Simulations of Brownian Motion

Author: Liza Godziashvili
Keywords: Brownian Motion, Diffusion, Random Walk, Langevin Equation
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In 1827, the Scottish botanist, Robert Brown, noticed that plant particles suspended in a liquid, moved chaotically in different directions. For years, this phenomenon remained an unsolved task. At the beginning of the 20th century, Einstein showed that the mean square displacement of a Brownian particle is proportional to the time of the movement (for long times). Three methods of Brownian motion analysis are discussed in the paper: correlation function method, random walk, or Monte-Carlo method, and the methods of numerical calculations of the Langevin equation. We considered the Brownian motion problem of a linear harmonic oscillator and simulated the solution for different parameters. We discussed exciton-induced wandering in the "nodes" of a one-dimensional chain and presented the results.