Many-particle Theory of Interacting Phonons in a CrystalMany-particle perturbation theory and diagram techniques are used to examine the effects of phonon-phonon interactions in an ideal insulating crystal. The perturbation theory and diagram techniques are introduced, and are used to obtain expressions for the free energy of an anharmonic crystal, correlation functions, thermal averages, the one-phonon Green function, and phonon lifetime and self-energy. Lattice thermal conductivity and the coherent scattering of thermal neutrons by nuclei in a perfect, single crystal are also treated. |
Contents
INTRODUCTION | 3 |
THE HAMILTONIAN OF THE PHONON FIELD | 5 |
FREE ENERGY OF AN ANHARMONIC CRYSTAL | 10 |
8 other sections not shown
Common terms and phrases
2wqj A-qj absorption operators anharmonic atom B(Ho+V B₁ B₂ basic diagram Bravais lattice Bwqj C+(qwjj calculation chapter class of diagrams components connected diagrams consider correlation function corresponding creation and absorption cylinder Debye-Waller factor described diagram contributing diagrams containing diagrams that contribute disconnected diagrams displacement Examples of diagrams expansion extensive quantities external lines following equation free energy free lattice given by Eq grams Hamiltonian harmonic lattice integrations involve K-lines Kaß lattice constants loops many-particle matrix element neutron bubbles neutron scattering neutron vertices one-phonon diagrams one-phonon Green function one-phonon peaks perturbation theory phonon-phonon interactions proper Q-vertex Q-vertices Q₁ Q₂ quantity relative order right-hand side scattering function scattering spectrum self-energy and lifetime shown in Fig summation t₁ t₂ temperature theorem thermal tion total contribution Tr{e U-it unit cell usn>T V-qj vertex wave vector