Coulomb Systems Research Articles

Erratum to: Bose–Einstein condensate and singularities of the frequency dispersion of the permittivity in a disordered Coulomb system

In the framework of linear response theory, we consider the frequency dispersion of the permittivity of a disordered Coulomb system in the presence of the one-particle Bose–Einstein condensate for nuclei. We show that the superconductivity of nuclei exists in such a system and is manifested in the Meissner effect for a weakly nonuniform low-frequency electromagnetic field. The obtained result offers an opportunity to solve the problem of the presence of the one-particle Bose–Einstein condensate in superfluid He-II based on direct experiments.

Solitonic natural orbitals.

The dependence of the natural amplitudes of the harmonium atom in its ground state on the confinement strength ω is thoroughly investigated. A combination of rigorous analysis and extensive, highly accurate numerical calculations reveals the presence of only one positive-valued natural amplitude ("the normal sign pattern") for all ω≥12. More importantly, it is shown that unusual, weakly occupied natural orbitals (NOs) corresponding to additional positive-valued natural amplitudes emerge upon sufficient weakening of the confinement. These solitonic NOs, whose shapes remain almost invariant as their radial positions drift toward infinity upon the critical values of ω being approached from below, exhibit strong radial localization. Their asymptotic properties are extracted from the numerical data and their relevance to calculations on fully Coulombic systems is discussed.

Absence of a Ground State for Bosonic Coulomb Systems with Critical Charge

We consider bosonic Coulomb systems with $N$-particles and $K$ static nuclei. Let $E_N^Z$ denote the ground state energy of a bosonic molecule of the total nuclear charge $Z$. We prove that the system has no normalizable ground state when $E_{N}^{N-1} = E_{N-1}^{N-1}$.

Communication: Systematic elimination of Stokes divergences emanating from complex phase space caustics.

Stokes phenomenon refers to the fact that an asymptotic expansion of complex functions can differ in different regions of the complex plane, and that beyond the so-called Stokes lines the expansion has an unphysical divergence. An important special case is when the Stokes lines emanate from phase space caustics of a complex trajectory manifold. In this case, symmetry determines that to second order there is a double coverage of the space, one portion of which is unphysical. Building on the seminal but laconic findings of Adachi, we show that the deviation from second order can be used to rigorously determine the Stokes lines and therefore the region of the space that should be removed. The method has applications to wavepacket reconstruction from complex valued classical trajectories. With a rigorous method in hand for removing unphysical divergences, we demonstrate excellent wavepacket reconstruction for the Morse, Quartic, Coulomb, and Eckart systems.

Highly accurate bound state calculations of the two-center molecular ions by using the universal variational expansion for three-body systems

The universal variational expansion for the non-relativistic three-body systems is explicitly constructed. Three-body universal expansion can be used to perform highly accurate numerical computations of the bound state spectra in arbitrary three-body systems, including Coulomb three-body systems with arbitrary particle masses and electric charges. Our main interest is related to the adiabatic three-body systems which contain one bound electron and two heavy nuclei of hydrogen isotopes: the protium $p$, deuterium $d$ and tritium $t$. We also consider the analogous (model) hydrogen ion ${}^{\infty}$H$^{+}_2$ with the two infinitely heavy nuclei. PACS number(s): 36.10.-k and 36.10.Dr

Bose–Einstein Condensate and Singularities of the Frequency Dispersion of the Permittivity in a Disordered Coulomb System

Bose–Einstein Condensate and Singularities of the Frequency Dispersion of the Permittivity in a Disordered Coulomb System

Matrix factorization method for actual atoms and molecules

Matrix mechanics is developed to describe the bound state spectra in few- and many-electron atoms, ions and molecules. Our method is based on the matrix factorization of many-electron (or many-particle) Coulomb Hamiltonians which are written in hyperspherical coordinates. As follows from the results of our study the bound state spectra of many-electron (or many-particle) Coulomb Hamiltonians always have the `ladder' structure and this fundamental fact can be used to determine and investigate the bound states in various few- and many-body Coulomb systems.

Thermodynamics and dynamics of two-dimensional systems with dipolelike repulsive interactions.

