# A Langevin equation for a two-dimensional rotating fluid

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

$\langle \Delta r \rangle \sim e^{\omega t}$.