Liquid Glass Transition
A Unified Theory From the Two Band Model
- 1st Edition - December 5, 2012
- Latest edition
- Author: Toyoyuki Kitamura
- Language: English
A glass is disordered material like a viscous liquid and behaves mechanically like a solid. A glass is normally formed by supercooling the viscous liquid fast enough to avoid cr… Read more
A glass is disordered material like a viscous liquid and behaves mechanically like a solid. A glass is normally formed by supercooling the viscous liquid fast enough to avoid crystallization, and the liquid-glass transition occurs in diverse manners depending on the materials, their history, and the supercooling processes, among other factors. The glass transition in colloids, molecular systems, and polymers is studied worldwide. This book presents a unified theory of the liquid-glass transition on the basis of the two band model from statistical quantum field theory associated with the temperature Green’s function method. It is firmly original in its approach and will be of interest to researchers and students specializing in the glass transition across the physical sciences.
- Examines key theoretical problems of the liquid-glass transition and related phenomena
- Clarifies the mechanism and the framework of the liquid-glass transition
Researchers, advanced students and professionals in physics, chemical engineering, mechanical engineering, materials science, and applied mathematics.
Preface
Chapter 1. Introduction
1.1 The Structure of the Condensed States and the Quantum Regime
1.2 The Two Band Model for the Liquid-Glass Transition
1.3 Perspective of This Book
References
Chapter 2. Sound and Elastic Waves in the Classical Theory
2.1 Sound in the Classical Fluid Mechanics
2.2 Elastic Waves in the Classical Elastic Theory
2.3 Sound and Phonons in the Classical Microscopic Theory
2.4 The Kauzmann Entropy, the Vogel– Tamman– Fulcher Law and Specific Heat
References
Chapter 3. Fundamentals of Quantum Field Theory
3.1 The Number Representation and the Fock Space
3.2 An Example of Unitarily Inequivalent Representations; The Bogoliubov Transformation of Boson Operators
3.3 The Physical Particle Representation and the Dynamical Map
3.4 Free Physical Fields for Physical Particles
3.5 The Physical Particle Representation and Perturbation Theory
3.6 The Spectral Representations of Two-Particle Green’s Functions
3.7 Invariance, the Noether Current and the Ward-Takahashi Relations
References
Chapter 4. Temperature Green’s Functions
4.1 Definition of the Temperature Green’s Functions
4.2 Perturbation Theory and the Wick’s Theorem at Finite Temperature
4.3 Feynman Diagrams
4.4 Dyson’s Equation
References
Chapter 5. Real Time Green’s Functions and Temperature Green’s Functions
5.1 Various Kinds of Green’s Functions
5.2 Linear Response and Density Correlation Function
5.3 A Linear Response Theory at Finite Temperature
References
Chapter 6. The Structure of Glasses Associated with Phonons
6.1 The WT relations at finite temperature
6.2 The two band model and Green’s functions
6.3 The Nambu-Goldstone theorem and phonons
6.4 The structure of phonons
I Phonon dispersion curves
II The width of phonons
References
Chapter 7. The Liquid-Glass Transition
7.1 Random Scattering Processes and the Bethe–Salpeter Equation
7.2 Intra-Band Density Fluctuations: Sound and Diffusion
7.3 Inter-Band Density Fluctuations: Phonons and Viscosity
7.4 The Kauzmann Entropy Crisis and the VTF Law; Specific Heat, Relaxation Times, and Transport Coefficients
7.5 The Intermediate Scattering Function
7.6 A Generalized Navier-Stokes Equation
References
Chapter 8. Phonon Operators in Nonlinear Interaction Potentials
8.1 The Dynamical Equation for Phonon Operators in Nonlinear Interaction Potentials
8.2 Solitons and Bound States of the Self-Consistent Potential by the Boson Transformation Method
8.3 Localized Modes for a Quartic Potential in the One Loop Approximation
References
Chapter 9. Phonon and Sound Fluctuation Modes and Thermal Conductivities
9.1 The Effective Interaction Hamiltonian for Phonon Fields and the Elementary Scattering Processes of Phonons
9.2 Phonon Density Fluctuations: Phonon Entropy Fluctuation Modes and Thermal Conductivities
9.3 The Effective Interaction for Sound Fields
9.4 Sound Density Fluctuations; Sound Entropy Mode and Sound Thermal Conductivity
9.5 The Anomaly of Thermal Conductivity and Specific Heat in Low Temperature Glasses
References
Chapter 10. The Liquid-Glass Transition in Multi-Component Liquids
10.1 The Model Hamiltonian and the Random Scattering Hamiltonian
10.2 Sound and Diffusivity
10.3 Phonons, Boson Peaks, and Viscosities in Multi-Component Liquids
10.4 Phonons, Boson Peaks, and Viscosities in Two-Component Liquids
10.5 The Kauzmann Entropy Crisis and the VTF Law; Specific Heat, Relaxation Times, and Transport Coefficients
10.6 Concluding Remarks
References
Chapter 11. Extension of the Two Band Model
11.1 Excitations in a Bose-Condensed Liquid
11.2 A Model on the Origin of RNA
11.3 A Model on the Financial Panic
References
- Edition: 1
- Latest edition
- Published: December 5, 2012
- Language: English
TK
Toyoyuki Kitamura
Affiliations and expertise
Emeritus Professor, Nagasaki Institute of Applied Science, Nagasaki, JapanRead Liquid Glass Transition on ScienceDirect