Abstract
The paper is devoted to the problem of the determination of regular forces acting on microscopic and smaller objects in fluids when the presence of thermal noise affects the results of measurements. One of the methods on how these forces are determined is the measurement of the drift velocity of Brownian particles. Traditionally such experiments are interpreted on the basis of the overdamped Langevin equation. An exact expression has been obtained for this velocity within the linear hydrodynamic theory of the Brownian motion in incompressible fluids, when the external force is constant and when the particle is in a harmonic potential well. It is shown that for sufficiently short experimental times the influence of the hydrodynamic memory effects in the drift velocity determination is significant. The obtained solutions contain algebraic long-time tails due to which the results expected from the standard theory are approached very slowly with the increase of time.
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