Critical Dynamics of Sound

Abstract

Measurements of acoustic velocity and attenuation is one of the best methods available for studying the dynamics of solids, liquids and gases near phase transitions. Acoustic waves act as a very sensitive probe of order parameter fluctuations, and hence often display strong “anomalies” near the phase transition temperature T_c. In principle, many experimental methods used in investigations of phase transitions are capable of, giving some information about critical dynamics, but in different regions of the space of variables q, ω, ξ^-1, τ¹ illustrated in Fig. 1. Here q is the wavevector, ω is frequency, ξ is the correlation length and τ is the characteristic time given by τ = ξ^zf(qξ) in the scaling region. In Fig.1 the vertical axis is essentially a temperature axis, but it assumes a double meaning: both as an inverse length axis ξ^-1, and as an inverse time axis τ^-1. At the origin q , ω, ξ^-1, τ^-1 = 0 true divergence of the order parameter susceptibility occurs. The inner “core” of Fig.1, where q, ω , ξ^-1, τ^-1 are small but finite, is the critical, or asymptotic scaling region. Outside this region corrections to scaling are important.