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An Introduction To Integrable Techniques For One Dimensional Quantum Systems
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Book Synopsis An Introduction to Integrable Techniques for One-Dimensional Quantum Systems by : Fabio Franchini
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 180 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.
Book Synopsis Symmetries and Integrability of Difference Equations by : Decio Levi
Download or read book Symmetries and Integrability of Difference Equations written by Decio Levi and published by Springer. This book was released on 2017-06-30 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.
Book Synopsis Models of Quantum Matter by : Hans-Peter Eckle
Download or read book Models of Quantum Matter written by Hans-Peter Eckle and published by Oxford University Press. This book was released on 2019-07-29 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important task of theoretical quantum physics is the building of idealized mathematical models to describe the properties of quantum matter. This book provides an introduction to the arguably most important method for obtaining exact results for strongly interacting models of quantum matter - the Bethe ansatz. It introduces and discusses the physical concepts and mathematical tools used to construct realistic models for a variety of different fields, including condensed matter physics and quantum optics. The various forms of the Bethe ansatz - algebraic, coordinate, multicomponent, and thermodynamic Bethe ansatz, and Bethe ansatz for finite systems - are then explained in depth and employed to find exact solutions for the physical properties of the integrable forms of strongly interacting quantum systems. The Bethe ansatz is one of the very few methodologies which can calculate physical properties non-perturbatively. Arguably, it is the only such method we have which is exact. This means, once the model has been set up, no further approximations or assumptions are necessary, and the relevant physical properties of the model can be computed exactly. Furthermore, an infinite set of conserved quantities can be obtained. The quantum mechanical model under consideration is fully integrable. This makes the search for quantum models which are amenable to an exact solution by the Bethe ansatz, and which are quantum integrable, so important and rewarding. The exact solution will provide benchmarks for other models, which do not admit an exact solution. Bethe ansatz techniques provide valuable insight into the physics of strongly correlated quantum matter.
Book Synopsis Correlations in Low-Dimensional Quantum Gases by : Guillaume Lang
Download or read book Correlations in Low-Dimensional Quantum Gases written by Guillaume Lang and published by Springer. This book was released on 2018-12-29 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book addresses several aspects of thermodynamics and correlations in the strongly-interacting regime of one-dimensional bosons, a topic at the forefront of current theoretical and experimental studies. Strongly correlated systems of one-dimensional bosons have a long history of theoretical study. Their experimental realisation in ultracold atom experiments is the subject of current research, which took off in the early 2000s. Yet these experiments raise new theoretical questions, just begging to be answered. Correlation functions are readily available for experimental measurements. In this book, they are tackled by means of sophisticated theoretical methods developed in condensed matter physics and mathematical physics, such as bosonization, the Bethe Ansatz and conformal field theory. Readers are introduced to these techniques, which are subsequently used to investigate many-body static and dynamical correlation functions.
Book Synopsis Hydrodynamic Scales Of Integrable Many-body Systems by : Herbert Spohn
Download or read book Hydrodynamic Scales Of Integrable Many-body Systems written by Herbert Spohn and published by World Scientific. This book was released on 2024-02-27 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad introduction to integrable systems with many degrees of freedom. Within a much larger orbit, discussed are models such as the classical Toda lattice, Calogero fluid, and Ablowitz-Ladik discretized nonlinear Schrödinger equation. On the quantum mechanical side, featured are the Lieb-Liniger delta-Bose gas and the quantum Toda lattice. As a genuinely novel twist, the study deals with random initial data described by generalized Gibbs ensembles with parameters of slow spatial variation. This is the hydrodynamic scale, in spirit similar to the ballistic Euler scale of nonintegrable simple fluids. While integrable microscopic particle models are very diverse, the central theme of this book is to elucidate their structural similarity on hydrodynamic scales.
Book Synopsis Functional Methods for the Solution of One-Dimensional Quantum Systems by : Tobias Wirth
Download or read book Functional Methods for the Solution of One-Dimensional Quantum Systems written by Tobias Wirth and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2011-02 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The framework of the Quantum Inverse Scattering Method is used to study the hamiltonian of the XXX and XXZ spin chain with general boundary fields. Key ingredient is the underlying algebraic structure which is a combination of the Yang-Baxter algebra and a so-called Reflection algebra including boundary fields of arbitrary direction and strength. For spin chains with diagonal boundary fields this setup has been well studied using algebraic Bethe ansatz and the inverse problem was solved by Kitanine for infinite chain lengths. These results are picked up and generalized to arbitrary lengths using non-linear integral equations. In the case of non-diagonal boundary fields the lack of a reference state or pseudo vacuum prohibits the solution by algebraic Bethe ansatz. The method of separation of variables is not constrained in that sense and is applied to the XXX chain and a spin-boson model. Finally a different approach to the case of non-diagonal boundary conditions is studied. Starting from the so-called fusion hierarchy non-linear integral equations are derived bearing the possibility to extract information about an eigenvalue of a specific state.
Book Synopsis Quantum Integrable Systems by : Asesh Roy Chowdhury
Download or read book Quantum Integrable Systems written by Asesh Roy Chowdhury and published by CRC Press. This book was released on 2004-01-28 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
Book Synopsis Elements of Classical and Quantum Integrable Systems by : Gleb Arutyunov
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 414 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.
