Chemical Stability of Binary Coulomb Compounds

Chemical stability of binary Coulomb compounds is studied through extensive calculation of their Madelung energies. A remarkable finding is that the compounds with disordered ionic arrangements in a certain range of the composition are stable against chemical separation beyond the charge ratio around 6; clearly the entropic effect due to finite temperature promotes the mixing of ions of different species. For the ordered AB₃‐type compounds, there exists a crystalline structure which is more chemically bounded than that of Dyson (1971). Relative stability o the ordered and disordered compounds is also discussed.     

Energies of mass-asymmetric Coulomb systems

It is found that particle-mass-symmetric and particle-mass-asymmetric Coulomb systems are adiabatically similar. Expressions are proposed for the mass dependence of upper and lower bounds on the energies of asymmetric systems, and an expression approximating these energies is given. The energies of the families of mesic molecules that are adiabatically similar to the mesic molecules dpμ, tpμ, and tdμ are investigated with the aid of these expressions.     

Thermodynamic functions of Coulomb systems

Thermodynamic functions are needed for the discussion of phase transitions in gaseous and solid state plasmas. In this paper detailed numerical data for the Hartree-Fock and the Montroll-Ward (ring sum) contributions to the pressure for symmetrical multicomponent plasmas are given at any degree of degeneration.For the Montroll-Ward pressure especially also isotherms are given. There is good agreement with limiting results derived analytically.     

Crystallization in two-component Coulomb systems

The analysis of Coulomb crystallization is extended from one-component to two-component plasmas. Critical parameters for the existence of Coulomb crystals are derived for both classical and quantum crystals. In the latter case, a critical mass ratio of the two charged components is found, which is of the order of 80. Thus, holes in semiconductors with sufficiently flat valence bands are predicted to spontaneously order into a regular lattice. Such hole crystals are intimately related to ion Coulomb crystals in white dwarf and neutron stars as well as to ion crystals produced in the laboratory. A unified phase diagram of two-component Coulomb crystals is presented and is verified by first-principles computer simulations.     

Ionization energies of bosonic Coulomb systems

We consider atomic and molecular systems with fixed nuclei where the electrons are assumed to be bosons. Then the ionization energies are rigorously computable in the limit of large particle numbers.     

Monotonicity and concavity in Coulomb systems

The eigenvalues ofH()=H ₀+H ^*, whereH ^* is an arbitrary Coulomb potential, decrease with increasing 0. Linear and parabolic bounds for the ground-state energy are presented. These bounds are applied to the biexciton and the exciton at a neutral donor.     

Mean field theory for Coulomb systems

We study a classical charge symmetric system with an external charge distributionq in three dimensions in the limit that the plasma parameter zero. We prove that ifq is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean field(x) where is given by-+ 2z sinh() =q This is the mean field equation of Debye and Hückel. The proof uses the sine-Gordon transformation, the Mayer expansion, and a correlation inequality.Work partially supported by NSF Grant MCS 82-02115.     

Solutions of Hartree-Fock equations for Coulomb systems

This paper deals with the existence of multiple solutions of Hartree-Fock equations for Coulomb systems and related equations such as the Thomas-Fermi-Dirac-Von Weizäcker equation.Partially supported by CEA-DAM     

Coulomb drag in coherent mesoscopic systems

We present a theory for Coulomb drag between two mesoscopic systems. Our formalism expresses the drag in terms of scattering matrices and wave functions, and its range of validity covers both ballistic and disordered systems. The consequences can be worked out either by analytic means, such as the random matrix theory, or by numerical simulations. We show that Coulomb drag is sensitive to localized states, which usual transport measurements do not probe. For chaotic 2D systems we find a vanishing average drag, with a nonzero variance. Disordered 1D wires show a finite drag, with a large variance, giving rise to a possible sign change of the induced current.     

The Hartree-Fock theory for Coulomb systems

For neutral atoms and molecules and positive ions and radicals, we prove the existence of solutions of the Hartree-Fock equations which minimize the Hartree-Fock energy. We establish some properties of the solutions including exponential falloff.Research partially supported by U.S. National Science Foundation Grant MCS-75-21684Research partially supported by U.S. National Science Foundation under Grants MPS-75-11864 and MPS-75-20638. On leave from Departments of Mathematics and Physics, Princeton University, Princeton, NJ08540, USA     

On the existence of four-particle Coulomb systems

Whether bound states of Coulomb systems composed of four particles with unit charges (quadrions), a ⁺ b ⁺ c ⁻ d ⁻, exist is demonstrated to be determined by the masses of the constituent particles. Relations that make it possible to establish the existence of a large number quadrions with different masses of the particles are derived. The energies of reference quadrions of different symmetry, a positronium molecule, a ⁺ a ⁺ a ⁻ a ⁻, a ⁺ b ⁺ a ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻, are determined and groups of stable asymmetric quadrions corresponding to them are identified. A relationship between the stability of a number of quadrions and three-particle systems (trions) was found. The results shows that, among all the 406 four-particle independent combinations of electrons, muons, pions, kaons, protons, deuterons, and tritium nuclei or their antiparticles, there are 227 bound quadrions.     

