Questions related to phonons as applicable to the field of materials science.
Phonons are the quasiparticles associated with atomic motion within the harmonic approximation.
In the harmonic approximation, the motion of atoms is described locally, taking into account quadratic terms only in the expansion of the total energy around the equilibrium position of atoms. These quadratic terms are typically calculated using finite difference methods (using supercells), or, in the context of density functional theory, linear response methods (density functional perturbation theory).
Phonons are described by the relation between their energy (frequency) and their momentum (wave vector). These phonon dispersions capture information such as the speed of sound in a material (slope of acoustic modes) or the spectra observed in infrared and Raman experiments.
Phonons also form the building blocks for theories such as those of anharmonic lattice dynamics (to capture phonon-phonon interactions) or electron-phonon coupling (with applications in superconductivity and transport).