Download or read book An Introduction to Integrable Techniques for One Dimensional Quantum Systems written by Fabio Franchini and published by Springer. This book was released on 2017-05-25 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.
Download or read book Elements of Classical and Quantum Integrable Systems written by Gleb Arutyunov and published by Springer. This book was released on 2019-07-23 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.
Download or read book New Trends In Quantum Integrable Systems Proceedings Of The Infinite Analysis 09 written by Boris Feigin and published by World Scientific. This book was released on 2010-10-29 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project “Method of Algebraic Analysis in Integrable Systems” in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years.Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics.Through these topics, the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.
Download or read book Dynamics of One Dimensional Quantum Systems written by Yoshio Kuramoto and published by Cambridge University Press. This book was released on 2009-08-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise and accessible account of the dynamical properties of one-dimensional quantum systems, for graduate students and new researchers.
Download or read book The One Dimensional Hubbard Model written by Fabian H. L. Essler and published by Cambridge University Press. This book was released on 2005-02-07 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics.
Download or read book Integrable Systems in Quantum Field Theory and Statistical Mechanics written by M. Jimbo and published by Elsevier. This book was released on 2014-05-19 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Sys Quantum Field Theory
Download or read book Quantum Systems in Chemistry and Physics written by Alfonso Hernández-Laguna and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes collect forty-four selected papers from the scientific contributions presented at the Third European Workshop on Quantum Systems in Chemistry and Physics, held in Granada (Spain), April 19–22, 1998. Ninety-nine scientists from Bulgaria, Columbia, Cuba, Denmark, Finland, France, Germany, Hungary, Israel, Italy, Mexico, Netherlands, Norway, Poland, Russia, Slovakia, Spain, Sweden, United Ki- dom, Uruguay and Venezuela attended the workshop, discussing the state of the art, new trends, and future evolution of the methods and applications. The workshop took place at the ‘Los Alixares’ Hotel, where 45 lectures were given by prominent members of the scientific community; in addition, 49 posters were presented in two very animated sessions. The success of this workshop is due, without doubt, to the excellent tradition initiated at the previous workshops, organised by Prof. R. McWeeny in San Miniato, Pisa (Italy), 1996, and by Prof. S. Wilson in Oxford (United Kingdom), 1997. These workshops create occasions for meetings and disc- sions on the current state of the art, emerging methods and applications and new trends in this area of science. The three meetings were sponsored and partially supported by the European Union (EU) in the frame of the Cooperation in Science and Technology (COST) chemistry actions.
Download or read book Thermodynamics of One Dimensional Solvable Models written by Minoru Takahashi and published by Cambridge University Press. This book was released on 1999-03-28 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exactly solvable models are very important in physics from a theoretical point of view and also from the experimentalist's perspective, because in such cases theoretical results and experimental results can be compared without ambiguity. This is a book about an important class of exactly solvable models in physics. The subject area is the Bethe-ansatz approach for a number of one-dimensional models, and the setting up of equations within this approach to determine the thermodynamics of these systems. It is a topic that crosses the boundaries among condensed matter physics, mathematics and field theory. The derivation and application of thermodynamic Bethe-ansatz equations for one-dimensional models are explained in detail. This technique is indispensable for physicists studying the low-temperature properties of one-dimensional substances. Written by the originator of much of the work in the subject, this book will be of great interest to theoretical condensed matter physicists.
Download or read book Quantum Correlations in Field Theory and Integrable Systems written by Stefano Evangelisti and published by Minkowski Institute Press. This book was released on 2013-05-31 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This doctoral thesis analytically and numerically examines some of the most important concepts in quantum correlations in low-dimensional physics: entanglement and out-of-equilibrium dynamics. As John Bell once said: "Entanglement expresses the spooky nonlocality inherent to quantum mechanics", and its study not only concerns the foundations of any quantum theory, but also has important applications in quantum information and condensed matter theory, amongst others. The first chapters are devoted to the study of "entanglement entropies", a popular measure of the "quantumness" of a physical system. The main focus of the analysis is the one-dimensional XYZ spin-1/2 chain in equilibrium, an interacting theory which in addition to being integrable also has interesting scaling limits, such as the sine-Gordon field theory. Moving away from equilibrium the subsequent chapters deal with the dynamics of quantum correlators after an instantaneous quantum quench. The emphasis is on two different models and techniques; the transverse field Ising chain is studied using the form-factor approach and the O(3) non-linear sigma model is studied by means of the semi-classical theory. In the final chapter the author highlights an important general result: in the absence of long-range interactions in the final Hamiltonian the dynamics of a quantum system are determined by the same statistical ensemble that describes static correlations.
