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Solitons play a fundamental role in ordering processes in crystals, where the collective motion is essential for mesoscopic disorder in thermal equilibrium. The first edition of this book detailed the essential mechanism of structural changes where solitons play the fundamental role of boson statistics for irreversible thermodynamics in crystals; explaining the structural transformations and mesoscopic disorder, and the nonlinear mechanism of superconductivity. A major development and extension presented in this new edition is in the application of soliton theory to polymers and liquid crystals, in addition to capturing the theoretical developments and newer experimental results of soliton analysis in general. This updated text also emphasises the thermodynamics of soft modes, pseudospins and order variables for finite lattice displacements. Soliton statistics of the nonlinear order variables are also logically discussed. Written as an introductory treatise, with respect to the soliton concept in matter, with exercises provided, this book will help to further develop readers' understanding of the subject.
Preface
Introduction
Part I Binary Transitions
1 Phonons and Internal Energies in Stable Lattices
2 Displacive Order Variables in Collective Mode and Adiabatic Potentials
3 Pseudospin Clusters and the Born-Huang Principle: Corrective Order-Variables as Solitons in Crystals
4 The Mean-Field Approximation and Critical Phase Fluctuations
Part II Experimental Studies On Critical Anomalies And Soft Modes
5 Scattering Experiments on Critical Anomalies
6 Magnetic Resonance Studies of Critical Anomalies
7 Soft Modes of Lattice Displacements
Part III Soliton Theory Of Lattice Dynamics
8 Nonlinear Dynamics in Finite Crystals: Displacive Waves, Complex Adiabatic Potentials and Pseudopotentials
9 Opposite Weiss’ Fields for Nonlinear Order Variables and Entropy Production: the Korteweg-deVries Equation for Transitions between Conservative States
10 Soliton Mobility in Dynamic Phase Space: Time-Temperature Conversion in Thermal Processes
11 Toda’s Theorem of the Soliton Lattice
12 Phase Solitons in Adiabatic Processes: Topological Correlations in Mesoscopic Domain Boundaries
Part IV Superconducting, Magnetic, Polymer And Liquid Crystals
13 Phonons, Solitons and Electrons in Metallic Phases
14 Soliton Theory of Superconducting Transitions
15 High-Tc Superconductors
16 Superconducting Phases in Metallic Crystals
17 Magnetic Crystals
18 Crystalline Polymer and Liquid Crystals
Concluding Remarks
Appendix Hyperbolic and Elliptic Functions