English translation

The frequency-dependent sound velocity and adiabatic compressibility are expressed as:

Here, the frequency-dependent specific heat capacity is denoted by c̃_p; g is the dimensionless coupling constant, (T_critS′_crit)/V_crit; V_crit is the critical volume; and u_crit is the sound velocity at the critical point.

The critical contribution to the specific heat capacity, which determines the complex sound velocity through Eq. (3.31), obeys the following thermodynamic dependence:

Using the diffusion coefficient, discussed further in Section 3.2,

where k_B is the Boltzmann constant, one obtains:

For completeness, Eq. (3.34) is an approximation. The actual form of this relation is considered in Section 3.2 in the discussion of the results from mode-coupling theory. Equation (3.35), together with the relations in Table 2.1 describing the critical behaviour of the correlation length, provides the foundation for dynamic scaling.

Original mathematical notation preserved from the thesis.