}{dt^{2}} = - f \frac{dx(t)}{dt} +{\cal F}_{x}(t).
     \label{eq:Langevin}$$ Here $x(t)$ is a coordinate of the diffusing particle, $m$ is the particle mass, $f$ is the particle’s drag coefficient, and ${\cal F}_{x}(t)$ is the random force, called *random* because in the Langevin model the values of ${\cal F}_{x}(t)$ at different instants in time are uncorrelated. Within the model, ${\cal F}_{x}$ cannot be predicted beyond stating that ${\cal F}_{x}$ has certain statistical properties.

The canonical literature treatment of the Langevin model as applied to quasielastic light scattering is the volume by Berne and Pecora[@berne1976a], notably their Section 5.9. Berne and Pecora show that the Langevin model is appropriate for polystyrene spheres in water, on the time and distances scales observed by quasielastic light scattering. From the Langevin model and the requirement that the system remains in thermal equilibrium, a series of conclusions about the statistical properties of the particle motion follow. In particular:

(i)

:   The mean-square average value of ${\cal F}_{x}(t)$ must be consistent – the fluctuation-dissipation theorem – with the drag coefficient $f$ and the thermal energy $k_{B}T$.

(ii)

:   The distribution $P(\Delta x)$ of particle displacements $\Delta x$ during a time interval $\Delta t$ is the same for all 