A van der Waals free energy in electrolytes revisited

A system of three electrolytes separated by two parallel planes is considered. Each region is described by a dielectric constant and a Coulomb fluid in the Debye-H\"uckel regime. In their book Dispersion Forces, Mahanty and Ninham have given the van der Waals free energy of this system. We rederive this free energy by a different method, using linear response theory and the electrostatic Maxwell stress tensor for obtaining the dispersion force.Comment: 7 pages. PACS numbers updated. References update

Surface correlations for two-dimensional Coulomb fluids in a disc

After a brief review of previous work, two exactly solvable two-dimensional models of a finite Coulomb fluid in a disc are studied. The charge correlation function near the boundary circle is computed. When the disc radius is large compared to the bulk correlation length, a correlation function of the surface charge density can be defined. It is checked, on the solvable models, that this correlation function does have the generic long-range behaviour, decaying as the inverse square distance, predicted by macroscopic electrostatics. In the case of a two-component plasma (Coulomb fluid made of two species of particles of opposite charges), the density correlation function on the boundary circle itself is conjectured to have a temperature-independent behaviour, decaying as the -4 power of the distance.Comment: 15 pages, Latex, submitted to J.Phys.:Condens.Matte

The Ideal Conductor Limit

This paper compares two methods of statistical mechanics used to study a classical Coulomb system S near an ideal conductor C. The first method consists in neglecting the thermal fluctuations in the conductor C and constrains the electric potential to be constant on it. In the second method the conductor C is considered as a conducting Coulomb system the charge correlation length of which goes to zero. It has been noticed in the past, in particular cases, that the two methods yield the same results for the particle densities and correlations in S. It is shown that this is true in general for the quantities which depend only on the degrees of freedom of S, but that some other quantities, especially the electric potential correlations and the stress tensor, are different in the two approaches. In spite of this the two methods give the same electric forces exerted on S.Comment: 19 pages, plain TeX. Submited to J. Phys. A: Math. Ge

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov's fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current correlation function is found to be integrable in space, in both classical and quantum regimes.Comment: 19 pages, 1 figur

The two-dimensional two-component plasma plus background on a sphere : Exact results

An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made of a uniformly charged background, positive particles, and negative particles, on the surface of a sphere. At the special value $\Gamma = 2$ of the reduced inverse temperature, the classical equilibrium statistical mechanics is worked out~: the correlations and the grand potential are calculated. The thermodynamic limit is taken, and as it is approached the grand potential exhibits a finite-size correction of the expected universal form.Comment: 23 pages, Plain Te

Classical Coulomb Systems:Screening and Correlations Revisited

From the laws of macroscopic electrostatics of conductors (in particular the existence of screening) taken for granted, one can deduce universal properties for the thermal fluctuations in a classical Coulomb system at equilibrium. The universality is especially apparent in the long-range correlations of the electrical potentials and fields. The charge fluctuations are derived from the field fluctuations. This is a convenient way for studying the surface charge fluctuations on a conductor with boundaries. Explicit results are given for simple geometries. The potentials and the fields have Gaussian fluctuations, except for a short-distance cutoff.Comment: 17 pages,TE

Correlations in a confined magnetized free-electron gas

Equilibrium quantum statistical methods are used to study the pair correlation function for a magnetized free-electron gas in the presence of a hard wall that is parallel to the field. With the help of a path-integral technique and a Green function representation the modifications in the correlation function caused by the wall are determined both for a non-degenerate and for a completely degenerate gas. In the latter case the asymptotic behaviour of the correlation function for large position differences in the direction parallel to the wall and perpendicular to the field, is found to change from Gaussian in the bulk to algebraic near the wall.Comment: 24 pages, 10 figures, submitted to J. Phys. A: Math. Ge

Models with short and long-range interactions: phase diagram and reentrant phase

We study the phase diagram of two different Hamiltonians with competiting local, nearest-neighbour, and mean-field couplings. The first example corresponds to the HMF Hamiltonian with an additional short-range interaction. The second example is a reduced Hamiltonian for dipolar layered spin structures, with a new feature with respect to the first example, the presence of anisotropies. The two examples are solved in both the canonical and the microcanonical ensemble using a combination of the min-max method with the transfer operator method. The phase diagrams present typical features of systems with long-range interactions: ensemble inequivalence, negative specific heat and temperature jumps. Moreover, in a given range of parameters, we report the signature of phase reentrance. This can also be interpreted as the presence of azeotropy with the creation of two first order phase transitions with ensemble inequivalence, as one parameter is varied continuously

Spatial and temporal variations in PM10 and PM2.5 across Madrid metropolitan area in 1999–2008

AbstractThis paper presents a summary of the results obtained from the particulate matter (PM) data collected over the 1999–2008 period from representative sites of the Madrid air basin (an urban traffic site, an urban background site and a rural site) which is located in the centre of Spain. A number of PM10 and PM2.5 filters were obtained with high volume samplers and cut-off inlets and chemically analyzed. Pollutants recorded in this area at the Air Quality monitoring stations were also analyzed. The influence of the atmospheric transport scenarios on the levels of PM was investigated by means of atmospheric back-trajectories, satellite imagery and meteorological synoptic charts. Source apportionment studies were performed to characterize the main PM sources whenever was possible. Their contributions to bulk PM levels showed clear spatial patterns, linked to characteristic meteorological scenarios

Two-dimensional one-component plasma on a Flamm's paraboloid

We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Gamma=2 on the Riemannian surface known as Flamm's paraboloid which is obtained from the spatial part of the Schwarzschild metric. At this special value of the coupling constant, the statistical mechanics of the system are exactly solvable analytically. The Helmholtz free energy asymptotic expansion for the large system has been found. The density of the plasma, in the thermodynamic limit, has been carefully studied in various situations