QUASI-CLASSICAL SELF-CONSISTENT THEORY OF ANHARMONIC CRYSTALS

Using the unsymmetrized self-consistent field method the quasi-classical expansion of the one-particle density matrices is considered. The integral equations for the first quantum corrections to the classical one-particle probability densities are derived. The exact solution for the perfect crystals with the strong anharmonicity of the fourth order is found and used to calculate the first quantum correction to the effective amplitudes of the strongly anharmonic vibrations of atoms. The solution is obtained also for the semi-infinite linear chain as the simplest model of the anharmonic crystal with the surface.