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.

arXiv comment9 pages, 4 figures

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Cited by in corpus (15)

• Lindemann melting criterion in two dimensions
• Thermal conductivity of strongly coupled Yukawa fluids
• Dispersion relations of Yukawa fluids at weak and moderate coupling
• Ion drift instability in a strongly coupled collisional complex plasma
• Instantaneous shear modulus of Yukawa fluids across coupling regimes
• Description of longitudinal modes in moderately coupled Yukawa systems with the static local field correction
• Vibrational model of heat transfer in strongly coupled Yukawa fluids (dusty plasma liquids)
• Elastic properties of Yukawa crystals
• Quasi-universal behaviour of shear relaxation times in simple fluids
• Neutron star crust in Voigt approximation II: general formula for electron screening correction for effective shear modulus
• Note: Sound velocities of generalized Lennard-Jones ($n-6$) fluids near freezing
• Modified Bridgman formula for the thermal conductivity of complex (dusty) plasma fluids
• Note: Shoving model and the glass transition in one-component plasma
• Variational approach to Yukawa fluids. II. Instantaneous elastic moduli and sound velocities
• Inferring partial crystalline order in liquids from electrical resistivity