Statistical Properties of Thermal Noise Driving the Brownian Particles in Fluids

In several recent works high-resolution interferometric detection allowed to study the Brownian motion of optically trapped microparticles in air and fluids. The observed positional fluctuations of the particles are well described by the generalized Langevin equation with the Boussinesq-Basset “history force” instead of the Stokes friction, which is valid only for the steady motion. Recently, also the time correlation function of the thermal random force Fth driving the Brownian particles through collisions with the surrounding molecules has been measured. In the present contribution we propose a method to describe the statistical properties of Fth in incompressible fluids. Our calculations show that the time decay of the correlator 〈Fth(t)Fth(0)〉 is significantly slower than that found in the literature. It is also shown how the “color” of the thermal noise can be determined from the measured positions of the Brownian particles.