Related papers: Counter-ions at single charged wall: Sum rules
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
We study the minimum energy configuration of a uniform distribution of negative charge subject to Coulomb repulsive self-interaction and attractive interaction with a fixed positively charged domain. After having established existence and…
In this paper we study the electrostatic interaction of a heterogeneously charged wall with a neutral semipermeable membrane. The wall consists of periodic stripes, where the charge density varies in one direction. The membrane is in a…
We derive general expressions for the sum rules of the eigenvalues of drums of arbitrary shape and arbitrary density, obeying different boundary conditions. The formulas that we present are a generalization of the analogous formulas for one…
The electron-positive fermion gas in three dimensions and $T=0$ is modeled as two independent fermion gases interacting via the coulomb interaction. The main advantage of the simple model is that all existing results from the electron gas…
The model under consideration is the two-dimensional Coulomb gas of $\pm$ charged hard disks with diameter $\sigma$. For the case of pointlike charges $(\sigma=0)$, the system is stable against collapse of positive-negative pairs of charges…
We investigate the interplay between three possible properties of stationary point processes: i) Finite Coulomb energy with short-scale regularization, ii) Finite $2$-Wasserstein transportation distance to the Lebesgue measure and iii)…
It is shown, how the normalization sum rules of the spin-parallel and spin-antiparallel pair densities of the homogeneous electron gas become sum rules for the scattering phase shifts of the Overhauser two-body wave functions (geminals),…
The model under consideration is a semi-infinite two-dimensional two-component plasma (Coulomb gas), stable against bulk collapse for the dimensionless coupling constant $\beta<2$, in contact with a dielectric wall of dielectric constant…
Various sum rules accounting for the coupling between density and particle excitations and emphasizing in an explicit way the role of the Bose-Einstein condensation are discussed. Important consequences on the fluctuations of the particle…
Quasi one-dimensional systems are systems of particles in domains which are of infinite extent in one direction and of uniformly bounded size in all other directions, e.g. on a cylinder of infinite length. The main result proven here is…
We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero…
We investigate the ion distribution and overcharging at charged interfaces with dielectric inhomogeneities in the presence of asymmetric electrolytes containing polyvalent and monovalent ions. We formulate an effective "dressed counterion"…
We report molecular dynamics simulation of the (overall neutral) system consisting of an immobile macroion surrounded by the electrolyte of multivalent counterions and monovalent coions. As expected theoretically, counterions adsorb on the…
The Kohn-Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high…
Thermodynamic quantities of Coulomb plasmas consisting of point-like ions immersed in a compressible, polarizable electron background are calculated for ion charges Z=1 to 26 and for a wide domain of plasma parameters ranging from the…
Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one…
When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws…
We theoretically study electrostatic properties of electric double layer using a generalized Poisson-Boltzmann approach taking into account the orientational ordering of water dipoles and the excluded volume effect of water molecules as…
The description of a conducting medium in thermal equilibrium, such as an electrolyte solution or a plasma, involves nonlinear electrostatics, a subject rarely discussed in the standard electricity and magnetism textbooks. We consider in…