Abstract
AbstractA system of phonons and local excitations is considered. The coupling of both subsystems is taken linear in the phonon coordinates. The generalized Langevin equations of the phonon density operator and of the subsequent mixed dipole operators are considered. The elimination of the dipole operators, a decomposition of the averaged second order occupations and specified further assumptions lead to the evolution equation of the phonon distribution function, which contains the local occupation numbers. In full analogy the time evolution of the local occupation numbers can be derived. A Markoff assumption, which is justified for realistic systems, and a restriction to slowly varying phonon densities lead to a rate equation type of a Peierls‐Boltzmann equation, which is coupled to the kinetic equations of the local occupations.
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