S. Scandolo, ICTP

Lesson 20 (Phonons)

The lesson starts with discussing the vibrations of the one-dimensional chain of coupled oscillators. The equation of motion was solved in the last lesson. The modes with low correspond to sound waves.

Later in the lecture, the equation of motion for a diatomic system is solved. The interactions are modeled as springs in this case as well, however, the "spring" between the atoms of a cell has a different spring constant. The equations can be turned into an eigenvalue problem once more. The most significant difference from the simple chain is that for every spatial mode there are two frequencies. This is due to the increase of the degrees of freedom per unit cell. Now we have two modes for each cell instead of one. (E.g. the motion of the center of mass of the diatomic system and their relative vibration.)