Coulomb Systems Research Articles

The Jancovici–Lebowitz–Manificat Law for Large Fluctuations of Random Complex Zeroes

Consider a Gaussian Entire Function $$f(z) = \sum_{k=0}^\infty \zeta_k \frac{z^k}{\sqrt{k!}}\, ,$$ where $${\zeta_0, \zeta_1, \dots }$$ are Gaussian i.i.d. complex random variables. The zero set of this function is distribution invariant with respect to the isometries of the complex plane. Let n(R) be the number of zeroes of f in the disk of radius R. It is easy to see that $${\mathbb{E}n(R) = R^2}$$ , and it is known that the variance of n(R) grows linearly with R (Forrester and Honner). We prove that, for every α > 1/2, the tail probability $${\mathbb{P} \{ |n(R) - R^2 | > R^\alpha \}}$$ behaves as exp $${\left[-R^{\varphi (\alpha)}\right]}$$ with some explicit piecewise linear function $${\varphi(\alpha)}$$ . For some special values of the parameter α, this law was found earlier by Sodin and Tsirelson, and by Krishnapur. In the context of charge fluctuations of a one-component Coulomb system of particles of one sign embedded into a uniform background of another sign, a similar law was discovered some time ago by Jancovici, Lebowitz and Manificat.

Self-consistent spectral function for non-degenerate Coulomb systems and analytic scaling behaviour

Novel results for the self-consistent single-particle spectral function and self-energy are presented for non-degenerate one-component Coulomb systems at various densities and temperatures. The GW(0)-method for the dynamical self-energy is used to include many-particle correlations beyond the quasi-particle approximation. The self-energy is analysed over a broad range of densities and temperatures (n = 1017 cm−3–1027 cm−3, T = 102 eV/kB–104 eV/kB). The spectral function shows a systematic behaviour, which is determined by collective plasma modes at small wavenumbers and converges towards a quasi-particle resonance at higher wavenumbers. In the low density limit, the numerical results comply with an analytic scaling law that is presented for the first time. It predicts a power-law behaviour of the imaginary part of the self-energy, ImΣ ∝ −n1/4. This resolves a long time problem of the quasi-particle approximation which yields a finite self-energy at vanishing density.

Explanation of the formation dynamics of the bound state with ion implantation

Taking into account the structure and the size of localized electrons the density matrix of localized electrons is analytically derived. In the framework of Kohn's approximation the analytical expression is used for the density matrix, and the additional potential for the three-body Coulomb systems is determined. Our result shows that, the consideration of the structure and size of localized electrons leads to an additional potential. If the size parameter is small, then the additional potential is the oscillator one. This gives a possibility to explain experimental results.

“Phantom ion effect” and the contact potential of the water-vapor interface

The contact (junction) potential between water-vapor and water-oil interfaces is studied theoretically. Unlike the previous studies, we show that ionic contribution to the contact potential vanishes when the concentration of aqueous electrolyte goes to zero. The incorrect prediction of a large ionic contribution to the junction potential in the infinite dilution limit, obtained in the earlier studies, is traced back to the inappropriate use of the grand-canonical ensemble for strongly inhomogeneous Coulomb systems. It is shown that for these systems, the thermodynamic limit is not reached even when the number of particles is astronomically large, on the order of 10(24). There is, therefore, no equivalence between statistical ensembles. For realistic, finite size systems, canonical calculation predicts a vanishing ionic contribution to the junction potentials of water-vapor and water-oil interfaces even for very concentrated electrolyte solutions.

On solutions of Coulomb system and its generalization to the Aharonov–Bohm effect

The paper numerically analyzes the Aharonov–Bohm effect of an infinitely thin magnetic flux for its influence on a two- or three-dimensional (3d) solutions of Coulomb system in momentum and coordinate spaces. For any definitive eigenstate, it is shown that the flux shifts the position of the most probable radius (MPR) of a probability distribution inward or outward in momentum or coordinate spaces, respectively. Moreover, the probability density of the shifted MPR is amplified in the momentum space, while reduced in the coordinate space. Since the Coulomb force among charged particles dominate the structure of matter, shifting of the MPR controlling by the flux effect may be beneficial to the construction of nanostructure by manipulating the atomic and molecular bonds.

Fast-Projectile Stopping Power of Quantal Multicomponent Strongly Coupled Plasmas

The Bethe-Larkin formula for the fast-projectile stopping power is extended to multicomponent plasmas. The results are to contribute to the correct interpretation of the experimental data, which could permit us to test existing and future models of thermodynamic, static, and dynamic characteristics of strongly coupled Coulomb systems.