Book Synopsis Entanglement in Spin Chains by : Abolfazl Bayat
Download or read book Entanglement in Spin Chains written by Abolfazl Bayat and published by Springer Nature. This book was released on 2022-09-26 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.
Book Synopsis Classical and Quantum Nonlinear Integrable Systems by : A Kundu
Download or read book Classical and Quantum Nonlinear Integrable Systems written by A Kundu and published by CRC Press. This book was released on 2019-04-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories
Book Synopsis Algebraic Bethe Ansatz And Correlation Functions: An Advanced Course by : Nikita Slavnov
Download or read book Algebraic Bethe Ansatz And Correlation Functions: An Advanced Course written by Nikita Slavnov and published by World Scientific. This book was released on 2022-05-12 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is unlikely that today there is a specialist in theoretical physics who has not heard anything about the algebraic Bethe ansatz. Over the past few years, this method has been actively used in quantum statistical physics models, condensed matter physics, gauge field theories, and string theory.This book presents the state-of-the-art research in the field of algebraic Bethe ansatz. Along with the results that have already become classic, the book also contains the results obtained in recent years. The reader will get acquainted with the solution of the spectral problem and more complex problems that are solved using this method. Various methods for calculating scalar products and form factors are described in detail. Special attention is paid to applying the algebraic Bethe ansatz to the calculation of the correlation functions of quantum integrable models. The book also elaborates on multiple integral representations for correlation functions and examples of calculating the long-distance asymptotics of correlations.This text is intended for advanced undergraduate and postgraduate students, and specialists interested in the mathematical methods of studying physical systems that allow them to obtain exact results.
Book Synopsis Advanced Quantum Mechanics by : Reinhold Blumel
Download or read book Advanced Quantum Mechanics written by Reinhold Blumel and published by Jones & Bartlett Publishers. This book was released on 2010-04-28 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a coherent introduction to Gutzwiller’s trace formula accessible to well-prepared science, mathematics, and engineering students who have taken introductory courses in linear algebra, classical, and quantum mechanics. In addition to providing an enrichment of the undergraduate curriculum, this book may serve as the primary text for graduate courses on semiclassical methods. Since periodic-orbit expansions may be used to solve all types of wave systems that typically occur in mathematics, phyics, and engineering, this book is attractice for professional scientists and engineers as well. Following a thorough review of elementary concepts in classical and quantum mechanics the reader is introduced to the idea of classical periodic orbits, the foundation of Gutzwiller’s approach to quantum spectra. The trace formula itself is derived following an introduction to Feynman’s path integrals. Numerous applications, including the exact solutions of “unsolvable” one-dimensional quantum problems, illustrate the power of Gutzwiller’s method. Worked examples throughout the text illustrate the material and provide immediate “hands-on” demonstrations of tools and concepts just learned. Problems at the end of each section invite the reader to consolidate the acquired knowledge.
Book Synopsis Quantum Inverse Scattering Method and Correlation Functions by : V. E. Korepin
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.
Book Synopsis Introduction to the Statistical Physics of Integrable Many-body Systems by : Ladislav Šamaj
Download or read book Introduction to the Statistical Physics of Integrable Many-body Systems written by Ladislav Šamaj and published by Cambridge University Press. This book was released on 2013-05-16 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Including topics not traditionally covered, such as (1+1)-dimensional QFT, this book considers a wide range of models and their applications.
Book Synopsis Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems by : Laurens Vanderstraeten
Download or read book Tensor Network States and Effective Particles for Low-Dimensional Quantum Spin Systems written by Laurens Vanderstraeten and published by Springer. This book was released on 2017-08-10 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. Combining these developments, it subsequently uses the formalism of tensor network states to derive an effective particle description for one- and two-dimensional spin systems that exhibit strong quantum correlations. These techniques arise from the combination of two themes in many-particle physics: (i) the concept of quasiparticles as the effective low-energy degrees of freedom in a condensed-matter system, and (ii) entanglement as the characteristic feature for describing quantum phases of matter. Whereas the former gave rise to the use of effective field theories for understanding many-particle systems, the latter led to the development of tensor network states as a description of the entanglement distribution in quantum low-energy states.
Book Synopsis Non-equilibrium Dynamics of One-Dimensional Bose Gases by : Tim Langen
Download or read book Non-equilibrium Dynamics of One-Dimensional Bose Gases written by Tim Langen and published by Springer. This book was released on 2015-05-22 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a series of experiments with ultracold one-dimensional Bose gases, which establish said gases as an ideal model system for exploring a wide range of non-equilibrium phenomena. With the help of newly developed tools, like full distributions functions and phase correlation functions, the book reveals the emergence of thermal-like transient states, the light-cone-like emergence of thermal correlations and the observation of generalized thermodynamic ensembles. This points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution, and lays the groundwork for a universal framework of non-equilibrium physics. The thesis investigates a central question that is highly contested in quantum physics: how and to which extent does an isolated quantum many-body system relax? This question arises in many diverse areas of physics, and many of the open problems appear at vastly different energy, time and length scales, ranging from high-energy physics and cosmology to condensed matter and quantum information. A key challenge in attempting to answer this question is the scarcity of quantum many-body systems that are both well isolated from the environment and accessible for experimental study.
Book Synopsis Statistical Mechanics of Lattice Systems by : Sacha Friedli
Download or read book Statistical Mechanics of Lattice Systems written by Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
