The mean lifetime τ of a fluctuation can be calculated using the autocorrelation function discussed above:

The correlation function follows a simple exponential law:

To analyze the energy spectrum, the autocorrelation function must be Fourier-transformed (see Fig. 4.16):

Figure 4.16. Schematic correlation function and corresponding spectrum, as discussed in Section 4.6.2 and Eq. (4.45).

The formalism described in this section can be applied to many physical processes in which the scattering amplitude of a volume element Δvᵢ varies. However, the method has a physical limit. The cubic scattering volume V = L³ must not be smaller than approximately 10 nm × 10 nm × 10 nm, because otherwise the difference in the numbers of particles diffusing into and out of the volume would be too small.

This limitation is not important for critical binary systems, since the correlation length ξ increases near the critical point, as discussed in the theoretical section.

Original mathematical notation and illustrations are preserved as extracted image assets.