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4 Critical Contribution, Dynamic Scaling and Crossover Theory

where ∆T = T −Tc(p) and index c denotes critical parameters. Moreover, the adiabatic temperature variation (∂∆T/∂p)S in Eq.(4.1), expressed by: ∂∆T

produces a dimensionless parameter g, which represents the system-specific coupling constant and describes the magnitude of coupling between critical density fluctuations and the propagating sound wave:

Substitution of Eq.(4.2) and Eq.(4.3) into Eq.(4.1) yields a relationship which is accessi- ble to experiments:

The sound velocity can be expressed as:

where cs,c denotes the sound velocity at the critical point. Approximately one can de- scribe the sound velocity cs by the following relation:

The next step in the procedure of Bhattacharjee and Ferrell considers the frequency ω for an applied pressure signal with its time dependence given by exp(−iωt). Furthermore, with the aid of the frequency-dependent specific heat ˜Cp(ω) it is possible to express the sound velocity cs in Eq.(4.6) and the compressibility βS in Eq.(4.4) as frequency- dependent quantities1:

1tilde denotes complex quantities, except for critical exponents

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