A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correla-

During the past decade a number of attempts to formulate a continuum description of complex states of matter have been proposed to circumvent more cumbersome many-body and simulation methods. Typically these have been quantum systems (e.g., electrons) and the resulting phenomenologies collectively often called "quantum hydrodynamics". However, there is extensive work from the past based in non-equilibrium statistical mechanics on the microscopic origins of macroscopic continuum dynamics that has not been exploited in this context. Although formally exact, its original target was the derivation of Navier-Stokes hydrodynamics for slowly varying states in space and time. The objective here is to revisit that work for the present interest in complex quantum states -possible strong degeneracy, strong coupling, and all space-time scales. The result is an exact representation of generalized hydrodynamics suitable for introducing controlled approximations for diverse specific cases, and for critiquing existing work. * ij (r, t ′ |y) ∂ i u j + Ψ 0j (r|y(t))t * ij (r, t|y) (S126)

A theoretical description of shell structure for charged particles in a harmonic trap is explored at strong coupling conditions of Γ = 50 and 100. The theory is based on an extension of the hypernetted chain approximation to confined systems plus a phenomenological representation of associated bridge functions. Predictions are compared to corresponding Monte Carlo simulations and quantitative agreement for the radial density profile is obtained.

A system of N classical Coulomb charges trapped in a harmonic potential displays shell structure and orientational ordering. The local density profile is well understood from theory, simulation, and experiment. Here, pair correlations are considered for this highly inhomogeneous system for both the fluid and ordered states. In the former, it is noted that there is a close relationship to pair correlations in the uniform OCP. For the ordered state, it is shown that the disordered "tiling" is closely related to the ground state Thomson sites for a single sphere.Comment: 8 pages, 3 figues. Results presented at "Strongly Coupled Coulomb Systems", Budapest, Hungary, July 2011. Conference proceedings to be published in "Contribution to Plasma Physics

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.