A01=Vladimir Inozemtsev
Adler System
Author_Vladimir Inozemtsev
Burgers-Hopf Equation
Calogero Ansatz
Calogero System
Calogero-moser Equation
Calogero-Sutherland-Moser System
Category=PHD
Classical Systems
Completely Integrable
Elliptic Potential
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Integrable Models
Lax Pair
Lax Relations
Lie Algebras
Liouville Theorem
Morse Potential
Multiparticle Dynamical System
Olshanetsky-Perelomov System
One-Dimensional Systems
Quantum Integrability
Quasiparticles
Rational Potential
Spin Chain
Sutherland System
Trigonometric Potential
Weierstrass Elliptic Function
Product details
- ISBN 9781800613812
- Publication Date: 05 Jun 2023
- Publisher: World Scientific Europe Ltd
- Publication City/Country: GB
- Product Form: Hardback
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It is commonly known that three or more particles interacting via a two-body potential is an intractable problem. However, similar systems confined to one dimension yield exactly solvable equations, which have seeded widely pursued studies of one-dimensional n-body problems. The interest in these investigations is justified by their rich and quantitative insights into real-world classical and quantum problems, birthing a field that is the subject of this book. Spanning four bulk chapters, this book is written with the hope that readers come to appreciate the beauty of the mathematical results concerning the models of many-particle systems, such as the interaction between light particles and infinitely massive particles, as well as interacting quasiparticles. As the book discusses several unsolved problems in the subject, it functions as an insightful resource for researchers working in this branch of mathematical physics.In Chapter 1, the author first introduces readers to interesting problems in mathematical physics, with the prime objective of finding integrals of motion for classical many-particle systems as well as the exact solutions of the corresponding equations of motions. For these studied systems, their quantum mechanical analogue is then developed in Chapter 2. In Chapter 3, the book focuses on a quintessential problem in the quantum theory of magnetism: namely, to find all integrable one-dimensional systems involving quasiparticles of interacting one-half spins. Readers will study the integrable periodic chains of interacting one-half spins and discover the integrals of motion for such systems, as well as the eigenvectors of their corresponding Hamiltonians. In the last chapter, readers will study about integrable systems of quantum particles, with spin and mutual interactions involving rational, trigonometric, or elliptic potentials.
