Physics in One Dimension

1. Front Matter

   Pages I-IX

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2. Introductory Lecture

   1. Front Matter

      Pages 1-1

      PDF

   2. How to Reduce Practically Any Problem to One Dimension

      • Daniel C. Mattis

      Pages 3-10

3. Solitons

   1. Front Matter

      Pages 11-11

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   2. An Overview of Soliton Mathematics

      • David W. McLaughlin

      Pages 13-26

   3. Statistical Mechanics of Solitons

      • Alan R. Bishop

      Pages 27-46

   4. The Quantum Inverse Scattering Method and Applications to Spin Chains

      • M. Fowler

      Pages 47-58

   5. Bethe Ansatz, Connection Between One-Dimensional Models and Their Classification

      • E. Berkcan, L. N. Cooper

      Pages 59-62

   6. Quantum Statistics of Solitons

      • Kazumi Maki

      Pages 63-74

   7. Classical Statistical Mechanics of Soliton-Bearing Systems

      • T. Schneider, E. Stoll

      Pages 75-86

   8. Multistable Driven Systems

      • M. Büttiker, R. Landauer

      Pages 87-99

   9. Inherent Effects of Discretization in an Interacting Kink-Phonon System

      • N. Theodorakopoulos, R. Klein

      Pages 100-103

   10. Ising Models, Solitons, and the Devil’s Staircase

       • Per Bak

       Pages 104-112

4. Magnetic Chains

   1. Front Matter

      Pages 113-113

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   2. Quantum Spin Chains

      • Jill C. Bonner, H. W. J. Blöte, Hans Beck, Gerhard Müller

      Pages 115-128

   3. Dynamic Correlations in Classical Heisenberg Chains

      • Stephen W. Lovesey

      Pages 129-139

   4. Dynamics of One-Dimensional Magnets: Neutron Scattering Studies

      • M. Steiner

      Pages 140-152

   5. Solitons in One-Dimensional Magnets with Various Symmetries

      • H. J. Mikeska

      Pages 153-156

   6. A Comparison of Static and Dynamic Properties of One-Dimensional Magnets and Corresponding sG Systems

      • J. M. Loveluck, T. Schneider, E. Stoll, H. R. Jauslin

      Pages 157-160

   7. Evidence for Soliton Excitations in the One-Dimensional Antiferromagnet TMMC

      • L. P. Regnault, J. P. Boucher, J. Rossat-Mignod, J. P. Renard, J. Bouillot, W. G. Stirling

      Pages 161-164

In 1966, E.H. Lieb and D.C. r1attis published a book on "Mathematical Physics in One Dimension" [Academic Press, New York and London] which is much more than just a collection of reprints and which in fact marked the beginnings of the rapidly growing interest in one-dimensional problems and materials in the 1970's. In their Foreword, Lieb and r~attis made the observation that " ... there now exists a vast literature on this subject, albeit one which is not indexed under the topic "one dimension" in standard indexing journals and which is therefore hard to research ... ". Today, the situation is even worse, and we hope that these Proceedings will be a valuable guide to some of the main current areas of one-dimensional physics. From a theoretical point of view, one-dimensional problems have always been very attractive. Many non-trivial models are soluble in one dimension, while they are only approximately understood in three dimensions. Therefore, the corresponding exact solutions serve as a useful test of approximate ma­ thematical methods, and certain features of the one-dimensional solution re­ main relevant in higher dimensions. On the other hand, many important phe­ nomena are strongly enhanced, and many concepts show up especially clearly in one-dimensional or quasi -one-dimensional systems. Among them are the ef­ fects of fluctuations, of randomness, and of nonlinearity; a number of in­ teresting consequences are specific to one dimension.

• Dimension
• Linearer Leiter
• Magnetische Ordnung
• Physics
• Soliton
• diffusion
• dynamics
• lattice dynamics
• mathematical physics
• mechanics
• neutron diffraction
• polymer
• scattering

• Brown Boveri Research Center, Baden-Dättwil, Switzerland

  Jakob Bernasconi

• IBM Research Center, Rüschlikon, Switzerland

  Toni Schneider

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