This Letter presents variational ground-state and excited-state wave functions which describe the condensation of a two-dimensional electron gas into a new state of matter.

Anomolous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations

Complex (dusty) plasmas: current status, open issues, perspectives

Electrostatic correlations play an important role in physics, chemistry and biology. In plasmas they result in thermodynamic instability similar to the liquid–gas phase transition of simple molecular fluids. For charged colloidal suspensions the electrostatic correlations are responsible for screening and colloidal charge renormalization. In aqueous solutions containing multivalent counterions they can lead to charge inversion and flocculation. In biological systems the correlations account for the organization of cytoskeleton and the compaction of genetic material. In spite of their ubiquity, the true importance of electrostatic correlations has come to be fully appreciated only quite recently. In this paper, we will review the thermodynamic consequences of electrostatic correlations in a variety of systems ranging from classical plasmas to molecular biology.

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Electrostatic correlations: from plasma to biology

Standard Ewald sums, which calculate, e.g., the electrostatic energy or the force in periodically closed systems of charged particles, can be efficiently speeded up by the use of the fast Fourier transformation (FFT). In this article we investigate three algorithms for the FFT-accelerated Ewald sum, which have attracted widespread attention, namely, the so-called particle–particle–particle mesh (P3M), particle mesh Ewald (PME), and smooth PME method. We present a unified view of the underlying techniques and the various ingredients which comprise those routines. Additionally, we offer detailed accuracy measurements, which shed some light on the influence of several tuning parameters and also show that the existing methods — although similar in spirit — exhibit remarkable differences in accuracy. We propose a set of combinations of the individual components, mostly relying on the P3M approach, that we regard to be the most flexible. The issue of estimating the errors connected with particle mesh routines is reserved to paper II.

How to mesh up Ewald sums. I. A theoretical and numerical comparison of various particle mesh routines

Complex (dusty) plasmas are composed of a weakly ionized gas and charged microparticles and represent the plasma state of soft matter. Complex plasmas have several remarkable features: Dynamical time scales associated with microparticles are ``stretched'' to tens of milliseconds, yet the microparticles themselves can be easily visualized individually. Furthermore, since the background gas is dilute, the particle dynamics in strongly coupled complex plasmas is virtually undamped, which provides a direct analogy to regular liquids and solids in terms of the atomistic dynamics. Finally, complex plasmas can be easily manipulated in different ways---also at the level of individual particles. Altogether, this gives us a unique opportunity to go beyond the limits of continuous media and study---at the kinetic level---various generic processes occurring in liquids or solids, in regimes ranging from the onset of cooperative phenomena to large strongly coupled systems. In the first part of the review some of the basic and new physics are highlighted which complex plasmas enable us to study, and in the second (major) part strong coupling phenomena in an interdisciplinary context are examined. The connections with complex fluids are emphasized and a number of generic liquid and solid-state issues are addressed. In summary, application oriented research is discussed.

Complex plasmas: An interdisciplinary research field

We present results from extensive Monte Carlo simulations of the fluid phase of the two-dimensional classical one-component plasma (OCP). The difficulties associated with the infinite range of the logarithmic Coulomb interaction are eliminated by confining the particles to the surface of a sphere. The results are compared to those obtained for a planar system with screened Coulomb interactions and periodic boundary conditions; in this case the infinite tail of the Coulomb interaction is treated as a perturbation. The “exact” simulation results are used to test various approximate theories, including a semiempirical modification of the hypernetted-chain (HNC) integral equation. The OCP freezing transition is located at a couplingγ= e2/kBT−140.

A Monte Carlo study of the classical two-dimensional one-component plasma

A model system of electrolyte solution is studied by molecular dynamics simulation. The results show how the polarizability of the molecules and the ratio of the molecular diameters of the ions and solvent molecules affect the properties of the system. The computation of the frequency dependent dielectric constant and conductivity in terms of correlation functions of the electrical current and microscopic polarization is discussed. A general solution of this problem is given for systems of arbitrary shape composed of nonpolarizable ions and solvent molecules. Three particular cases are considered in detail: the infinite system; a spherical system in contact with a dielectric and conducting continuum; a system with periodic boundary conditions. The zero frequency limit of the dielectric constant and conductivity is investigated.

Theoretical calculation of ionic solution properties

We present results of Monte Carlo simulations in the isothermal–isobaric ensemble and the Gibbs ensemble for the fluid of dipolar hard spheres. These results preclude the existence of a gas–liquid transition for a wide range of densities and temperatures.

Search of the gas-liquid transition of dipolar hard spheres

Reassessment of the critical temperature and density of the restricted primitive model of an ionic fluid by Monte Carlo simulations performed for system sizes with linear dimension up to L/σ=34 and sampling of ∼109 trial moves leads to Tc*=0.049 17±0.000 02 and ρc*=0.080±0.005. Finite size scaling analysis based in the Bruce–Wilding procedure gives critical exponents in agreement with those of the three-dimensional Ising universality class. An analysis similar to that proposed by Orkoulas et al. [Phys. Rev. E 63, 051507 (2001)], not relying on an a priori knowledge of the universality class, leads to an inaccurate estimate of Tc* and to unexpected behavior of the specific heat and value of the critical exponent ratio γ/ν.

Critical behavior of the restricted primitive model revisited

We generalize previous work [J. Chem. Phys. 85, 6645 (1986)] on the relation between the frequency‐dependent dielectric constant and conductivity and time correlation functions of electrical current and polarization in electrolyte solutions by allowing the ions and solvent molecules to be polarizable. Detailed results are given for the infinite system (no boundary), spherical system embedded in a continuum and periodic boundary conditions. The Stillinger–Lovett (SL) sum rules are derived for these geometries. It is shown, in particular, that they provide a means of calculating the high frequency dielectric constant in a molecular dynamics simulation. A test of the phenomenological coefficient‐susceptibility relations and the SL conditions is presented in part II by performing molecular dynamics simulations on a model electrolyte solution with different boundary conditions.

Jean-Michel Caillol

Papers

A Monte Carlo study of the classical two-dimensional one-component plasma

Theoretical calculation of ionic solution properties

Search of the gas-liquid transition of dipolar hard spheres

Critical behavior of the restricted primitive model revisited

Electrical properties of polarizable ionic solutions. I. Theoretical aspects