Liquid Glass Transition

Liquid Glass Transition

A Unified Theory From the Two Band Model

1st Edition - December 1, 2012

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  • Author: Toyoyuki Kitamura
  • eBook ISBN: 9780124071704
  • Paperback ISBN: 9780323282932

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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.

Key Features

  • 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.

Table of Contents

  • 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


    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


    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


    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


    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


    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


    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


    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


    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


    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


    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


Product details

  • No. of pages: 400
  • Language: English
  • Copyright: © Elsevier 2012
  • Published: December 1, 2012
  • Imprint: Elsevier
  • eBook ISBN: 9780124071704
  • Paperback ISBN: 9780323282932

About the Author

Toyoyuki Kitamura

Affiliations and Expertise

Emeritus Professor, Nagasaki Institute of Applied Science, Nagasaki, Japan

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