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Classical and Quantum Nonlinear Integrable Systems

2019-04-23 Science
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Release : 2019-04-23
Genre : Science
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Book Rating : 615/5 ( reviews)

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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. This book was released on 2019-04-23. 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

Quantum Integrable Systems

2004-01-28 Science
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Release : 2004-01-28
Genre : Science
Kind : eBook
Book Rating : 011/5 ( reviews)

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Book Synopsis Quantum Integrable Systems by : Asesh Roy Chowdhury

Download or read book Quantum Integrable Systems written by Asesh Roy Chowdhury. This book was released on 2004-01-28. 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

Nonlinear Classical and Quantum Integrable Systems with PT-symmetries

2019
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Release : 2019
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Book Synopsis Nonlinear Classical and Quantum Integrable Systems with PT-symmetries by : Julia Cen

Download or read book Nonlinear Classical and Quantum Integrable Systems with PT-symmetries written by Julia Cen. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt:

Elements of Classical and Quantum Integrable Systems

2019-07-23 Science
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Release : 2019-07-23
Genre : Science
Kind : eBook
Book Rating : 98X/5 ( reviews)

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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. This book was released on 2019-07-23. 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.

Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds

2013-04-09 Science
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Release : 2013-04-09
Genre : Science
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Book Rating : 941/5 ( reviews)

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Book Synopsis Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds by : A.K. Prykarpatsky

Download or read book Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds written by A.K. Prykarpatsky. This book was released on 2013-04-09. Available in PDF, EPUB and Kindle. Book excerpt: 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).

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