilibrium, quantum statistical mechanics, localization of normal modes and eigenstates in disordered chains, and a number of other contemporary concerns.
Introduction To The Statistical Physics Of Integrable Many Body Systems
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Author : Ladislav Šamaj
language : en
Publisher: Cambridge University Press
Release Date : 2013-05-16
Introduction To The Statistical Physics Of Integrable Many Body Systems written by Ladislav Šamaj and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-16 with Science categories.
Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related Yang–Baxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.
Bosonization
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Author : Michael Stone (Ph. D.)
language : en
Publisher: World Scientific
Release Date : 1994
Bosonization written by Michael Stone (Ph. D.) and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
Bosonization is a useful technique for studying systems of interacting fermions in low dimensions. It has applications in both particle and condensed matter physics.This book contains reprints of papers on the method as used in these fields. The papers range from the classic work of Tomonaga in the 1950's on one-dimensional electron gases, through the discovery of fermionic solitons in the 1970's, to integrable systems and bosonization on Riemann surfaces. A four-chapter pedagogical introduction by the editor should make the book accessible to graduate students and experienced researchers alike.
Optical Properties Of Low Dimensional Materials
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Author : Yoshihiko Kanemitsu
language : en
Publisher: World Scientific
Release Date : 1996-01-18
Optical Properties Of Low Dimensional Materials written by Yoshihiko Kanemitsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-18 with Technology & Engineering categories.
This book surveys recent experimental and theoretical studies on optical properties of low-dimensional materials, e.g., artificial crystals in zeolites, C60 and its related compounds, silicon nanostructures including porous Si, II-VI and III-V semiconductor quantum structures, and Pb-based natural quantum-well systems. The eight excellent detailed review articles are written by authorities on each field in Japan. All the materials introduced in this book yield new optical phenomena originating from their mesoscopic and low-dimensional characters contributing to a new research field of condensed matter and optical physics.