Coulomb Systems Research Articles

Spherical confinement of coulombic systems inside an impenetrable box: H atom and the Hulthén potential

The generalized pseudospectral method is used to study spherical confinement in two simple Coulombic systems: (i) well celebrated and heavily studied H atom (ii) relatively less explored Hulthén potential. In both instances, arbitrary cavity size as well as low and higher states are considered. Apart from bound state eigenvalues, eigenfunctions, expectation values, quite accurate estimates of the critical cage radius for H atom for all the 55 states corresponding to , are also examined. Some of the latter are better than previously reported values. Degeneracy and energy ordering under the isotropic confinement situation are discussed as well. The method produces consistently high‐quality results for both potentials for small as well as large cavity size. For the H atom, present results are comparable to best theoretical values, while for the latter, this work gives considerably better estimates than all existing work so far. © 2014 Wiley Periodicals, Inc.

Towards Stronger Coulomb Coupling in an Ultracold Neutral Plasma

AbstractUltracold neutral plasmas are strongly coupled Coulomb systems that are generated by photoionizing lasercooled atoms close to the ionization threshold. The strong coupling parameter Γ is limited at times later than ∼100 ns by disorder‐induced heating. A recent simulation predicted that higher values of Γ can be realized in ultracold neutral plasmas if the plasma ions are excited to higher ionization states. In this paper we present recent results from an experiment that increases the strong coupling of an ultracold neutral plasma by promoting the plasma ions to the second ionization state. Using laser‐induced fluorescence we map out the ion velocity distribution of the Ca+ ions in a partially doubly ionized plasma and show that the heating due to the second ionization depends on the timing of the second ionization laser pulses. We compare our results to MD simulations, which estimate that Γ increases from approximately 2.5 to 3.6. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On one approach to the definition of Burnett kinetic coefficients of dense charged matter

The microscopic expressions of the Burnett kinetic coefficients corresponding to thermal disturbances (temperature, mass velocity, etc.) have been found in the long-wavelength and low-frequency limits of the correlations functions. The formulae are derived to determine the values of the linearized Burnett kinetic coefficients. The values of the linearized Burnett kinetic coefficients have been calculated for the model Coulomb system using some available approximations.

Optical second-harmonic generation in a two-dimensional system

Several parameters that affect the optical second-harmonic generation (SHG) coefficients in the two-dimensional Coulomb system have been discussed. Due to the changes of the Coulomb potential coefficients and geometric factor, it is shown that the optical SHG coefficients' changes are effectively controlled. Moreover, the SHG coefficients depend strongly on the system size and relaxation time.

Resolving structural transitions in spherical dust clusters.

Finite systems in confining potentials are known to undergo structural transitions similar to phase transitions. However, these systems are inhomogeneous, and their "melting" point may depend on the position in the trap and vary with the particle number. Focusing on three-dimensional Coulomb systems in a harmonic trap a rich physics is revealed: in addition to radial melting we demonstrate the existence of intrashell disordering and intershell angular melting. Our analysis takes advantage of a novel melting criterion that is based on the spatial two- and three-particle distribution functions and the associated reduced entropy which can be directly measured in complex plasma experiments.

Conductivity of warm dense matter including electron-electron collisions.

We present an approach that can resolve the controversy with respect to the role of electron-electron collisions in calculating the dynamic conductivity of dense plasmas. In particular, the dc conductivity is analyzed in the low-density, nondegenerate limit where the Spitzer theory is valid and electron-electron collisions lead to the well-known reduction in comparison to the result considering only electron-ion collisions (Lorentz model). With increasing degeneracy, the contribution of electron-electron collisions to the dc conductivity is decreasing and can be neglected for the liquid metal domain where the Ziman theory is applicable. We give expressions for the effect of electron-electron collisions in calculating the conductivity in the warm dense matter region, i.e., for strongly coupled Coulomb systems at arbitrary degeneracy.

Quadratic algebra structure and spectrum of a new superintegrable system in N-dimension

We introduce a new superintegrable Kepler–Coulomb system with non-central terms in N-dimensional Euclidean space. We show this system is multiseparable and allows separation of variables in hyperspherical and hyperparabolic coordinates. We present the wave function in terms of special functions. We give an algebraic derivation of spectrum of the superintegrable system. We show how the symmetry algebra of the N-dimensional Kepler–Coulomb system is deformed to a quadratic algebra with only three generators and structure constants involving a Casimir operator of Lie algebra. We construct the quadratic algebra and the Casimir operator. We show this algebra can be realized in terms of deformed oscillator and obtain the structure function which yields the energy spectrum.

