Effective Schrödinger equations, governing the mean movement of a system influenced by fast oscillating external perturbation, are derived. The method represents a direct and straightforward quantum extension of the Kapitza’s approach provided in the Schrödinger picture. First-order terms (over inverse frequency of external driving) in effective Hamiltonians that cannot be eliminated by a unitary transformation, have been derived. Additional terms, in comparison with a standard equation, are similar to those found in the classical case and they may be responsible for a variety of new interesting effects.
The correlative, or improved, unsymmetrized self-consistent field method (CUSF) is developed to study surface properties of anharmonic crystals. The equations for moments of the one-particle functions of atoms are obtained. Their solution determines the lattice relaxation near the surface, the amplitudes of anharmonic vibrations of atoms and the self-consistent potentials. A calculation method of the Helmholtz free energy of anharmonic crystal — vapour interface is developed. As an application, the properties of the singular surfaces of two-dimensional models with square and hexagonal lattices are calculated.
A statistical theory of anharmonic crystal—vapour interfaces is developed based on the correlative unsymmetrized self‐consistent field method (CUSF). The nonlinear integral equations for the one‐particle probability densities of atomes near the solid surface and their self‐consistent potentials are transformed into the transcendental equations for the moments of the distributions. Their solution determines the lattice relaxation near the surface, the amplitudes of the anharmonic vibrations of atoms, their anisotropy, and the self‐consistent potentials as well. As an application the structural and dynamical properties of an f.c.c. crystal in which the nearest neighbours interact are studied.
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