Large charge fluctuations in classical Coulomb systems

The typical fluctuation of the net electric chargeQ contained in a subregion of an infinitely extended equilibrium Coulomb system is expected to grow only as S, whereS is the surface area of. For some cases it has been previously shown thatQ/S has a Gaussian distribution as ¦¦. Here we study the probability law for larger charge fluctuations (large-deviation problem). We discuss the case when both ¦¦ andQ are large, but now withQ of an order larger than S. For a given value ofQ, the dominant microscopic configurations are assumed to be those associated with the formation of a double electrical layer along the surface of. The probability law forQ is then determined by the free energy of the double electrical layer. In the case of a one-component plasma, this free energy can be computed, for large enoughQ, by macroscopic electrostatics. There are solvable two-dimensional models for which exact microscopic calculations can be done, providing more complete results in these cases. A variety of behaviors of the probability law are exhibited.     

On the Coulomb interaction in granular systems

The previous theories on the behaviour of the conductivity of high-resistivity granular metals are analysed in terms of the Coulomb interaction between the charge carriers. In these theories a non-interacting system of carriers is considered, but it turns out that the Coulomb interaction is involved elsewhere in the calculations. Leaving out this interaction is shown to be a rather wrong assumption. The application of the Efros-Shklovskii theory leads to a real Coulomb gap. A second method is used to confirm the existence of this gap, which width is determined. The results we obtain seem to be consistent with those obtained on the systems with impurities.     

On the dielectric susceptibility of classical Coulomb systems

This paper reports exact and numerical results on the shape dependence of the dielectric susceptibility of the one-component plasma (O.C.P.) in two dimensions. Some apparently conflicting predictions of phenomenological electrostatics and statistical mechanics are resolved. We prove indeed that, for a disk shaped two-dimensional one-component plasma at the particular temperatureT ₀ =q ² (2K _B )^–1, the Clausius-Mossotti relation is exactly fulfilled. It yields a value of the susceptibility which is twice that given by the second moment Stillinger-Lovett sum rule. Similar results are reported for the strip geometry. These discrepancies are explained in terms of shape dependent versus shape independent thermodynamic limits. We report also exact and numerical results on the size dependence of the dielectric susceptibility of the systems quoted above.     

Coulomb systems seen as critical systems: Ideal conductor boundaries

When a classical Coulomb system has macroscopic conducting behavior, its grand potential has universal finite-size corrections similar to the ones which occur in the free energy of a simple critical system: the massless Gaussian field. Here, the Coulomb system is assumed to be confined, by walls made of an ideal conductor material; this choice corresponds to simple (Dirichlet) boundary conditions for the Gaussian field. For ad-dimensional (d2) Coulomb system confined in a slab of thicknessW, the grand potential (in units ofk _B T) per unit area has the universal term (d/2)(d)/2^dd/2W^d–1. For a two-dimensional Coulomb system confined, in a disk of radiusR, the grand potential (in units ofk _B T) has the universal term (1/6) lnR. These results, of general validity, are checked on two-dimensional solvable models.Laboratoire Associé au Centre National de la Recherche Scientifique-URA 63.     

The charge fluctuations in classical Coulomb systems

We study the asymptotic behavior of the charge fluctuations (Q – (Q )² in infinite classical systems of charged particles, and show, under certain clustering assumptions, that if the charge fluctuations are not extensive, then they are necessarily of the order of the surface ¦¦. Moreover, when the canonical sum rules that are typical for equilibrium states of particles interacting with long-range forces hold true, we prove a central limit theorem for the normalized charge variable ¦¦^–1/2((Q – (Q )) in two and three dimensions. In one dimension, the probability distribution of the charge itself converges. The latter case is illustrated by the example of the one-dimensional Coulomb gas.     

Calculation of the stability domain for Coulomb systems

A variational method is proposed for calculating the values of particle mass corresponding to the dissociation threshold of an atomic-molecular system. The calculations of the dissociation stability domain for three-particle Coulomb systems demonstrate the high effectiveness of the method as compared to the traditional variational principle for calculating energy.     

Equilibrium equations and symmetries of classical Coulomb systems

In this paper we establish the validity of the BBGKY equilibrium equations for Coulomb states which have been obtained as thermodynamic limit of finite volume states. We also give a new derivation of thel-sum rules for phases constructed by the cluster expansion. These sum rules are interpreted as Ward identities associated to a symmetry of the screening phase.Supported by the Swiss National Foundation for Scientific Research.