Method for laser spectroscopy of metastable pionic helium atoms

The PiHe collaboration is currently attempting to carry out laser spectroscopy of metastable pionic helium atoms using the high-intensity π− beam of the ring cyclotron facility of the Paul Scherrer Institute. These atoms are heretofore hypothetical three-body Coulomb systems each composed of a helium nucleus, a π− occupying a Rydberg state, and an electron occupying the 1s ground state. We briefly review the proposed method by which we intend to detect the laser spectroscopic signal. This complements our experiments on metastable antiprotonic helium atoms at CERN.

Time-evolving a matrix product state with long-ranged interactions

We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting one-dimensional systems, such as Coulombic and dipolar systems, and quasi two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.

Relations Among Two Methods for Computing the Partition Function of the Two-Dimensional One-Component Plasma

The two-dimensional one-component plasma ---2dOCP--- is a system composed by $n$ mobile particles with charge $q$ over a neutralizing background in a two-dimensional surface. The Boltzmann factor of this system, at temperature $T$, takes the form of a Vandermonde determinant to the power $\Gamma = q^2/(2\pi\varepsilon k_BT)$, where $\Gamma$ is the coupling constant of this Coulomb system. The partition function of the model has been computed exactly for the even values of the coupling constant $\Gamma$, and a finite number of particles $n$, by two means: 1) by recognizing that the Boltzmann factor is the square of a Jack polynomial and expanding it in an appropriate monomial base, and 2) by mapping the system onto a 1-dimensional chain of interacting fermions. In this work the connection among the two methods is derived, and some properties of the expansion coefficients for the power of the Vandermonde determinant are explored.

Critical opalescence and the true dielectric state in a Coulomb system

To study the critical opalescence effect in a two-component Coulomb system consisting of single-type electrons and nuclei, we consider the limit relations for static structure factors and analyze the singularities of the dielectric permittivity. We show that the critical opalescence effect can be observed not only at the critical point corresponding to the gas-liquid phase transition but also near the true dielectric state with zero static conductivity. With the available experimental data taken into account, we assume that the true dielectric state is the limit state of the liquid-liquid phase transition accompanied by sharp variations in the electrical conduction of the substances. We find that if the thermodynamic parameters correspond to the true dielectric state, then the critical opalescence effect can arise in the case where the squared fluctuation in the total number of electrons and nuclei in a two-component Coulomb system becomes infinite, as this occurs at the critical point corresponding to the gas-liquid phase transition.

Nature of long-range order in stripe-forming systems with long-range repulsive interactions.

We study two dimensional stripe forming systems with competing repulsive interactions decaying as r(-α). We derive an effective Hamiltonian with a short-range part and a generalized dipolar interaction which depends on the exponent α. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for α<2 long-range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When α≥2 no long-range order is possible, but a phase transition in the Kosterlitz-Thouless universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids (α=1) and dipolar magnetic films (α=3). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.

Exactly solvable deformations of the oscillator and Coulomb systems and their generalization

We present two maximally superintegrable Hamiltonian systems Hλ and Hη that are defined, respectively, on an N-dimensional spherically symmetric generalization of the Darboux surface of type III and on an N-dimensional Taub-NUT space. Afterwards, we show that the quantization of Hλ and Hη leads, respectively, to exactly solvable deformations (with parameters λ and η) of the two basic quantum mechanical systems: the harmonic oscillator and the Coulomb problem. In both cases the quantization is performed in such a way that the maximal superintegrability of the classical Hamiltonian is fully preserved. In particular, we prove that this strong condition is fulfilled by applying the so-called conformal Laplace-Beltrami quantization prescription, where the conformal Laplacian operator contains the usual Laplace- Beltrami operator on the underlying manifold plus a term proportional to its scalar curvature (which in both cases has non-constant value). In this way, the eigenvalue problems for the quantum counterparts of Hλ and Hη can be rigorously solved, and it is found that their discrete spectrum is just a smooth deformation (in terms of the parameters λ and η) of the oscillator and Coulomb spectrum, respectively. Moreover, it turns out that the maximal degeneracy of both systems is preserved under deformation. Finally, new further multiparametric generalizations of both systems that preserve their superintegrability are envisaged.

