Dynamical structure functions for charged particle bilayers and superlattices

Anomalous behavior of plasma response functions at strong coupling

Using data from equilibrium molecular dynamics computer simulations we have built up a catalog of response functions for the Coulomb one-component plasma over a wide range of Γ coupling values, including the strongly coupled Γ>1 liquid regime. We focus on the domain of negative compressibility (Γ>3), where the proper response displays an acausal behavior, implying a modification of the relation between its real and imaginary parts in the Kramers-Kronig relations. We give a description of the details of this acausal feature, in both the frequency and time domains. We show that the viscoelastic pole of the density response function morphs into an imaginary pole in the upper ω half-plane that is responsible for the anomalous behavior of the response in this coupling range. By examining the plasmon dispersion relation through the dielectric response function, rather than via the peaks of the dynamical structure function, we obtain a more reliable representation for the dispersion. We demonstrate that there is an intimate link between the formation of the roton minimum in the dispersion and the negative compressibility of the system. The feasibility of the extension of our analysis to systems with a short-range interaction is explored.

Sound speed in Yukawa one-component plasmas across coupling regimes

A many-body system of charged particles interacting via a pairwise Yukawa potential, the so-called Yukawa one-component plasma (YOCP), is a good approximation for a variety of physical systems. Such systems are completely characterized by two parameters: the screening parameter, κ, and the nominal coupling strength, Γ. It is well known that the collective spectrum of the YOCP is governed by a longitudinal acoustic mode, both in the weakly and strongly coupled regimes. In the long-wavelength limit, the linear term in the dispersion (i.e., ω=sk) defines the sound speed s. We study the evolution of this latter quantity from the weak- through the strong-coupling regimes by analyzing the dynamic structure function S(k,ω) in the low-frequency domain. Depending on the values of Γ and κ and w=s/v_{th} (i.e., the ratio between the phase velocity of the wave and the thermal speed of the particles), we identify five domains in the (κ,Γ) parameter space in which the physical behavior of the YOCP exhibits different features. The competing physical processes are the collective Coulomb-like versus binary-collision-dominated behavior and the individual particle motion versus quasilocalization. Our principal tool of investigation is molecular dynamics (MD) computer simulation from which we obtain S(k,ω). Recent improvements in the simulation technique have allowed us to obtain a large body of high-quality data in the range Γ={0.1-10000} and κ={0.5-5}. The theoretical results based on various models are compared in order to see which one provides the most cogent physical description and the best agreement with MD data in the different domains.

Sum rules for electron-hole bilayer and two-dimensional point dipole systems

We formulate and analyze the third-frequency-moment sum rules for the two-dimensional (point) dipole system (2DDS) and the mass-symmetric electron-hole bilayer (EHB) in their strongly coupled liquid phases. The former, characterized by the repulsive interaction potential φ_{D}(r)=μ^{2}/r^{3} (μ is the electric dipole moment), reasonably well approximates the latter in the d → 0 limit (d is the interlayer spacing), a conjecture that is further supported by the findings of the present work. We explore the extent to which the in-phase sum rule for the closely spaced EHB may or may not reconcile with its 2DDS sum-rule counterpart. This is the main emphasis of the present work.

Transverse dielectric matrix and shear mode dispersion in strongly coupled electronic bilayer liquids

The authors develop a transverse dielectric matrix and from it they calculate the shear mode dispersion in strongly coupled charged-particle bilayer liquids in the T=0 quantum domain. The formulation is based on the classical quasilocalized charge approximation (QLCA) and extends the QLCA formalism into the quantum domain. Its development parallels and complements the development of a similarly extended longitudinal dielectric matrix formalism reported in a recent companion work [K. I. Golden, H. Mahassen, G. J. Kalman, G. Senatore, and F. Rapisarda, Phys. Rev. E 71, 036401 (2005)]. Using pair correlation function data generated from diffusion Monte Carlo simulations, the authors calculate the dispersion of the in-phase and out-of-phase shear modes over a wide range of high-r(s) values and layer separations. Over the coupling range 10< or =r(s)< or =30 and for layer separations 0.2/sqrt[pi(n)]< or =d< or =0.5/sqrt[pi(n)] , the present study predicts the existence of a robust out-of-phase gapped shear mode dispersion in the domain of the q,omega -plane above the left boundary of the RPA single-pair excitation region; under these conditions, the out-of-phase collective excitation is entirely immune to Landau damping and can be safely considered to be mostly unaffected by diffusive-migrational damping.

Dielectric matrix and plasmon dispersion in strongly coupled electronic bilayer liquids

We develop a dielectric matrix and analyze plasmon dispersion in strongly coupled charged-particle bilayers in the T = 0 quantum domain. The formulation is based on the classical quasilocalized charge approximation (QLCA) and extends the QLCA formalism into the quantum domain. Its development, which parallels that of the two-dimensional companion paper [Phys. Rev. E 70, 026406 (2004)] by three of the authors, generalizes the single-layer scalar formalism therein to a bilayer matrix formalism. Using pair correlation function data generated from diffusion Monte Carlo simulations, we calculate the dispersion of the in-phase and out-of-phase plasmon modes over a wide range of high- r(s) values and layer separations. The out-of-phase spectrum exhibits an exchange-correlation induced long-wavelength energy gap in contrast to earlier predictions of acoustic dispersion softened by exchange and correlations. The energy gap is similar to what has been previously predicted for classical charged-particle bilayers and subsequently confirmed by recent molecular dynamics computer simulations.

Dielectric response function and plasmon dispersion in a strongly coupled two-dimensional Coulomb liquid

We have formulated a dielectric response function for strongly coupled two-dimensional Coulomb liquids in the T=0 quantum domain. The formulation is based on the classical quasilocalized charge approximation [G. Kalman and K.I. Golden, Phys. Rev. A 41, 5516 (1990); K.I. Golden and G. Kalman, Phys. Plasmas 7, 14 (2000)] and extends the QLCA formalism into the quantum domain. We calculate the dispersion of the longitudinal plasmon mode for r(s) =10, 20, 40 and the resulting dispersion curves are compared with recent experimental results. We also conjecture the possible existence of a new high-wave-number collective excitation in close proximity to the right boundary of the pair continuum.

Collective modes of quasi-two-dimensional Yukawa liquids

Particles in dusty plasmas are often confined to a quasi-two-dimensional arrangement. In such layers--besides the formation of compressional and (in-plane) shear waves--an additional collective excitation may also show up, as small-amplitude oscillations of the particles perpendicular to the plane are also possible. We explore through molecular dynamics simulations the properties (fluctuation spectra, dispersion relation, Einstein frequency) of this out-of-plane transverse mode in the strongly coupled liquid phase of Yukawa systems.

Dynamical structure functions, collective modes, and energy gap in charged-particle bilayers

The dynamical properties of strongly coupled charged-particle bilayers are investigated by molecular dynamics (MD) simulation and theoretical analysis. The spectra of the current correlation functions show the existence of two (in-phase and out-of-phase) longitudinal and two (in-phase and out-of-phase) transverse collective modes. The out-of-phase modes possess finite frequencies at wave numbers k-->0, confirming the existence of the predicted long-wavelength energy gap in the bilayer system. A theoretical model based on an extended Feynman ansatz for the dynamical structure functions provides predictions on the strength of the collective modes that are verified by the MD experiment.