Dynamics of One-Dimensional Quantum Systems
Inverse-Square Interaction Models

A concise and accessible account of the dynamical properties of one-dimensional quantum systems, for graduate students and new researchers.

Yoshio Kuramoto (Author), Yusuke Kato (Author)

9781107424722, Cambridge University Press

Paperback / softback, published 7 August 2014

488 pages
24.4 x 17 x 2.5 cm, 0.77 kg

One-dimensional quantum systems show fascinating properties beyond the scope of the mean-field approximation. However, the complicated mathematics involved is a high barrier to non-specialists. Written for graduate students and researchers new to the field, this book is a self-contained account of how to derive the exotic quasi-particle picture from the exact solution of models with inverse-square interparticle interactions. The book provides readers with an intuitive understanding of exact dynamical properties in terms of exotic quasi-particles which are neither bosons nor fermions. Powerful concepts, such as the Yangian symmetry in the Sutherland model and its lattice versions, are explained. A self-contained account of non-symmetric and symmetric Jack polynomials is also given. Derivations of dynamics are made easier, and are more concise than in the original papers, so readers can learn the physics of one-dimensional quantum systems through the simplest model.

Preface
1. Introduction
Part I. Physical Properties: 2. Single-component Sutherland model
3. Multi-component Sutherland model
4. Spin chain with 1/r2 interactions
5. SU(K) spin chain
6. Supersymmetric t-J model with 1/r2 interaction
Part II. Mathematics Related to 1/r2 Systems: 7. Jack polynomials
8. Yang-Baxter relations and orthogonal eigenbasis
9. SU(K) and supersymmetric Yangians
10. Uglov's theory
Epilogue
References
List of symbols
Index.

Subject Areas: Mathematical physics [PHU], Condensed matter physics [liquid state & solid state physics PHFC]