Theoretical description of Coulomb balls: fluid phase

Finite-temperature quantum effects on confined charges

A quantum system of N Coulomb charges confined within a harmonic trap is considered over a wide range of densities and temperatures. A recently described construction of an equivalent classical system is applied in order to exploit the rather complete classical description of harmonic confinement via liquid-state theory. Here, the effects of quantum mechanics on that representation are described with attention focused on the origin and nature of shell structure. The analysis extends from the classical strong Coulomb coupling conditions of dusty plasmas to the opposite limit of low temperatures and large densities characteristic of "warm, dense matter."

Shell formation in short like-charged polyelectrolytes in a harmonic trap

Inspired by recent experiments and simulations on pattern formation in biomolecules by optical tweezers, a theoretical description based on the reference interaction site model (RISM) is developed to calculate the equilibrium density profiles of small polyelectrolytes in an external potential. The formalism is applied to the specific case of a finite number of Gaussian and rodlike polyelectrolytes trapped in a harmonic potential. The density profiles of the polyelectrolytes are studied over a range of lengths and numbers of polyelectrolytes in the trap, and the strength of the trap potential. For smaller polymers we recover the results for point charges. In the mean field limit the longer polymers, unlike point charges, form a shell at the boundary layer. When the interpolymer correlations are included, the density profiles of the polymers show sharp shells even at weaker trap strengths. The implications of these results are discussed.

Dynamics of strongly correlated and strongly inhomogeneous plasmas

Kinetic and fluid equations are derived for the dynamics of classical inhomogeneous trapped plasmas in the strong coupling regime. The starting point is an extended Singwi-Tosi-Land-Sjölander (STLS) ansatz for the dynamic correlation function, which is allowed to depend on time and both particle coordinates separately. The time evolution of the correlation function is determined from the second equation of the Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy. We study the equations in the linear limit and derive a nonlocal equation for the fluid displacement field. Comparisons to first-principles molecular dynamics simulations reveal an excellent quality of our approach thereby overcoming the limitations of the broadly used STLS scheme.

Structural properties of anisotropically confined binary Coulomb balls

We investigate the structural properties of a small binary system of dusty plasma subjected to an anisotropic external confinement. We have found that the ground state can form various symmetrical configurations, which generally correspond to variations of a multiple-ring structure. The presence of such structures is given through a detailed phase diagram constructed for the systems with N=18 and 24 particles. Furthermore, we show that the configurations of multiple rings can present a persistent behavior for the case in which the number of less-charged particles is equal to a multiple of the number of particles per ring. Finally, we discuss the main characteristics of the transitions of first and second orders since these are related to the main configurational changes of the ground states.

Density functional theory for the ground state of spherically confined dusty plasma

The spatial structure of dusty plasma confined in a spherical microcavity has been investigated by use of the density functional theory for classical fluids, in which all particles undergo an isotropic harmonic potential and the interparticle interaction is described by the hard-core Yukawa potential. The fundamental measure theory of Rosenfeld and its modified versions have been used in the energy functional to incorporate hard-core interactions between particles. Based on the variational principle, the equilibrium density profile can be obtained by use of an iteration calculation with the average density of particles as an input. In terms of density profiles presented under various conditions, the roles of the trapped parameter, coupling parameter, screening parameter, and the average number density of particles are discussed, and significant influences of these factors on the structure of confined dusty plasma are found.

Shell models of two-dimensional Coulomb crystals: assessment and comparison with the three-dimensional case

Three shell models, differing in accuracy and computational cost, are formulated for two-dimensional Coulomb crystals. Offering a new means of predicting and analyzing properties of these species, the new models also provide new insights into their previously derived three-dimensional counterparts. In particular, analysis of the individual components of the energy error points out to the neglect of the positional relaxation as the main source of the differences between the approximate and exact energies. Within the realm of shell models, the two-dimensional case turns out to be somewhat more challenging than the three-dimensional one. Due to the lack of exact closed-form expressions for the optimal shell radii, it is computationally more expensive and the energy predictions at the same level of approximation are less accurate (as indicated by the maximum relative energy error of 0.15% vs. that of 0.03% found for spherical Coulomb crystals).

