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Brownian Motion: Langevin Equation

Chapter 6 Brownian motion : LangevinEquationThe theory of Brownian motion is perhaps the simplest approximate way to treat thedynamics of nonequilibrium systems. The fundamental Equation is called the Langevinequation; it contain both frictional forces and random forces. The fluctuation-dissipationtheorem relates these forces to each random motion of a small particle (about one micron in diameter) immersed in afluid with the same density as the particle is called Brownian motion . Early investigationsof this phenomenon were made by the biologist Robert Brown on pollen grains and alsodust particles or other object of colloidal modern era in the theory of Brownian motion began with Albert Einstein.

Consider a large particle (the Brownian particle) immersed in a uid of much smaller particles (atoms). Here the radius of the Brownian particle is typically 10 9m <a< 5 10 7m. The agitated motion of the large particle is much slower than that of the atoms and is the result of random and rapid collisions due to density uctuations in the uid.

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