On the Coulomb–dipole transition in mesoscopic classical and quantum electron–hole bilayers

We study the Coulomb-to-dipole transition which occurs when the separation d of an electron–hole bilayer system is varied with respect to the characteristic in-layer distances. An analysis of the classical ground state configurations for harmonically confined clusters with N ⩽ 30 electron–hole pairs reveals that the energetically most favourable state can differ from that of two-dimensional pure dipole or Coulomb systems. Performing a normal mode analysis for the N = 19 cluster it is found that the lowest mode frequencies exhibit drastic changes when d is varied. Furthermore, we present quantum-mechanical ground states for N = 6, 10 and 12 spin-polarized electrons and holes. We compute the single-particle energies and orbitals in self-consistent Hartree–Fock approximation over a broad range of layer separations and coupling strengths between the limits of the ideal Fermi gas and the Wigner crystal.

Electron stripping and reattachment at atomic centers using attosecond half-cycle pulses

We investigate the response of two three-body Coulomb systems when driven by attosecond half-cycle pulses: The electron transfer between two hydrogen atomic centers and the double ionization of the helium atom. Using very short half-cycle pulses (HCPs) which effectively deliver ``kicks'' to the electrons, we first study how a carefully chosen sequence of HCPs can be used to control to which of one of the two fixed atomic centers the electron gets reattached (HCP assisted electron transfer). Moving from one electron in two atomic centers to two electrons in one atomic center we then study the double ionization from the ground state of He by a sequence of attosecond time-scale HCPs, with each electron receiving effectively a ``kick'' from each HCP. We investigate how the net electric field of the sequence of HCPs affects the total and differential ionization probabilities.

Asymptotic regularity of solutions to Hartree–Fock equations with Coulomb potential

AbstractWe study the asymptotic regularity of solutions to Hartree–Fock (HF) equations for Coulomb systems. To deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo‐differential operators on conical manifolds. First, the non‐self‐consistent‐field case is considered, which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator, which guarantee ellipticity for the local part of the Fock operator on the open stretched cone ℝ+ × S2. This proves the existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed‐point approach based on Cancès and Le Bris analysis of the level‐shifting algorithm, we show via another bootstrap argument that the corresponding self‐consistent‐field solutions to the HF equation have the same type of asymptotic regularity. Copyright © 2008 John Wiley & Sons, Ltd.

Self-adjoint extensions of Coulomb systems in 1, 2 and 3 dimensions

We study the nonrelativistic quantum Coulomb hamiltonian (i.e., inverse of distance potential) in R n , n = 1 , 2 , 3 . We characterize their self-adjoint extensions and, in the unidimensional case, present a discussion of controversies in the literature, particularly the question of the permeability of the origin. Potentials given by fundamental solutions of Laplace equation are also briefly considered.

On the theory of nonlinear response in a nonideal plasma

A theory of nonlinear response is developed for studying nonlinear phenomena and nonlinear transport processes in nonideal Coulomb systems. Temporal plasma echo and transformation of waves in a nonideal Coulomb system are studied on the basis of the theory of nonlinear response to mechanical perturbations. General constraints imposed on nonlinear response functions are considered, and the model for determining quadratic response functions is formulated. The conditions for the emergence of temporal plasma echo and wave transformation are determined. It is shown that these nonlinear effects in a nonideal plasma can be initiated by ultrashort field pulses. A theory of transport is developed for determining the Burnett transport properties of a nonideal multielement plasma. A procedure is proposed for comparing the phenomenological conservation equations for a charged continuous medium and equations of motion for the operators of corresponding dynamic variables. The Mori algorithm is used for deriving the equations of motion for operators of dynamic variables in the form of generalized Langevin equations. The linearized Burnett approximation is considered in detail. The properties of the matrices of coefficients of higher-order derivatives in the system of conservation equations in the linearized Burnett approximation, which are important for hydrodynamic applications, are discussed. Various versions of the theory of nonlinear response are compared.

Alternative descriptors of Coulomb systems and their relationship to the kinetic energy

A family of quantities capable of fully determining every property of a Coulomb system is defined. Making use of the differential virial theorem of Nagy and March, a first-order differential equation for the functional derivative of the kinetic energy functional is derived for spherically symmetric systems.

Ion Association in [bmim][PF6]/Naphthalene Mixtures: An Experimental and Computational Study

Mixtures of room temperature ionic liquids (IL) with neutral organic molecules provide a valuable testing ground to investigate the interplay of the ionic and molecular-dipolar state in dense Coulomb systems at near ambient conditions. In the present study, the viscosity eta and the ionic conductivity sigma of 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6])/naphthalene mixtures at T = 80 degrees C have been measured at 10 stoichiometries spanning the composition range from pure naphthalene to pure [bmim][PF6]. The viscosity grows nearly monotonically with increasing IL mole fraction ( x), whereas the conductivity per ion displays a clear peak at x approximately 15%. The origin of this maximum has been investigated using molecular dynamics simulations based on a classical force field. Snapshots of the simulated samples show that the conductivity maximum is due to the gradual transition in the IL component from an ionic state at high x to a dipolar fluid made of neutral ion pairs at low x. At concentrations x < 0.20 the ion pairs condense into molecular-thin filaments bound by dipolar forces and extending in between nanometric droplets of IL. These results are confirmed and complemented by the computation of dynamic and transport properties in [bmim][PF6]/naphthalene mixtures at low IL concentration.

