Classical And Quantum Aspects Of Completely Integrable Nonlinear Systems
Download Classical And Quantum Aspects Of Completely Integrable Nonlinear Systems full books in PDF, epub, and Kindle. Read online free Classical And Quantum Aspects Of Completely Integrable Nonlinear Systems ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Classical and Quantum Nonlinear Integrable Systems
Author | : A Kundu |
Publisher | : CRC Press |
Total Pages | : 310 |
Release | : 2019-04-23 |
Genre | : Science |
ISBN | : 1420034618 |
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
Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds
Author | : A.K. Prykarpatsky |
Publisher | : Springer Science & Business Media |
Total Pages | : 555 |
Release | : 2013-04-09 |
Genre | : Science |
ISBN | : 9401149941 |
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).
Nonlinear Waves: Classical and Quantum Aspects
Author | : Fatkhulla Abdullaev |
Publisher | : Springer Science & Business Media |
Total Pages | : 563 |
Release | : 2006-03-02 |
Genre | : Science |
ISBN | : 1402021909 |
Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.
Quantum Integrable Systems
Author | : Asesh Roy Chowdhury |
Publisher | : CRC Press |
Total Pages | : 425 |
Release | : 2004-01-28 |
Genre | : Science |
ISBN | : 0203498011 |
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
Symmetries and Singularity Structures
Author | : Muthuswamy Lakshmanan |
Publisher | : Springer Science & Business Media |
Total Pages | : 219 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642760465 |
Proceedings of the Workshop, Bharathidasan University, Tiruchirapalli, India, November 29 - December 2, 1989
Elements of Classical and Quantum Integrable Systems
Author | : Gleb Arutyunov |
Publisher | : Springer |
Total Pages | : 414 |
Release | : 2019-07-23 |
Genre | : Science |
ISBN | : 303024198X |
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.
Fifty Years of Mathematical Physics
Author | : Molin Ge |
Publisher | : World Scientific Publishing Company |
Total Pages | : 596 |
Release | : 2016-02-16 |
Genre | : Science |
ISBN | : 9814340960 |
This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.
Integrability of Nonlinear Systems
Author | : Yvette Kosmann-Schwarzbach |
Publisher | : Springer Science & Business Media |
Total Pages | : 358 |
Release | : 2004-02-17 |
Genre | : Science |
ISBN | : 9783540206309 |
The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.
Superintegrability in Classical and Quantum Systems
Author | : Piergiulio Tempesta |
Publisher | : American Mathematical Soc. |
Total Pages | : 362 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821833294 |
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).