Comment on ‘‘Long-time tails in angular momentum correlations’’ [J. Chem. Phys. 103, 1582 (1995)]

Abstract

It is shown that the shape-dependence of the coefficient of the long-time tail of the angular velocity autocorrelation function of a Brownian particle, as predicted for both two and three dimensions from the fluctuation–dissipation theorem and linearized hydrodynamics, agrees with recent computer simulations. The disagreement with a mode-coupling calculation suggests that the latter should be revised.

Long-time behavior of the angular velocity autocorrelation function

“…Our view 1,2,4 is that these hydrodynamic calculations are only appropriate for tethered particles and are not applicable to the freely reorienting case, but these opinions are not universally shared. [6][7][8] In this Communication we seek to show that the linearized hydrodynamic equations for an incompressible fluid do indeed predict a shape independent tail for the AVACF, in agreement with simulation and microscopic theory, provided the particle is free to reorient. We consider a Brownian particle with initial velocity and angular velocity v͑0͒ and ͑0͒, respectively, and with its center of mass kept fixed ͑as in the simulation work͒.…”

“…To do the first stage, we make use of the induced force formalism, [5][6][7][8]10 appropriate for stick boundary conditions. This formalism has normally been used to treat stationary boundaries, but it is easily generalized to cater for moving boundaries as well.…”

“…As stated previously, 4 the previous hydrodynamic calculations [5][6][7][8] have first taken an infinite mass and size limit for the particle and then considered the long-time limit of the AVACF. This is equivalent to assuming a zero rotational diffusion constant when calculating time-dependent rotational friction coefficients and mobilities and a shapedependent tail ensues.…”

Comment on “Long-time behavior of the angular velocity autocorrelation function” [J. Chem. Phys. 105, 9695 (1996)]

“…In our previous Comment 5 we have been careful to distinguish between the angular velocity relaxation function (t) and the correlation function C R (t) of Brownian motion. According to the fluctuation-dissipation theorem the correlation function is proportional to the relaxation function in the linear regime.…”