Green’s function approach to phonon hydrodynamics in solids

In the first part the Green’s function approach developed byKadanoff andBaym is used to derive a transport equation for phonons in a dielectric anharmonic crystal. The approximations which reduce this generalized equation to the Peierls equation are exhibited. In the second part, neglecting Umklapp processes, the linearized equation is applied to hydrodynamic phenomena. In a system close to local thermal equilibrium second sound and Poiseuille flow may exist. The damping through normal processes is approximately calculated by a momentum-dependent relaxation time. The coupling between the phonon and the dilatation fields is discussed.