Cooperative Phenomena and the Decay of the Angular Momentum Correlation Function at Long Times

A hydrodynamic solution for the decay of the angular momentum of an initially moving volume element in an otherwise stationary, compressible, viscous fluid predicts a long time decay of the angular momentum autocorrelation function which behaves as ${\mathrm{[\eta }}_s{\mathrm{t\hspace{0.17em}/\hspace{0.17em}M\rho ]}}^{\text{−(d+2)/2}}$ where ${\eta }_s$ is the shear viscosity, $\mathrm{M\rho }$ is the mass density, and $d$ is the dimension of the system. This slow decay, which would not lead to the divergence of the rotational diffusion coefficient, or of the spin–rotation relaxation time, is caused by a vortex field which results from the interaction between a structured particle and host fluid. This result is analogous to the long time tail in the linear momentum autocorrelation function recently reported by Alder and Wainwright.