Dispersion relations of Yukawa fluids at weak and moderate coupling

Abstract

In this paper we compare different theoretical approaches to describe the dispersion of collective modes in Yukawa fluids when the interparticle coupling is relatively weak, so that the kinetic and potential contributions to the dispersion relation compete with each other. A thorough comparison with the results from molecular dynamics simulation allows us to conclude that, in the investigated regime, the best description is provided by the sum of the generalized excess bulk modulus and the Bohm-Gross kinetic term.

Description of longitudinal modes in moderately coupled Yukawa systems with the static local field correction

“…A similar expression has been obtained by Khrapak & Couëdel based on physical intuition [31]. These investigators constructed the dispersion relation by; inspecting the second frequency moment of the longitudinal current fluctuations (which corresponds to the fourth frequency moment rule for the dynamic structure factor [42]) as well as the second frequency moment of the transverse current fluctuations, rewriting the potential contribution to these moments in terms of the generalized instantaneous elastic moduli [48], conjecturing that the transverse mode cutoff at the moderate coupling regime [49][50][51] allows the omission of the contribution of the shear modulus to the longitudinal modulus (which then becomes equal to the bulk modulus [52]) and manually adding the Bohm-Gross term in order to ensure a proper transition to the weak coupling regime.…”

“…We note that their conjecture can also be justified in view of the neglected energy dissipation of the QLCA [53], that has been recently revisited on the basis of the self-consistent method of moments [54]. Overall, in normalized units, their semi-phenomenological QLCA-inspired dispersion relation reads as [31]…”

“…In the liquid portion of the Yukawa phase diagram, this regime is bounded above by the Frenkel line (dynamic crossover corresponding to the emergence of shear stiffness at undamped natural frequencies or the appearance of the transverse mode in the spectrum) [32] and bounded below by the Kirkwood line (structural crossover from monotonic decay to exponentially damped oscillatory decay of the total correlation function) [33]. A recent work by Khrapak & Couëdel [31] has investigated the dispersion relations of Yukawa fluids in this regime, where kinetic and potential contributions are comparable. A semi-phenomenological dispersion relation was constructed that is based on the ad hoc addition of the Bohm-Gross kinetic term to a QLCA-inspired potential term which demonstrated very good agreement with simulation results.…”

“…In addition, particular attention has been paid to the long wavelength limit and to the acquisition of practical expressions for the sound velocities [22][23][24][25]. The ever-growing availability of exact results from molecular dynamics (MD) simulations has helped to distinguish the inherent limitations, quantify the level of accuracy and determine the different applicability ranges of the aforementioned theoretical methods [10,13,16,23,24,[26][27][28][29][30][31]. Given the large number of available approaches, it is expected that there are strong similarities and differences amongst them.…”

Stability of two-dimensional complex plasma monolayers in asymmetric capacitively coupled radio-frequency discharges

“…is the frequency of the lattice modes with wave number k, the current fluctuation spectra J L,T (k, f ) were fitted to a double-Lorentzian form [50,51]: Any modification of the discharge parameters (p Ar and/or P W ) has an impact on the plasma and therefore on the sheath properties. It is then evident that since the microparticle monolayer levitates in the rf sheath above the powered electrode, any changes of the discharge parameters also affect the monolayer properties.…”