Quantum field theory of the liquid–glass transition

A unified theory of the liquid–glass transition based on the two band model in the harmonic potential approximation is presented. The structure of phonons is clarified starting with the viewpoint of the spontaneous breakdown of the spatially translational and rotational symmetry. The phonon frequency in the short wavelength regime corresponds to the boson peak. The Kauzmann paradox on the Kauzmannʹs entropy crisis and the Vogel–Tamman–Fulcher (VTF) law on the relaxation times and the transport coefficients are elucidated: the Kauzmann entropy originates from the sound instability at a reciprocal particle distance at the sound instability temperature very close to the Kauzmann temperature. The sound instability temperature indicates the fragility of the liquid. The hopping amplitude of the particles is proportional to the configuration number corresponding to the Kauzmann entropy and determines the VTF law, the α-relaxation, while the magnitude of the randomness of the harmonic frequencies of particles is proportional to the configuration number corresponding to the inter-band fluctuation entropy and determines the β-relaxation. The glass transition temperature is the temperature at which the Kauzmann entropy crossovers the inter-band fluctuation entropy. Nonlinear phonon dynamics for solitons, their carrying bound states and intrinsic localized modes at finite temperatures is also investigated. Finally, the sound and the phonon entropy fluctuation modes and the respective thermal conductivities are derived.