Liquid-liquid phase transition in solutions of ionic liquids with halide anions: Criticality and corresponding states

Abstract Measurements of the liquid-liquid phase diagrams of solutions of the ionic liquids (ILs) 1-dodecyl-3-methylimidazolium chloride (C12mimCl) in arenes (benzene, toluene, o-xylene, tetraline) and 1-tetradecyl-3-methylimidazolium chloride (C14mimCl) in CCl4 are reported and compared with those of solutions of trihexyl-tetradecyl-phosphonium halides (P666 14Cl, P666 14Br) in hydrocarbons and 1-alkyl-3-methylimidazolium tetrafluoroborates (CnmimBF4) in alcohols and water. The phase diagrams of solutions of tetrapentyl-ammonium bromide (N5555Br) in water and KI in SO2 are also discussed. Except for the KI/SO2 system, which features a lower critical solution point (LCSP), all systems have an upper critical solution point (UCSP) and show corresponding-states behavior. The experimental data are compared with results from simulations and theory concerning the model fluid of charged hard spheres in a dielectric continuum, termed restricted primitive model (RPM). The analysis in terms of of RPM variables shows agreement with the location of the critical point (CP) of the model with noticeable systematic deviations. However, for protic solvents, the CP becomes an LCSP, while in aprotic solvents the CP is a UCSP as expected for Coulomb systems. This indicates that in aprotic solvents, the phase transition is essentially determined by the Coulomb interactions, while in the solutions in protic solvents with hydrogen bonds, both Coulomb and solvophobic interactions are important.

Charged exciton resonances in two and three dimensions

Resonances of three-body Coulomb systems are investigated in two and three dimensions. The complex scaling method combined with the stochastic variational approach has been used to calculate the position (energy and width) of the resonance states. The dependence of the resonance states on the mass ratio of the constituents and the dimensionality of the space is studied. It is found that the width of the resonance states behaves very differently in 2D and 3D for molecule-like cation systems. The calculated lifetimes of the resonances are in the nano- and picosecond region, and these states might be experimentally observable in excitonic trions in semiconductor quantum dots.

Yukawa potentials in systems with partial periodic boundary conditions. II. Lekner sums for quasi-two-dimensional systems

Yukawa potentials may be long-ranged when the Debye screening length is large. In computer simulations, such long-ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we provided Ewald sums for quasi-two-dimensional systems with Yukawa interaction potentials [J. Chem. Phys. 126, 056101 (2007); Molec. Phys. paper I of this series]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two-dimensional systems with Yukawa interaction potentials and we give numerical tests for practical implementations. The main result of this paper is to emphasize that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work: Lekner sums should not be used for quasi-two-dimensional systems with Yukawa interaction potentials.

A re-statement of the Hohenberg–Kohn theorem and its extension to finite subspaces

Bearing in mind the insight into the Hohenberg–Kohn theorem for Coulomb systems provided recently by Kryachko (Int J Quantum Chem 103:818, 2005), we present a re-statement of this theorem through an elaboration on Lieb’s proof as well as an extension of this theorem to finite subspaces.

Warm Dense Matter and Strongly Coupled Plasmas Created by Intense Heavy Ion Beams and XUV-Free Electron Laser: An Overview of Spectroscopic Methods

High density plasma physics, radiation emission/scattering and related atomic physics, spectroscopy and diagnostics are going to make large steps forward due to new experimental facilities providing beams of intense heavy ions and X/XUV free electron laser radiation. These facilities are currently being established at GSI-Darmstadt and DESY-Hamburg in Germany to access new and complementary parameter regimes for basic research which have never been obtained in laboratories so far: homogenous benchmark samples near solid density and temperatures from eV up to keV. This will provide important impact to many disciplines like astrophysics, atomic physics in dense environments, dense and strongly coupled plasma effects, radiation emission, equation of state. The spectroscopic analysis of the radiation emission plays a key role in this research to investigate the dynamics of electric fields in multi-particle coupled Coulomb systems and the modification of plasma statistics.

Probing ultrafast electron correlation with double attosecond pulses

Double ionization of He by two intense attosecond pulses has been investigated by using the time-dependent close-coupling method. By adjusting the time delay between the two attosecond pulses so as to coordinate the sequential two-photon absorption in He, we can examine electron correlation effects in this three-body Coulomb system. The double-ionization cross-sections from sequential two-photon absorption indicate that the correlation time between the two electrons [partially/fully ionized], on the order of ∼1.5 fs in the specific case of photon energy eV, can be measured. This demonstrates the feasibility of directly probing ultrafast electron correlation in the time domain.

Polynomial Solution of Non-Central Potentials

We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.