Dynamics of one-dimensional quantum systems : inverse-square interaction models

Yoshio Kuramoto, Yusuke Kato

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.

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[目次]

  • 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.

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この本の情報

書名 Dynamics of one-dimensional quantum systems : inverse-square interaction models
著作者等 倉本 義夫
加藤 祐輔
Kato Yusuke
Kuramoto Yosio
出版元 Cambridge University Press
刊行年月 2009
ページ数 xii, 474 p.
大きさ 26 cm
ISBN 9780521815987
NCID BA91047124
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言語 英語
出版国 イギリス
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