Classical And Quantum Nonlinear Integrable Systems
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Author | : A Kundu |
Publisher | : CRC Press |
Total Pages | : 320 |
Release | : 2019-04-23 |
Genre | : Science |
ISBN | : 9781420034615 |
Download Classical and Quantum Nonlinear Integrable Systems Book in PDF, Epub and Kindle
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
Author | : Asesh Roy Chowdhury |
Publisher | : CRC Press |
Total Pages | : 425 |
Release | : 2004-01-28 |
Genre | : Science |
ISBN | : 0203498011 |
Download Quantum Integrable Systems Book in PDF, Epub and Kindle
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
Author | : Julia Cen |
Publisher | : |
Total Pages | : |
Release | : 2019 |
Genre | : |
ISBN | : |
Download Nonlinear Classical and Quantum Integrable Systems with PT-symmetries Book in PDF, Epub and Kindle
Author | : Gleb Arutyunov |
Publisher | : Springer |
Total Pages | : 414 |
Release | : 2019-07-23 |
Genre | : Science |
ISBN | : 303024198X |
Download Elements of Classical and Quantum Integrable Systems Book in PDF, Epub and Kindle
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.
Author | : A.K. Prykarpatsky |
Publisher | : Springer Science & Business Media |
Total Pages | : 555 |
Release | : 2013-04-09 |
Genre | : Science |
ISBN | : 9401149941 |
Download Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds Book in PDF, Epub and Kindle
In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).
Author | : P. Tempesta, P. Winternitz, J. Harnad, W. Miller, Jr., G. Pogosyan, and M. Rodriguez |
Publisher | : American Mathematical Soc. |
Total Pages | : 364 |
Release | : |
Genre | : Differential equations, Partial |
ISBN | : 9780821870327 |
Download Superintegrability in Classical and Quantum Systems Book in PDF, Epub and Kindle
Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).
Author | : Piergiulio Tempesta |
Publisher | : American Mathematical Soc. |
Total Pages | : 362 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821833294 |
Download Superintegrability in Classical and Quantum Systems Book in PDF, Epub and Kindle
Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).
Author | : John P. Harnad |
Publisher | : American Mathematical Soc. |
Total Pages | : 282 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821820931 |
Download Integrable Systems: From Classical to Quantum Book in PDF, Epub and Kindle
This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in r s3risingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a nice cross-section of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an up-to-date introduction and an overview of many of the main areas of study in the theory of integral systems.
Author | : Yvette Kosmann-Schwarzbach |
Publisher | : Springer |
Total Pages | : 396 |
Release | : 1997-11-18 |
Genre | : Mathematics |
ISBN | : |
Download Integrability of Nonlinear Systems Book in PDF, Epub and Kindle
The theory of nonlinear systems and, in particular, of integrable systems is related to several very active fields of research in theoretical physics. Many mathematical aspects of nonlinear systems, both continuous and discrete, are analyzed here with particular emphasis on the domains of inverse-scattering techniques, singularity analysis, the bilinear formalism, chaos in nonlinear oscillators, Lie-algebraic and group-theoretical methods, classical and quantum integrability, bihamiltonian structures. The book will be of considerable interest to those who wish to study integrable systems, and to follow the future developments, both in mathematics and in theoretical physics, of the theory of integrability.
Author | : Mauro Carfora |
Publisher | : World Scientific |
Total Pages | : 194 |
Release | : 1992-04-30 |
Genre | : |
ISBN | : 9814554766 |
Download Integrable Systems And Quantum Groups Book in PDF, Epub and Kindle
This volume contains lectures on recent advances in the theory of integrable systems and quantum groups. It introduces the reader to attractive areas of current research.