Coulomb Systems Research Articles

Fine structure of a one-dimensional discrete point system

We consider a system of N points x 1 < ... < x N on a segment of the real line. An ideal system (crystal) is a system where all distances between neighbors are the same. Deviation from idealness is characterized by a system of finite differences ∇ 1 = x x+1 − x i , ∇ +1 = ∇ +1 − ∇ , for all possible i and k. We find asymptotic estimates as N → ∞, k→∞, for a system of points minimizing the potential energy of a Coulomb system in an external field.

Heterogeneous crystallization in colloids and complex plasmas: the role of binary mobilities

Both charged colloidal suspensions and complex (dusty) plasmas represent classical many-body strongly coupled Coulomb systems. Here we discuss their basic properties and focus on their heterogeneous crystallization from an undercooled melt. In particular, a model with different mobilities is proposed which is realizable in binary mixtures of charged particles. Within this binary-mobility model, the crystallization behaviour near a structured wall is explored by Brownian dynamics computer simulations. As a result, the propagation velocity of the crystal–fluid interface is a nonmonotonic function of the mobility ratio (if expressed in terms of an averaged mobility).

Abstract criteria for multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators

We consider a system of nonlinear coupled equations involving magnetic Schrödinger operators and general potentials. We provide the criteria for the existence of multiple solutions to these equations. As special cases we get the classical results on existence of infinitely many distinct solutions within Hartree and Hartree–Fock theory of atoms and molecules subject to an external magnetic fields. We also extend recent results within this theory, including Coulomb system with a constant magnetic field, a decreasing magnetic field and a “physically measurable” magnetic field.

Necessary conditions of the equivalence of canonical and grand canonical ensembles in Coulomb system thermodynamics

It was found that the equivalence of the grand canonical and canonical ensembles for the Coulomb systems is possible only when charged particles of different types in calculating the physical quantities are considered as formally “independent” ones, and the quasi-neutrality condition is used in the final stage of calculations. The phase equilibrium condition is obtained and the expression is derived for the isothermal compressibility of matter as a two-component Coulomb system, which corresponds to the known limit relations for static structure factors. On this basis, it is demonstrated that the critical point of matter, considering as the Coulomb system is determined from the condition of vanishing mean square of fluctuations of the total charge per unit volume.

Editorial: Ionic Liquids: The Fundamentals and Forces Driving Their Rise

During the last decade there has been an explosion of interest in ionic liquids. If the keywords “ionic liquid” or “ionic liquids” are used for a literature research in the Web of Science, more than seven thousand entries can be found for 2011. That is a tenfold increase in the number of publications dealing with ionic liquids over the past decade, and the field shows no signs of slowing down. Ionic liquids have changed from a lab curiosity to materials of tremendous academic and industrial interest. This new and remarkable liquid substance with unique and fascinating properties offers a phenomenal opportunity for new science and technology. The interest in these new materials is due to their wide range of possible applications as solvents for reaction and material processing, as extraction media or as working fluids in mechanical applications. Originating in the field of electrochemistry and based upon their wide electrochemical windows and good conductivities, ionic liquids have found useful applications in sensors, solar cells, solid-state photocells, batteries, separation devices and as thermal fluids, lubricants, hydraulic fluids, ionogels and fuels.

Time-independent density-functional theory for excited states of Coulomb systems

A Coulomb density is special because it determines not only its Hamiltonian but the degree of excitation as well. We derive Euler equations for excited-state energies and densities that depend only on the electron density. Unlike existing formulations, additional functions and indices are not required; with these functionals, the equations of excited-state density functional theory strongly resemble those of ground-state theory. A critical analysis of the new functionals is included.

On the quantum statistics of bound states within the Rutherford model of matter

AbstractThe quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei), is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the divergence of the partition function, elaborated by Herzfeld, Planck, Brillouin and Rompe, are discussed. Beyond this, the modern state of art is presented and new results are given which explain why bound states according to a discrete part of the spectra occur only in a valley in the temperature‐density plane. Based on the actual state of the quantum statistics of Coulomb systems, virial expansions within the canonical ensemble and the grand ensemble and combinations are derived. The following transitions along isotherms are studied: (i) the formation of bound states occurring by increasing the density from low to moderate values, (ii) the disappearance of bound state effects at higher densities due to medium effects. Within the physical picture isotherms of pressure for Hydrogen are calculated in a broad density region, and it is shown that in the region between 20 000 K and 100 000 K and particle densities below 1022 cm‐3 the cross‐over from full to partial ionization may be well described by the contributions of extended ring diagrams and ladder diagrams.

Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a+b+c−d− four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e+e+e−e−) and quadrions of the a+b+b−b−, a+b+a−b−, and a+a+b−c− types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.

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.

Classical scaling and the correspondence between the coupled rate equation and molecular dynamics models for the evolution of ultracold neutral plasma

Coupled rate equation calculations demonstrate that the variational rate theory models for the three-body electron–electron–ion scattering dynamics associated with ultracold plasma evolution scale with density in accordance with the classical mechanics of a Coulomb system. Completeness of scaling requires a broad domain of Rydberg levels over which a quasi-equilibrium can be established. For given initial conditions, the predicted evolution of electron temperature with time changes with the choice of nmax, i.e. the highest Rydberg orbital populated by three-body recombination. But, if the criterion that defines nmax scales with density, then the results scale. Molecular dynamics calculations distinguish bound Rydberg states by an electron–ion distance criterion, Rmax, which is represented in scaled coordinates by Rmax = rmaxaws, where aws represents the Wigner–Seitz radius and rmax is chosen arbitrarily. The rate equation calculations best conform with the output of molecular dynamics simulations for values of nmax defined by a thermal criterion, . In a hydrogenic limit, the thermal criterion equates with a scaled distance criterion when rmax = Γe/2, where Γe = e2/4πϵ0awskBTe describes the degree of electron correlation. Molecular dynamics simulations conventionally attenuate the Coulomb potential by means of a term, C, . Reference to rate equation calculations suggests a connection between the soft-core term, C, and nmin, the lowest Rydberg level considered in the relaxation of the plasma to a quasi-steady state.

Bound States in Coulomb Systems ‐ Old Problems and New Solutions

AbstractWe analyze the quantum statistical treatment of bound states in Hydrogen considered as a system of electrons and protons. Within this physical picture we calculate analytically isotherms of pressure for Hydrogen in a broad density region and compare to some results from the chemical picture. Our study is restricted to the range of intermediate temperatures 104K &lt; T &lt; 105K and not too high densities n &lt; 1024 protons per cm3, the formation of molecules is neglected. First we resume in detail the two transitions along isotherms:(i) formation of bound states occurring by increasing the density from low to moderate values,(ii) the destruction of bound states in the high density region, modelled here by Pauli‐Fock effects. Avoiding chemical models we will show, why bound states according to a discrete part of the spectra occur only in a valley in the T‐p plane. First we study virial expansions in the canonical ensemble and then in the grand canonical ensemble. We show that in fugacity representations the population of bound states saturates at higher density and that a combination of both representations provides quickly converging equations of state. In the case of degenerate systems we calculated first the density‐dependent energy levels, and find the pressure in Hartree‐Fock‐Wigner approximation showing the prominent role of Pauli blocking and Fock effects in the selfenergy (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Fermion correlation inequalities derived from G- and P-conditions

It is shown in this paper that the G-Condition and the P-Condition from representability imply the fermion correlation estimate from [1] which, in turn, is known to yield a nontrivial bound on the accuracy of the Hartree–Fock approximation for large Coulomb systems.

Integrable generalizations of oscillator and Coulomb systems via action–angle variables

Oscillator and Coulomb systems on N-dimensional spaces of constant curvature can be generalized by replacing their angular degrees of freedom with a compact integrable (N−1)-dimensional system. We present the action–angle formulation of such models in terms of the radial degree of freedom and the action–angle variables of the angular subsystem. As an example, we construct the spherical and pseudospherical generalization of the two-dimensional superintegrable models introduced by Tremblay, Turbiner and Winternitz and by Post and Winternitz. We demonstrate the superintegrability of these systems and give their hidden constant of motion.

Convergent close-coupling calculations of helium single ionization by antiproton impact

We apply the fully quantum-mechanical convergent close-coupling method to the calculation of antiproton scattering on the ground state of helium. The helium target is treated as a three-body Coulomb system using frozen-core and multiconfiguration approximations. The electron-electron correlation of the target is fully treated in both cases. Though both calculations yield generally good agreement with experiment for the total ionization cross sections, the multiconfiguration results are substantially higher at the lower energies than the frozen-core ones. Calculated longitudinal ejected electron and recoil-ion momentum distributions for the single ionization of helium are in good agreement with the experiment.

