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Solitons in crystalline processes : irreversible thermodynamics of structural phase transitions and superconductivity /
Solitons play a fundamental role in ordering processes in crystals. In the first edition, the essential mechanism of structural changes where solitons play the fundamental role of boson statistics was detailed for irreversible thermodynamics in crystals; explaining not only structural transformation...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
IOP Publishing,
[2020]
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| Edición: | 2nd edition. |
| Colección: | IOP ebooks. 2020 collection.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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. Lattice symmetry and the internal energy in crystals
- 0.6. Timescales for sampling modulated structure and thermodynamic measurements
- 0.7. Statistical theories and the mean-field approximation
- 0.8. Remarks on notations in mesoscopic states
- part I. Binary transitions. 1. Phonons and lattice stability
- 1.1. The space symmetry group and the internal energy 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 Weiss' potentials
- 2.1. One-dimensional ionic chain
- 2.2. Practical examples of displacive order variables
- 2.3. The Born-Oppenheimer approximation and adiabatic Weiss' potentials
- 2.4. The Bloch theorem for collective order variables
- 3. Pseudospin clusters and the Born-Huang principle : coherent order-variables as solitons in crystals
- 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. The mean-field theories and critical phase fluctuations at transition temperatures
- 4.1. Landau's theory and Curie-Weiss' law
- 4.2. Fluctuations of pseudospin clusters in adiabatic potentials
- 4.3. Observing critical phase anomalies
- 4.4. Intrinsic and 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 pseudopins
- 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. Nonlinear dynamics in finite crystals : displacive waves, complex adiabatic potentials and pseudopotentials
- 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 in mesoscopic phases
- 8.5. Klein-Gordon equation for the Weiss potential
- 8.6. Pseudopotentials in mesoscopic phases
- 9. Opposite Weiss fields for nonlinear order variables and entropy production : the Korteweg-deVries equation for transitions between conservative states
- 9.1. Dispersive equations in asymptotic approximation
- 9.2. The Korteweg-deVries equation
- 9.3. Thermodynamic solutions of the Korteweg-deVries equation
- 9.4. Isothermal transitions in the Eckart potential
- 9.5. Condensate pinning by the Eckart potentials
- 9.6. Elemental solitons as Boson particles
- 9.7. Riccati's thermodynamic transitions
- 10. Soliton mobility in dynamical phase space : time-temperature conversion for thermal processes
- 10.1. Bargmann's theorem
- 10.2. Riccati's theorem and the modified Korteweg-deVries equation
- 10.3. Soliton mobility studied by computational analysis
- 11. Toda's theorem of the 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 soliton potentials
- 11.5. The Gel'fand-Levitan-Marchenko theorem
- 11.6. Entropy production at soliton singularities
- 11.7. The Toda lattice and the Korteweg-deVries equation
- 11.8. Topological strain mapping of mesoscopic Toda lattices
- 12. Phase solitons in adiabatic processes : topological correlations in the domain structure
- 12.1. The sine-Gordon equation
- 12.2. The Bäcklund transformation and domain boundaries
- 12.3. Computational studies of Bäcklund transformation
- 12.4. Trigonal structural transitions
- 12.5. Toda's theory of domain stability
- 12.6. Kac's theory of nonlinear development and domain boundaries
- 12.7. Domain separation : thermal and quasi-adiabatic transitions
- part IV. Superconducting, magnetic, polymer and liquid crystals. 13. Phonons, solitons and electrons in modulated lattices
- 13.1. Phonon statistics in metallic states
- 13.2. Solitons in modulated metals
- 13.3. Conduction electrons in normal metals
- 13.4. The multi-electron system
- 13.5. The Fermi-Dirac statistics
- 14. Soliton theory of superconducting transitions
- 14.1. The Fröhlich condensate and the Meissner effect
- 14.2. The Cooper pair and superconducting transition
- 14.3. Persistent supercurrents
- 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
- 16. Superconducting phases 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 ferrimagnetic states
- 17.9. Fluctuations in ferromagnetic and antiferromagnetic states
- 18. Crystalline polymers and liquid crystals
- 18.1. Transversal correlations in crystalline polymers
- 18.2. Liquid crystals.