Theoretical description of spherically confined, strongly correlated Yukawa plasmas

A theoretical description of the radial density profile for charged particles with Yukawa interaction in a harmonic trap is described. At strong Coulomb coupling shell structure is observed in both computer simulations and experiments. Correlations responsible for such shell structure are described here using a recently developed model based in density functional theory. A wide range of particle number, Coulomb coupling, and screening lengths is considered within the fluid phase. A hypernetted chain approximation shows the formation of shell structure, but fails to give quantitative agreement with Monte Carlo simulation results at strong coupling. Significantly better agreement is obtained within the hypernetted chain structure using a renormalized coupling constant, representing bridge function corrections.

Collective excitations of a spherically confined Yukawa plasma

The complete spectrum of eigenmodes of a spherically confined Yukawa plasma is presented, based on first-principle molecular dynamics simulations. These results are compared with a recent fluid theory for the multipole modes of this system [H. Kählert and M. Bonitz, Phys. Rev. E 82, 036407 (2010)] and with the exact N-particle eigenmodes in the crystalline phase. Simulations confirm the existence of high-order modes found in cold fluid theory. We investigate the influence of screening, coupling, and friction on the mode spectra in detail. Good agreement between theory and simulation is found for weak to moderate screening and low-order modes. In addition, a number of new modes are observed which are missing in the fluid theory. The relations between the breathing mode in the fluid theory, simulation, and the crystal eigenmode are investigated in further detail.

Shell model of assemblies of equicharged particles subject to radial confining potentials

A shell model of an assembly of N equicharged particles subject to an arbitrary radial confining potential N W(r), where W(r) is parameterized in terms of an auxiliary function Λ(t), is presented. The validity of the model requires that Λ(t) is strictly increasing and concave for any t ∈ (0, 1), Λ'(0) is infinite, and Λ(t) = -t(-1) Λ'(t)/Λ''(t) is finite at t = 0. At the bulk limit of N → ∞, the model is found to correctly reproduce the energy per particle pair and the mean crystal radius R(N), which are given by simple functionals of Λ(t) and Λ'(t), respectively. Explicit expressions for an upper bound to the cohesive energy and the large-N asymptotics of R(N) are obtained for the first time. In addition, variational formulation of the cohesive energy functional leads to a closed-form asymptotic expression for the shell occupancies. All these formulae involve the constant ξ that enters the expression -(ξ/2) n(3/2) for the leading angular-correlation correction to the minimum energy of n electrons on the surface of a sphere with a unit radius (the solution of the Thomson problem). The approximate energies, which constitute rigorous upper bounds to their exact counterparts for any value of N, include the cohesive term that is not accounted for by the mean-field (fluidlike) theory and its simple extensions but completely neglect the surface-energy correction proportional to N.

Fluid modes of a spherically confined Yukawa plasma

The normal modes of a three-dimensional Yukawa plasma in an isotropic harmonic confinement are investigated by solving the linearized cold fluid equations. The eigenmodes are found analytically and expressed in terms of hypergeometric functions. It is found that the mode frequencies solely depend on the dimensionless plasma parameter ξ=κR , where R is the plasma radius and κ is the inverse screening length. The eigenfrequencies increase monotonically with ξ and saturate in the limit ξ→∞ . Compared with the results in the Coulomb limit [D. H. E. Dubin, Phys. Rev. Lett. 66, 2076 (1991)10.1103/PhysRevLett.66.2076], we find an additional class of modes characterized by the number n which determines the number of radial nodes in the perturbed potential. These modes originate from the degenerate bulk modes of the Coulomb system. Analytical formulas for the eigenfrequencies are derived for limiting cases.