Thermal properties of ionic systems near the liquid-liquid critical point

Isobaric heat capacity per unit volume, C(p), and excess molar enthalpy, h(E), were determined in the vicinity of the critical point for a set of binary systems formed by an ionic liquid and a molecular solvent. Moreover, and, since critical composition had to be accurately determined, liquid-liquid equilibrium curves were also obtained using a calorimetric method. The systems were selected with a view on representing, near room temperature, examples from clearly solvophobic to clearly coulombic behavior, which traditionally was related with the electric permittivity of the solvent. The chosen molecular compounds are: ethanol, 1-butanol, 1-hexanol, 1,3-dichloropropane, and diethylcarbonate, whereas ionic liquids are formed by imidazolium-based cations and tetrafluoroborate or bis-(trifluromethylsulfonyl)amide anions. The results reveal that solvophobic critical behavior-systems with molecular solvents of high dielectric permittivity-is very similar to that found for molecular binary systems. However, coulombic systems-those with low permittivity molecular solvents-show strong deviations from the results usually found for these magnitudes near the liquid-liquid phase transition. They present an extremely small critical anomaly in C(p)-several orders of magnitude lower than those typically obtained for binary mixtures-and extremely low h(E)-for one system even negative, fact not observed, up to date, for any liquid-liquid transition in the nearness of an upper critical solution temperature.

Heliumlike and lithiumlike ionic sequences: Critical charges

In nonrelativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge $Z$ and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without any visible irregularities. Thus, for both systems the physical integer charges $Z=1,\phantom{\rule{0.222222em}{0ex}}2,...$ do not play a distinguished role as would be associated with charge quantization. By definition, a critical charge ${Z}_{\text{cr}}$ is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For both systems the critical charges are found, ${Z}_{\text{cr},2e}=0.910850$ and ${Z}_{\text{cr},3e}=2.0090$, respectively. Based on numerical analysis, the Puiseux expansion in fractional powers of $(Z\ensuremath{-}{Z}_{\text{cr}})$ is constructed for both systems. Our results indicate the existence of a square-root branch point singularity at ${Z}_{\text{cr}}$ with exponent 3/2. A connection between the critical charge and the radius of convergence of $1/Z$ expansion is briefly discussed.

Classical spectrum generating algebra of the Kepler–Coulomb system and action-angle variables

The classical spectrum generating algebra for the one-dimensional Kepler–Coulomb system is computed and a set of two corresponding constants of motion depending explicitly on time is obtained. Such constants supply the solution to the motion in an algebraic way. The connection of the spectrum generating algebra and the action-angle variables of the system is also shown.

Coulomb ensemble of charged diamagnetic macroparticles in an inhomogeneous magnetic field under microgravity conditions

The formation of strongly nonideal Coulomb systems of a large number (∼104) of charged diamagnetic macroparticles in a cusp magnetic trap under microgravity conditions has been experimentally studied. The experiments have performed in the Russian segment of the International Space Station in the framework of the Coulomb Crystal experiment. Using the data of the videorecording of the positions of the particles in the magnetic trap, the magnetic susceptibility and charge of the particles have been estimated and the period of the oscillations of the cloud of the particles, as well as the damping rate of oscillations, has been determined.

Critical charges of simple coulomb molecular systems: One‐two electron case

AbstractWe consider some Coulomb systems with several infinitely massive centers of charge Z and one or two electrons: (Z,e), (2Z,e), (3Z,e), (4Z,e), (2Z,e,e), and (3Z,e,e). It is shown that the physical, integer charges Z = 1,2,… do not play a distinguished role for the total energy and for the equilibrium configuration of a system, giving no indication of a charge quantization. By definition, a critical charge Zcr for a given Coulomb system (nZ,e) or (nZ,e,e) is a charge which separates the domain of the existence of bound states from the domain of unbound states (the domain of stability), the continuum (the domain of instability). For all the above‐mentioned systems critical charges Zcr as well as equilibrium geometrical configurations are found. Furthermore, an indication to a branch point singularity at Z = Zcr with exponent 3/2 was obtained. It is demonstrated that in the domain of the existence the optimal geometrical configuration for both (nZ,e) at n = 2,3,4 and (nZ,e,e) at n = 2,3 corresponds to the Platonic body. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Solutions to quasi-relativistic multi-configurative Hartree–Fock equations in quantum chemistry

We establish the existence of infinitely many distinct solutions to the multi-configurative Hartree–Fock type equations for N -electron Coulomb systems with quasi-relativistic kinetic energy − α − 2 Δ x n + α − 4 − α − 2 for the n th electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove the existence of a ground state. The results are valid under the hypotheses that the total charge Z tot of K nuclei is greater than N − 1 and that Z tot is smaller than a critical charge Z c . The proofs are based on a new application of the Lions–Fang–Ghoussoub critical point approach to nonminimal solutions on a complete analytic Hilbert–Riemann manifold, in combination with density operator techniques.