Unified description of sound velocities in strongly coupled Yukawa systems of different spatial dimensionality

Abstract

Sound velocities in classical single-component fluids with Yukawa (screened Coulomb) interactions are systematically evaluated and analyzed in one-, two-, and three spatial dimensions (${\mathcal D}=1,2,3$). In the strongly coupled regime the convenient sound velocity scale is given by $\sqrt{Q^2/\Delta m}$, where $Q$ is the particle charge, $m$ is the particle mass, $n$ is the particle density, and $\Delta=n^{-1/{\mathcal D}}$ is the unified interparticle distance. The sound velocity can be expressed as a product of this scaling factor and a dimension-dependent function of the screening parameter, $\kappa=\Delta/\lambda$, where $\lambda$ is the screening length. A unified approach is used to derive explicit expressions for these dimension-dependent functions in the weakly screened regime ($\kappa\lesssim 3$). It is also demonstrated that for stronger screening ($\kappa\gtrsim 3$), the effect of spatial dimensionality virtually disappears, the longitudinal sound velocities approach a common asymptote, and a one-dimensional nearest-neighbor approximation provides a relatively good estimate for this asymptote. This result is not specific to the Yukawa potential, but equally applies to other classical systems with steep repulsive interactions. An emerging relation to a popular simple freezing indicator is briefly discussed. Overall, the results can be useful when Yukawa interactions are relevant, in particular, in the context of complex (dusty) plasmas and colloidal suspensions.