A Langevin equation for a two-dimensional rotating fluid

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The Langevin equation essentially describes the dynamic behavior of variables under the action of stochastic terms, due to
its easy implementation and phenomenological interpretation it has been applied to a wide range of problems. In this sense it
occupies a paradigmatic position in statistical mechanics covering a wide range of applications to interdisciplinary areas
such as chemistry, biology, economics and quantitative linguistics. In this communication we consider the problem of floating
particles on a two-dimensional fluid of viscosity $\alpha$ and temperature $T$, which rotates at a constant angular velocity
$\omega$ around a fixed axis. In addition to the common viscous term $-\alpha \vec{v}$ proportional to particle velocity, the
non-inertial system introduces terms associated to centrifugal and Coriolis forces. As long as the Coriolis term introduces a
coupling between the Cartesian components the centrifugal term expelled the particles from the origin. We
investigates computationally and analytically the root-mean-square displacement (RMSD) $\langle \Delta r \rangle$ behavior of
particles as a function of model parameters. As a result of the competitive relationship between angular velocity and fluid
viscosity the system exhibits three regimes defined by different time scales. At the first two regimes $(t\leqslant 2\pi/\omega)$
, characterized by low angular velocities, we have a superdifusive behavior $\langle \Delta r \rangle \sim t^{\alpha}$ $(\alpha\geqslant 1/2)$
with a viscosity exponent dependence. On the other hand at the third regime we get an exponential dependence
$\langle \Delta r \rangle \sim e^{\omega t}$.