Thermodynamics and dynamics of a classical two-dimensional system with dipolelike isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical approximations. This interaction potential, which decays as an inverse cube of the interparticle distance, belongs to the class of very soft long-ranged interactions. As a result, the investigated system exhibits certain universal properties that are also shared by other related soft-interacting particle systems (like, for instance, the one-component plasma and weakly screened Coulomb systems). These universalities are explored in this article to construct a simple and reliable description of the system thermodynamics. In particular, Helmholtz free energies of the fluid and solid phases are derived, from which the location of the fluid-solid coexistence is determined. The quasicrystalline approximation is applied to the description of collective modes in dipole fluids. Its simplification, previously validated on strongly coupled plasma fluids, is used to derive explicit analytic dispersion relations for the longitudinal and transverse wave modes, which compare satisfactory with those obtained from direct MD simulations in the long-wavelength regime. Sound velocities of the dipole fluids and solids are derived and analyzed.

Accurate correlation energies in one-dimensional systems from small system-adapted basis functions

We propose a general method for constructing system-dependent basis functions for correlated quantum chemical calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and wavelets. In a one-dimensional mimic of Coulomb systems, it requires only 2-3 basis functions per electron to achieve chemical accuracy, and reproduces the natural orbitals. We illustrate its effectiveness for molecular energy curves and chains of many atoms. We discuss the promise and challenges for realistic quantum chemical calculations.

Inner pressure and energy of a Coulomb system in an electrodynamic trap

The results of calculations of the inner pressure and the energy of strongly coupled Coulomb systems in a Paul trap carried out by means of statistical theory of the liquid state are presented. Pair correlation functions of the Coulomb systems have been obtained. Full energy of the system, internal pressure, and the Coulomb coupling parameter Γ were calculated using the inter‐particle Coulomb potential. The considered system is highly non‐ideal with the coupling parameter of order Γ = 1010.

International Conference “Strongly Coupled Coulomb Systems” Kiel, Germany (July 30th–August 4th, 2017)

Contributions to Plasma PhysicsVolume 58, Issue 2-3 p. 76-81 PREFACE International Conference “Strongly Coupled Coulomb Systems” Kiel, Germany (July 30th–August 4th, 2017) First published: 25 March 2018 https://doi.org/10.1002/ctpp.201790032Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume58, Issue2-3Special Issue: International Conference Strongly Coupled Coulomb Systems July 30th – August 4th, 2017, Kiel, Germany, Part IIFebruary-March 2018Pages 76-81 RelatedInformation

Kinetic theory for strongly coupled Coulomb systems.

The calculation of dynamical properties for matter under extreme conditions is a challenging task. The popular Kubo-Greenwood model exploits elements from equilibrium density-functional theory (DFT) that allow a detailed treatment of electron correlations, but its origin is largely phenomenological; traditional kinetic theories have a more secure foundation but are limited to weak ion-electron interactions. The objective here is to show how a combination of the two evolves naturally from the short-time limit for the generator of the effective single-electron dynamics governing time correlation functions without such limitations. This provides a theoretical context for the current DFT-related approach, the Kubo-Greenwood model, while showing the nature of its corrections. The method is to calculate the short-time dynamics in the single-electron subspace for a given configuration of the ions. This differs from the usual kinetic theory approach in which an average over the ions is performed as well. In this way the effective ion-electron interaction includes strong Coulomb coupling and is shown to be determined from DFT. The correlation functions have the form of the random-phase approximation for an inhomogeneous system but with renormalized ion-electron and electron-electron potentials. The dynamic structure function, density response function, and electrical conductivity are calculated as examples. The static local field corrections in the dielectric function are identified in this way. The current analysis is limited to semiclassical electrons (quantum statistical potentials), so important quantum conditions are excluded. However, a quantization of the kinetic theory is identified for broader application while awaiting its detailed derivation.

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system II. Vacuum energy

Nonperturbative vacuum polarization effects are explored for a supercritical Dirac–Coulomb system with [Formula: see text] in 2+1[Formula: see text]D, based on the original combination of analytical methods, computer algebra and numerical calculations, proposed recently in Refs. 1–3. Both the vacuum charge density [Formula: see text] and vacuum energy [Formula: see text] are considered. Due to a lot of details of calculation the whole work is divided into two parts I and II. Taking account of results, obtained in the part I4 for [Formula: see text], in the present part II, the evaluation of the vacuum energy [Formula: see text] is investigated with emphasis on the renormalization and convergence of the partial expansion for [Formula: see text]. It is shown that the renormalization via fermionic loop turns out to be the universal tool, which removes the divergence of the theory both in the purely perturbative and essentially nonperturbative regimes of the vacuum polarization. The main result of calculation is that for a wide range of the system parameters in the overcritical region [Formula: see text] turns out to be a rapidly decreasing function [Formula: see text] with [Formula: see text] and [Formula: see text] being the size of the external Coulomb source. To the end the similarity in calculations of [Formula: see text] in 2+1 and 3+1[Formula: see text]D is discussed, and qualitative arguments are presented in favor of the possibility for complete screening of the classical electrostatic energy of the Coulomb source by the vacuum polarization effects for [Formula: see text] in 3+1[Formula: see text]D.

