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## A Unified Theory From the Two Band Model

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1st Edition - December 4, 2012

Author: Toyoyuki Kitamura

Language: EnglishPaperback ISBN:

9 7 8 - 0 - 3 2 3 - 2 8 2 9 3 - 2

Hardback ISBN:

9 7 8 - 0 - 1 2 - 4 0 7 1 7 7 - 3

eBook ISBN:

9 7 8 - 0 - 1 2 - 4 0 7 1 7 0 - 4

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

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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

- No. of pages: 400
- Language: English
- Edition: 1
- Published: December 4, 2012
- Imprint: Elsevier
- Paperback ISBN: 9780323282932
- Hardback ISBN: 9780124071773
- eBook ISBN: 9780124071704

TK

Affiliations and expertise

Emeritus Professor, Nagasaki Institute of Applied Science, Nagasaki, JapanRead *Liquid Glass Transition* on ScienceDirect