Equilibration and aging of liquids of non-spherically interacting particles

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible processes in liquids is extended to describe the positional and orientational thermal fluctuations of the instantaneous local concentration profile $n(\mathbf{r},\Omega,t)$ of a suddenly-quenched colloidal liquid of particles interacting through non spherically-symmetric pairwise interactions, whose mean value $\overline{n}(\mathbf{r},\Omega,t)$ is constrained to remain uniform and isotropic, $\overline{n}(\mathbf{r},\Omega,t)=\overline{n}(t)$. Such self-consistent theory is cast in terms of the time-evolution equation of the covariance $\sigma(t)=\overline{\delta n_{lm}(\mathbf{k};t) \delta n^{\dagger}_{lm}(\mathbf{k};t)}$ of the fluctuations $\delta n_{lm}(\mathbf{k};t)=n_{lm}(\mathbf{k};t) -\overline{n_{lm}}(\mathbf{k};t)$ of the spherical harmonics projections $n_{lm}(\mathbf{k};t)$ of the Fourier transform of $n(\mathbf{r},\Omega,t)$. The resulting theory describes the non-equilibrium evolution after a sudden temperature quench of both, the static structure factor projections $S_{lm}(k,t)$ and the two-time correlation function $F_{lm}(k,\tau;t)\equiv\overline{\delta n_{lm}(\mathbf{k},t)\delta n_{lm}(\mathbf{k},t+\tau)}$, where $\tau$ is the correlation \emph{delay} time and $t$ is the \emph{evolution} or \emph{waiting} time after the quench. As a concrete and illustrative application we use the resulting self-consistent equations to describe the irreversible processes of equilibration or aging of the orientational degrees of freedom of a system of strongly interacting classical dipoles with quenched positional disorder.