β Scribed by Katja Lindenberg; Udayan Mohanty; V. Seshadri
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We derive stochashc equations for the motion of a rigid rotor m a hnear heat bath starting from a fully dynamical (Hamlltonlan) description We obtam a generahzed Langevm equation for the angular velocity of the rotor in which the fluctuations m the torque arise from the initial condmons of the heat bath The dlsslpaUon is m general nonhnear and is related to the fluctuaUons wa a fluctuatlon-d~sstpahon relation that is a natural consequence of our description
In the Langevln hmlt we show that our equations are eqmvalent to the phenomenologtcal Euler-Langewn equations However, whereas the latter are necessardy expressed in components referred to a body-fixed coordinate system, our representation ts vahd in an arbitrary system of axes and is in that sense more general Fmally, we also examine the reduction of our model to the rotational diffusion equatxon m the high viscosity hmlt We show that this reduchon can be carried out via standard methods of admbatic elimination if our representation of the rotor equations of motion ~s used
The study of rotational motion of molecules in fluids is of importance in the analysis of results obtained by a variety of spectroscopic techniquesl-6). A close analysis of the vast literature that exists on theoretical studies of rotational motion shows that there are fundamental difficulties in the understanding of the problem. The main difficulty is that there are various aspects
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Brownian motion of the hairs (stereocilia) of amphibian hair cells has been shown in experiments to be in the range of some nm. Our models of the Brownian motion of coupled harmonic oscillators with mechanical properties of stereocilia lead to similar displacements. Computer simulation shows that st