Jana Tothova, Lukas Glod, Gabriela Vasziova, Vladimir Lisy
The paper is devoted to the problem of the determination of regular and
thermal forces acting on microscopic and smaller objects in fluids. One of the
methods how regular forces are determined is the measurement of the drift
velocity of Brownian particles. We have obtained an exact expression for this
velocity within the hydrodynamic theory of the Brownian motion. It is shown
that the influence of the inertial and memory effects can be significant in the
force determination when the experimental times are sufficiently short. In the
second part of the work, within the same theory, we study the properties of the
thermal force driving the particles in incompressible fluids. We show that the
usual assumption for the Kubo's generalized Langevin equation (called the
"fundamental hypothesis") that the thermal force at a time t and the velocity
of the particle in preceding times are uncorrelated, leads to an unexpected
super-diffusion of the particle. To obtain the Einstein diffusion at long
times, the mentioned hypothesis must be abandoned, which however does not
contradict to causality. Finally, we consider the "color" of thermal noise,
recently measured experimentally [Th. Franosch et al., Nature 478, 85 (2011)],
and correct the interpretation of these experiments.
View original:
http://arxiv.org/abs/1202.4318
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