Quantum Statistical Mechanics of Electron-Phonon System
Hiroshi Ichimura · Progress of Theoretical Physics · 1956
The problem of the interaction between conduction electrons and the thermal vibration of the lattice ions in the metal is treated by a statistical mechanical method. We adopt the free electron and the phonon models as usual, using the Bloch-Bethe type interaction Hamiltonian. By the method of expanding the grand partition function in powers of the interaction parameter, we get a formula for the free energy of the system of conduction electrons in the presence of the interaction. A technique analogous to the renormalization method in the quantum mechanics is utilized in the calculation.