Microscopic model for the Langevin equation:  Force-force correlation function

G. M. Pritula A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov, Ukraine
A. V. Shkop V. N. Karazin Kharkiv National University, 4 Svobody Sq, 61022, Kharkov, Ukraine
D. A. Tkanov V. N. Karazin Kharkiv National University, 4 Svobody Sq, 61022, Kharkov, Ukraine
O. V. Usatenko A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian Academy of Science, 12 Proskura Street, 61085 Kharkov, Ukraine

Keywords: diffusion, Langevin force, correlation function, microscopic theory

Abstract

We look into the particle diffusion in a 1D atomic chain. We consider two different models. In the first one the lattice particles are supposed to move independently. The stochasticity of the motion in this case is achieved due to nonlinear oscillations of the lattice particles. In the second case the linear oscillations of the lattice particles are considered and the stochasticity of doping particle motion stems from the finiteness of phonon spectra. In both cases we derive the stochastic properties of the Langevin force. The found expressions for the correlation function of the Langevin force could be reduced to the white noise only at some limiting values of the lattice and thermostat parameters.

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