Nonperturbative vacuum polarization effects in two-dimensional supercritical Dirac–Coulomb system I. Vacuum charge density

Based on the original combination of analytical methods, computer algebra tools and numerical calculations, proposed recently in Refs. 1–3, the nonperturbative vacuum polarization effects in the 2+1[Formula: see text]D supercritical Dirac–Coulomb system with [Formula: see text] are explored. Both the vacuum charge density [Formula: see text] and vacuum energy [Formula: see text] are considered. The main result of the work is that in the overcritical region [Formula: see text] turns out to be a rapidly decreasing function [Formula: see text] with [Formula: see text] and [Formula: see text] being the size of the external Coulomb source. Due to a lot of details of calculation the whole work is divided into two parts I and II. In the present part I, we consider the evaluation and behavior of the vacuum density [Formula: see text], which further is used in part II for evaluation of the vacuum energy, with emphasis on the renormalization, convergence of the partial expansion for [Formula: see text] and behavior of the integral induced charge [Formula: see text] in the overcritical region.

Phase transitions in local equation-of-state approximation and anomalies of spatial charge profiles in non-uniform plasma

Impressive appearance of discontinuities in equilibrium spatial charge profiles in non-uniform Coulomb systems is under discussions in wide number of thermoelectrostatics problems. Such discontinuities are considered as peculiar micro-level manifestation of phase transitions and intrinsic macro-level non-ideality effects in local equation of state (EOS), which should be used for description of non-ideal ionic subsystem in frames of local-density (or “pseudofluid”, or “jellium” etc) approximation. Such discontinuities were discussed already by the authors for electronic subsystems. Special emphasis is made in present paper on the mentioned above non-ideality effects in non-uniform ionic subsystems, such as micro-ions profile within screening “cloud” around macro-ion in complex (dusty, colloid etc) plasmas, equilibrium charge profile in ionic traps or (and) in the neighborhood vicinity of “charged wall” etc). Multiphase EOS for simplified ionic model of classical charged hard spheres on uniformly compressible electrostatic compensating background was constructed and several illustrative examples of discussed discontinuous ionic profiles were calculated.

Two-Parameter Harmonic Oscillator Expansion Method for Calculating Non-Relativistic Ground State Energy of Coulomb Three-Particle Systems with Two Identical Particles

The variational method in oscillator representation with individual parameters for each Jacobi coordinate is applied to the non-relativistic calculation of the ground state energy of a number of three-particle Coulomb systems, consisting of two identical particles and a different one. The accuracy and convergence rate of the calculations in the constructed oscillator basis are studied up to a total of 28 oscillator quanta. The results are compared with those of the traditional approach using only one such nonlinear variational parameter. The method with individual parameters for Jacobi coordinates is found to possess a number of advantages as compared to the traditional approach.

Peculiarities of the momentum distribution functions of strongly correlated charged fermions

New numerical version of the Wigner approach to quantum thermodynamics of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. An explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted for by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. A new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been developed. Calculations of the momentum distribution functions and the pair correlation functions of degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of the obtained momentum distribution functions of strongly correlated Coulomb systems with the Maxwell–Boltzmann and the Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in high energy quantum ‘tails’.

Simulations of Coulomb systems confined by polarizable surfaces using periodic Green functions.

We present an efficient approach for simulating Coulomb systems confined by planar polarizable surfaces. The method is based on the solution of the Poisson equation using periodic Green functions. It is shown that the electrostatic energy arising from the surface polarization can be decoupled from the energy due to the direct Coulomb interaction between the ions. This allows us to combine an efficient Ewald summation method, or any other fast method for summing over the replicas, with the polarization contribution calculated using Green function techniques. We apply the method to calculate density profiles of ions confined between the charged dielectric and metal surfaces.

International Conference “Strongly Coupled Coulomb Systems” Kiel, Germany (July 30th–August 4th, 2017)

International Conference “Strongly Coupled Coulomb Systems” Kiel, Germany (July 30^th–August 4^th, 2017)

A tribute to Dietrich Kremp

Dietrich Kremp (1937–2017) made important contributions to statistical physics, especially quantum statistics, plasma physics, and the physics of electrolytes. He was a recognized member of the strongly coupled Coulomb systems and non‐ideal plasmas communities, and his text books continue to have a profound influence on these fields.