Taking into account the random scatterings due to random eigenfrequencies and random hopping matrices, we obtain the correlation functions for phonon and sound density fluctuations, which yield three and one entropy fluctuation modes at high frequencies, and three and one thermal conductivity at...

A quantum field theory of phonons in crystals developed in a two-band model is extended to a multi-band model. The Ward-Takahashi relations associated with the spontaneous breakdown of spatially translational and rotational symmetry are represented by use of atom and phonon Green's functions....

We solve the eigenvalue equation derived in paper I under the assumption that a localized or resonant mode is well-localized at a lattice site. Localized modes appear above the top of the phonon band for an appropriate positive quartic potential at any temperatures. Resonant modes appear in the...

A unified theory of lattice dynamics and melting is presented from the view-point of quantum field theory at finite temperature. The lattice dynamics and the melting in nonprimitive crystals which contain more than one atom in a unit cell are investigated in the random phase approximation using...

Randomly distributed atoms are considered in the harmonic potentials with random eigenfrequencies. The hopping of atoms makes energy dispersion curves of an atom. The correlation functions of density fluctuations in the intraband transition yield the freezing point, where the hopping is...

The Heisenberg equation for phonon operators in nonlinear lattices is derived establishing the interaction Hamiltonian included higher powers of particle-hole pairs in nonlinear lattices. A phonon operator consists of a particle-hole pair in the harmonic potential approximation in the two band...

The three-band model is applied to fcc structure crystals. The dynamical matrix is calculated by using fundamental coupling constants like chemical bondings. As the temperature decreases, the theory reduces that in the two-band model. There are three Nambu-Goldstone bosons which originate from...

The Ward-Takahashi relations associated with the spontaneous breakdown of spatially translational invariance are established in terms of Matsubara's finite temperature Green's functions. Atom and phonon Green's functions are constructed in the two band model and in the random phase approximation...

A self-consistent treatment of one-dimensional crystals is presented by considering the Ward-Takahashi relations which stand for the spontaneous breakdown of the spatial translational invariance. It is shown that the boson condensations of the gapless phonons demonstrate how molecules arrange...

The melting and the lattice dynamics are investigated from the view-point of a quantum field theory at finite temperature (thermo field theory). Our theory starts with ion cores and valence electrons interacting with each other as the first principle. The Ward-Takahashi relations play an...