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The Bethe Wavefunction

Michel Gaudin
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  • Date Published: March 2014
  • availability: Available
  • format: Hardback
  • isbn: 9781107045859

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  • Michel Gaudin's book La fonction d'onde de Bethe is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics. Available in English for the first time, this translation brings his classic work to a new generation of graduate students and researchers in physics. It presents a mixture of mathematics interspersed with powerful physical intuition, retaining the author's unmistakably honest tone. The book begins with the Heisenberg spin chain, starting from the coordinate Bethe Ansatz and culminating in a discussion of its thermodynamic properties. Delta-interacting bosons (the Lieb-Liniger model) are then explored, and extended to exactly solvable models associated to a reflection group. After discussing the continuum limit of spin chains, the book covers six- and eight-vertex models in extensive detail, from their lattice definition to their thermodynamics. Later chapters examine advanced topics such as multi-component delta-interacting systems, Gaudin magnets and the Toda chain.

    • In English for the first time, this is a translation of Michel Gaudin's uniquely influential masterpiece La fonction d'onde de Bethe
    • Retains Gaudin's unique style of presentation, mixing mathematics with powerful physical intuition
    • Gives detailed explanations that are difficult to find elsewhere in literature
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    Reviews & endorsements

    'The book presents in detail many important computations. This allows the beginner in the field to learn many of the techniques that are relevant for new applications. … [This] is an outstanding book which every library should have. It will be extremely useful both for graduate and postgraduate students. The book can also serve as a source of inspiration for an advanced physics course on integrable models both in condensed matter theory and statistical physics. The translator has done a great job making this book accessible to the much wider audience it deserves.' Gunter M. Schütz, Contemporary Physics

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    Product details

    • Date Published: March 2014
    • format: Hardback
    • isbn: 9781107045859
    • length: 360 pages
    • dimensions: 253 x 180 x 19 mm
    • weight: 0.77kg
    • contains: 27 b/w illus.
    • availability: Available
  • Table of Contents

    Foreword Michel Gaudin
    Translator's note
    Introduction
    1. The chain of spin-1/2 atoms
    2. Thermodynamic limit of the Heisenberg-Ising chain
    3. Thermodynamics of the spin-1/2 chain: limiting cases
    4. δ-interacting bosons
    5. Bethe wavefunctions associated to a reflective group
    6. Continuum limit of the spin chain
    7. The six-vertex model
    8. The eight-vertex model
    9. The eight-vertex model: eigenvectors and thermodynamics
    10. Identical particles with δ-interactions
    11. Identical particles with δ-interactions: general solution for two internal states
    12. Identical particles with δ-interactions: general solution for n components and limiting cases
    13. Various corollaries and extensions
    14. On the Toda chain
    References
    Index.

  • Author

    Michel Gaudin
    Michel Gaudin is recognised as one of the foremost experts in this field, and has worked at Commissariat à l'énergie atomique (CEA) and the Service de Physique Théorique, Saclay. His numerous scientific contributions to the theory of exactly solvable models are well-known, including his famous formula for the norm of Bethe wavefunctions.

    Translator

    Jean-Sébastien Caux, Universiteit van Amsterdam
    Jean-Sébastien Caux is a professor of the theory of low-dimensional quantum condensed matter at the University of Amsterdam. He has made significant contributions to the calculation of experimentally observable dynamical properties of these systems.

    Contributors

    Michel Gaudin

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