Mobility of a particle in a one-dimensional lattice with allowance for some anharmonic effects

The method of two-time Green's functions [1, 2] is used to derive equations of Fokker–Planck type in the case of a system consisting of a one-dimensional lattice and an impurity (anharmonic) particle. In accordance with this equation, the anharmonicity of the particle vibration influences the relaxation processes due to the interference of the anharmonic interaction with the elastic scattering of phonons. An expression is obtained for the diffusion coefficient of an anharmonic particle.