Download or read book Yang Baxter Equation in Integrable Systems written by Michio Jimbo and published by World Scientific. This book was released on 1990 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.
Download or read book Algebraic Aspects of Darboux Transformations Quantum Integrable Systems and Supersymmetric Quantum Mechanics written by Primitivo B. Acosta Humanez and published by American Mathematical Soc.. This book was released on 2012 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the 2010 Jairo Charris Seminar in Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, which was held at the Universidad Sergio Arboleda in Santa Marta, Colombia. The papers cover the fields of Supersymmetric Quantum Mechanics and Quantum Integrable Systems, from an algebraic point of view. Some results presented in this volume correspond to the analysis of Darboux Transformations in higher order as well as some exceptional orthogonal polynomials. The reader will find an interesting Galois approach to study finite gap potentials. This book is published in cooperation with Instituto de Matematicas y sus Aplicaciones (IMA).
Download or read book Quantum Inverse Scattering Method and Correlation Functions written by V. E. Korepin and published by Cambridge University Press. This book was released on 1997-03-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.
Download or read book Photons and Continuum States of Atoms and Molecules written by Carla Guidotti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1981 there has been an attempt in Europe to organize a series of small meetings/workshops/tavole rotonde with the aim of bringing together physi cists and chemists interested in problems concerning atoms or molecules in teracting with external photons where the continua are investigated. The number of problems that fall into this category turns out to be vast. However, it is not possible to make a strict separation into problems con cerning atomic and molecular collisions and those related to the usual spec troscopy. This admixture of two disciplines, discussions on the role of photons and on the interaction of external electromagnetic fields with the continuum provided a central motivation for these workshops. The fourth of this series of meetings was held at Cortona between June 16 and 20, 1986. It was attended by about 100 researchers in the field and there were 43 presentations, all having equal time. These talks form the subject matter of this volume. The idea of publishing the proceedings of these meetings is not new. It allows one to have small meetings in which the subject matter can be discussed at length in a lively atmosphere. However, after the meeting is over, the speakers can collect their thoughts and produce articles in which the results of their interaction with the other participants can be incorporated.
Download or read book Journal of Physics written by and published by . This book was released on 2001 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics In Theoretical Physics Proceedings Of The Second Pacific Winter For Theoretical Physics written by Yongmin Cho and published by World Scientific. This book was released on 1997-04-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, exciting new notions have been emerging in theoretical physics. The quantum nature of gravitation revealed in the physics of black holes, exotic excitations obeying fractional statistics, and integrable structure such as Yangian symmetry in low-dimensional models are some of the subjects presented in this volume.The spectrum of the talks at the School, reflected in the proceedings, is a wide one ranging from the phenomenology of particle physics to that of condensed matter physics, to topics of a mathematical nature. This is an indication that there is a robust interplay of ideas from diverse disciplines of theoretical physics in the Asia-Pacific region.
Download or read book Symmetries Integrable Systems and Representations written by Kenji Iohara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.
Download or read book What Is Integrability written by Vladimir E. Zakharov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E. D. Siggia and N. Ercolani, all authors of this volume were participants at the third of these workshops. All of them were acquainted with each other and with each other's work. Yet it seemed to be somewhat of a discovery that all of them were and are trying to understand the same problem - the problem of integrability of dynamical systems, primarily Hamiltonian ones with an infinite number of degrees of freedom. No doubt that they (or to be more exact, we) were led to this by the logical process of scientific evolution which often leads to independent, almost simultaneous discoveries. Integrable, or, more accurately, exactly solvable equations are essential to theoretical and mathematical physics. One could say that they constitute the "mathematical nucleus" of theoretical physics whose goal is to describe real clas sical or quantum systems. For example, the kinetic gas theory may be considered to be a theory of a system which is trivially integrable: the system of classical noninteracting particles. One of the main tasks of quantum electrodynamics is the development of a theory of an integrable perturbed quantum system, namely, noninteracting electromagnetic and electron-positron fields.
