Solitons in crystalline processes : statistical thermodynamics of structural phase transitions and mesoscopic disorder / Minoru Fujimoto.

Περιλαμβάνει βιβλιογραφικές παραπομπές.

Preface -- 0. Introduction -- 0.1. The internal energy of equilibrium crystals -- 0.2. Microscopic order variables and their fluctuations -- 0.3. Collective order variables in propagation -- 0.4. Crystal surfaces and entropy production -- 0.5. Timescales for sampling modulated structure and thermodynamic measurements -- 0.6. Statistical theories and the mean-field approximation

part I. Binary transitions -- 1. Phonons and internal energies of stable lattices -- 1.1. Symmetry group in crystals -- 1.2. Normal modes in a monatomic lattice -- 1.3. Quantized normal modes -- 1.4. Phonon field and momentum -- 1.5. Specific heat of monatomic crystals -- 1.6. Approximate phonon distributions -- 1.7. Phonon correlations

2. Displacive order variables in collective mode and adiabatic potentials -- 2.1. One-dimensional ionic chain -- 2.2. Displacive order variables -- 2.3. Born-Oppenheimer's asymptotic approximation and adiabatic potentials -- 2.4. The Bloch theorem for collective order variables

3. Pseudospin clusters and the Born-Huang principle -- 3.1. Pseudospins for binary displacements -- 3.2. The Born-Huang principle and pseudospin clusters -- 3.3. Properties of pseudospin clusters -- 3.4. Examples of pseudospin clusters

4. Critical phase fluctuations of pseudospin modes -- 4.1. Landau's theory and Curie-Weiss' law -- 4.2. Fluctuations of pseudospin clusters in adiabatic potentials -- 4.3. Observing critical anomalies -- 4.4. Extrinsic pinning

part II. Experimental studies on critical anomalies and soft modes -- 5. Scattering experiments on critical anomalies -- 5.1. X-ray diffraction -- 5.2. Diffuse diffraction from a modulated lattice -- 5.3. Neutron inelastic scatterings -- 5.4. Light scattering experiments

6. Magnetic resonance studies on critical anomalies -- 6.1. Magnetic resonance -- 6.2. Magnetic resonance in modulated crystals -- 6.3. Examples of transition anomalies

7. Soft modes of lattice displacements -- 7.1. The Lyddane-Sachs-Teller relation in dielectric crystals -- 7.2. Soft modes in perovskite oxides -- 7.3. Lattice response to collective pseudospins -- 7.4. Temperature dependence of soft-mode frequencies -- 7.5. Cochran's model of a ferroelectric transition -- 7.6. Symmetry change at Tc

part III. Soliton theory of lattice dynamics -- 8. Displacive waves and complex adiabatic potentials in finite crystals -- 8.1. Internal pinning of collective pseudospins -- 8.2. Transverse components and the cnoidal potential -- 8.3. Finite crystals and the domain structure -- 8.4. Lifshitz' incommensurability -- 8.5. The Klein-Gordon equation 1 -- 8.6. Pseudopotentials in crystals

9. The Weiss field of soliton potentials for developing nonlinearity -- 9.1. Dispersive equations in asymptotic approximation -- 9.2. The Korteweg-de Vries equation -- 9.3. Solutions of the Korteweg-de Vries equation -- 9.4. Thermodynamic transitions and the Eckart potential -- 9.5. Condensate pinning by the Eckart potentials -- 9.6. Elemental solitons at singular transitions -- 9.7. Riccati's thermodynamic transitions

10. Soliton mobility in time-temperature conversion -- 10.1. Bargmann's theorem of amplitude modulation -- 10.2. Riccati's theorem and the modified Korteweg-de Vries equation -- 10.3. Soliton mobility studied by computational analysis

11. Toda's theorem of soliton lattice -- 11.1. The Toda lattice -- 11.2. Developing nonlinearity with Toda's correlation potentials -- 11.3. Infinite periodic lattice -- 11.4. Scattering and capture by singular adiabatic potentials -- 11.5. The Gelfand-Levitan-Marchenko theorem -- 11.6. Entropy production at singularities -- 11.7. The Toda lattice and the Korteweg-de Vries equation -- 11.8. Topological strain mapping of mesoscopic Toda lattices

12. Transversal correlations and the domain structure -- 12.1. The Klein-Gordon equation 2 for phase modulation -- 12.2. The B�acklund transformation and domain boundaries -- 12.3. Computational studies of the B�acklund transformation -- 12.4. Trigonal structural transitions -- 12.5. Toda's theory of domain stability -- 12.6. Kac's theory of nonlinear development and boundary instability -- 12.7. Domain separation; thermal and quasi-adiabatic transitions -- 12.8. Transversal correlations in crystalline polymers

part IV. Superconducting and magnetic systems -- 13. Phonons, solitons and electrons in finite metallic phases -- 13.1. Phonon statistics in metallic states -- 13.2. Solitons in modulated metals -- 13.3. Conduction electrons in normal metallic states -- 13.4. The multi-electron system -- 13.5. The Fermi-Dirac statistics

14. Soliton theory of superconducting transitions -- 14.1. The Fr�ohlich condensate -- 14.2. The Cooper pair and superconducting transition -- 14.3. Persistent supercurrent -- 14.4. Critical energy gap and the superconducting ground state

15. High-Tc superconductors -- 15.1. Superconducting transitions under isothermal conditions -- 15.2. Protonic superconducting transitions under high-pressure conditions -- 15.3. Summary: superconducting transitions

16. Superconducting states in metallic crystals -- 16.1. Meissner's diamagnetism -- 16.2. Electromagnetic properties of superconductors -- 16.3. The Ginzburg-Landau equation -- 16.4. Field theories of superconducting transitions

17. Magnetic crystals -- 17.1. Microscopic magnetic moments -- 17.2. Brillouin's formula -- 17.3. Spin-spin exchange correlations -- 17.4. Collective propagation of Larmor's precession -- 17.5. Magnetic Weiss field -- 17.6. Spin waves -- 17.7. Magnetic anisotropy -- 17.8. Antiferromagnetic and ferromagnetic states -- 17.9. Fluctuations in ferromagnetic and antiferromagnetic states

Concluding remarks -- Appendices -- A. A note on liquid crystals -- B. A note on computational studies -- C. Hyperbolic and elliptic functions.

Solitons in Crystalline Processes is an introduction to the statistical thermodynamics of phase transitions in crystallized solids. This book is written as an introductory treatise with respect to the soliton concept, from structural transitions where the crystal symmetry changes, to magnets and superconductors, describing the role of nonlinear excitations in detail.