ABSTRACT
This chapter develops a general theory for the lattice thermal conductivity valid for both crystals and disordered systems. To be able to compute the thermal conductivity for a particular system one need to express the correlation function in term of the microscopic quantities which characterize the system: atomic positions, and force constants. The chapter derives the lattice dynamics and obtains the general expression for the energy flux operator. It also obtains the thermal conductivity as a sum of the product of heat capacity and diffusivity associated to each vibrational modes. In the hydrodynamic limit the physical quantities describing a system are considered to vary slowly in time and space. This way each part of the system can be assumed to be in a local equilibrium which allows to define locally the thermodynamic variables. The chapter investigates the response of a system to a temperature gradient from a quantum mechanical point of view.
