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 correlations is developed here by an extension of the hypernetted chain approximation, developed for bulk fluids, to the confined charges. The results reproduce all of the qualitative features observed in molecular dynamics simulations and experiments. These predictions are then tested quantitatively by comparison with new benchmark Monte Carlo simulations. Quantitative accuracy of the theory is obtained for the selected conditions by correcting the hypernetted chain approximation with a representation for the associated bridge functions.
Using the collective variables theory, we study the effect of competition between Coulomb and dispersion forces on the gas-liquid phase behaviour of a model ionic fluid, i.e. a charge-asymmetric primitive model with additional short-range attractive interactions. Both the critical parameters and the coexistence envelope are calculated in a one-loop approximation as a function of the parameter $α$ measuring the relative strength of the Coulomb to short-range interactions. We found the very narrow region of $α$ bounded from the both sides by tricritical points which separates the models with "no…
The structure factor for electric field correlations in the two dimensional Coulomb fluid is simulated and compared to theories of the dielectric function. Singular changes in the structure factor occur at the BKT insulator to conductor transition, as well as at a higher temperature correlation transition between a poor electrolyte and perturbed Debye-Hückel fluid. Structure factors are found to differ in the canonical and grand canonical ensembles, with the poor electrolyte showing full ensemble inequivalence. We identify mechanisms of `underscreening' and `pinch point' scattering that are re…
In classical semi-infinite Coulomb fluids, two-point correlation functions exhibit a slow inverse-power law decay along a uniformly charged wall. In this work, we concentrate on the corresponding amplitude function which depends on the distances of the two points from the wall. Recently [L. Šamaj, J. Stat. Phys. {\bf 161}, 227 (2015)], applying a technique of anticommuting variables to a 2D system of charged rectilinear wall with "counter-ions only", we derived a relation between the amplitude function and the density profile which holds for any temperature. In this paper, using the Möbius con…
The forging of strong correlations on decreasing temperature can take place without the arousal of conventional order. If this happens, as in some geometrically frustrated magnets, disorder can be a phenomenon more interesting than order itself. A Coulomb phase, for example, has critical-like pair-spin correlations, leading to neutron scattering \textit{pinch points} and emergent electromagnetism. Here we present a new instance of disorder in an Ising pyrochlore lattice: the \textit{Polarized Monopole Liquid} (PML), a dense monopole fluid with pinch points in the \textit{magnetic charge}-pair …
Thermodynamic potential of a neutral two-dimensional (2D) Cou\-lomb fluid, confined to a large domain with a smooth boundary, exhibits at any (inverse) temperature $β$ a logarithmic finite-size correction term whose universal prefactor depends only on the Euler number of the domain and the conformal anomaly number $c=-1$. A minimal free boson conformal field theory, which is equivalent to the 2D symmetric two-component plasma of elementary $\pm e$ charges at coupling constant $Γ=βe^2$, was studied in the past. It was shown that creating a non-neutrality by spreading out a charge $Q e$ at infin…
We have developed a field theory for strongly coupled Coulomb fluids, via introducing new functional--integral transformation of the electrostatic interaction energy. Our formalism not only reproduces the Lieb--Narnhofer lower bound, but also bridges logical gaps which previous approaches have involved.
Single-particle density matrix and superfluidity in the two-dimensional Bose Coulomb fluid
W. R. Magro和D. M. Ceperley [Phys. Rev. Lett. { \bf 73}，826（1994）]已经表明，具有对数相互作用的荷电玻色子的二维流体的基态不是玻色凝聚的，而是在单粒子密度矩阵$ρ(r)$中表现出代数非对角阶。我们使用的流体动力学哈密顿表示的密度和相位算子，结合超流分数的$f$求和规则，重现这些结果，并延长评估的密度矩阵有限温度$T$。这种方法允许我们在没有凝聚物的情况下将液体视为超流体。我们发现：（i）非对角序来自相位涨落之间的相关性;（ii）超流密度$n_s(T)$决定了$ρ(r)$幂律衰减的指数。我们还发现，在长波长的单粒子能谱中的等离子体激元间隙随着$T$的增加而减小，并在超流性开始的临界温度处关闭。
A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact {\sl via} long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson-Boltzmann and Maier-Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity of a charged planar wall, generalizing the standard Gouy-Chapman results. The nematic order parameter profile, the counter…
Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, $h_λ({\bf r},{\bf r}')$, where $λ$ determines the interaction strength. To obtain $h_λ({\bf r},{\bf r}')$ we use the Ornstein-Zernike equation, and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. As the two equations do not form a closed set, an approximate closure relation is required and it determines a type of an approximation. In the present work we investigate the random phase approximation (RPA) closure. We determine th…
Charge correlations in dense ionic fluids give rise to novel effects such as long-range screening and colloidal stabilization which are not predicted by the classic Debye-Huckel theory. We show that a Coulomb or charge-frustrated Ising model, which accounts for both long-range Coulomb and short-range molecular interactions, simply describes some of these ionic correlations. In particular, we obtain at mean field level and in simulations, a non-monotonic dependence of the screening length on the temperature. Using a combination of simulations and mean field theories, we study how the correlatio…
The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-Hückel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy $s_{\rm ex}$ can be used as a suitable indicator of the validity of the SE relation. In all cases considered th…
