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.

9 pages, 4 figures

References in corpus (8)

• Dynamical correlations and collective excitations of Yukawa liquids
• Emergence and evolution of $k$-gap in spectra of liquid and supercritical states
• Fluid approach to evaluate sound velocity in Yukawa systems (complex plasmas)
• Practical thermodynamics of Yukawa systems at strong coupling
• Collective modes in simple melts: Transition from soft spheres to the hard sphere limit
• Onset of transverse (shear) waves in strongly-coupled Yukawa fluids
• Ion sphere model for Yukawa systems (dusty plasmas)
• Fingerprints of different interaction mechanisms on the collective modes in complex (dusty) plasmas

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