Measurement of the speed of sound by observation of the Mach cones in a complex plasma under microgravity conditions

We report the first observation of the Mach cones excited by a larger microparticle (projectile) moving through a cloud of smaller microparticles (dust) in a complex plasma with neon as a buffer gas under microgravity conditions. A collective motion of the dust particles occurs as propagation of the contact discontinuity. The corresponding speed of sound was measured by a special method of the Mach cone visualization. The measurement results are incompatible with the theory of ion acoustic waves. The estimate for the pressure in a strongly coupled Coulomb system and a scaling law for the complex plasma make it possible to derive an evaluation for the speed of sound, which is in a reasonable agreement with the experiments in complex plasmas.

A Review of Studies on Strongly‐Coupled Coulomb Systems Since the Rise of DFT and SCCS‐1977

AbstractThe conferences on “Strongly Coupled Coulomb Systems” (SCCS) arose from the “Strongly Coupled Plas‐mas” meetings, inaugurated in 1977. The progress in SCCS theory is reviewed in an ‘author‐centered’ frame to limit its scope. Our efforts, i.e., with François Perrot, sought to apply density functional theory (DFT) to SCCS calculations. DFT was then poised to become the major computational scheme for condensed matter physics. The ion‐sphere models of Salpeter and others evolved into useful average‐atom models for finite‐T Coulomb systems, as in Lieberman's Inferno code. We replaced these by correlation‐sphere models that exploit the description of matter via density functionals linked to pair‐distributions. These methods provided practical computational means for studying strongly interacting electron‐ion Coulomb systems like warm‐dense matter (WDM). The staples of SCCS are wide‐ranged, viz., equation of state, plasma spectroscopy, opacity (absorption, emission), scattering, level shifts, transport properties, e.g., electrical and heat conductivity, laser‐ and shock‐created plasmas, their energy relaxation and transient properties etc. These calculations need pseudopotentials and exchange‐correlation functionals applicable to finite‐T Coulomb systems that may be used in ab initio codes, molecular dynamics, etc. The search for simpler computational schemes has proceeded via proposals for orbital‐free DFT, statistical potentials, classical maps of quantum systems using classical schemes like HNC to include strong coupling effects (CHNC). Laughlin's classical plasma map for the fractional quantum Hall effect (FQHE) is a seminal example where we report new results for graphene. (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The Dunkl–Coulomb problem in the plane

Abstract The Dunkl–Coulomb system in the plane is considered. The model is defined in terms of the Dunkl Laplacian, which involves reflection operators, with an r − 1 potential. The system is shown to be maximally superintegrable and exactly solvable. The spectrum of the Hamiltonian is derived algebraically using a realization of so ( 2 , 1 ) in terms of Dunkl operators. The symmetry operators generalizing the Runge–Lenz vector are constructed. On eigenspaces of fixed energy, the invariance algebra they generate is seen to correspond to a deformation of su ( 2 ) by reflections. The exact solutions are given as products of Laguerre polynomials and Dunkl harmonics on the circle.

Rayleigh approximation to ground state of the Bose and Coulomb glasses.

Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties.

On the properties of systems with Bose-Einstein condensate in the Coulomb model of matter

An alternative description of the equilibrium system of interacting bosons in the presence of a Bose-Einstein condensate, based on the initial consideration of the system in a very large but finite volume, is presented. Using exact sum rules for the spectral function, the existence of a discontinuity in the energy spectrum of quasiparticles at small momenta, associated with the presence of condensate and the Coulomb interaction, is shown. The possible existence of the Meissner effect in superfluid helium as a Coulomb system with Bose-Einstein condensate for nuclei is shown.

Singular analysis and coupled cluster theory.

The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to short-range correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation.

Fano-like anti-resonances in strongly coupled binary Coulomb systems

Molecular-dynamics (MD) simulations of a strongly coupled binary ionic mixture have revealed the appearance of sharp minima in the species-resolved dynamical density fluctuation spectra. This phenomenon is reminiscent of the well-known Fano anti-resonance, occurring in various physical processes. We give a theoretical analysis using the quasi-localized charge approximation, and demonstrate that the observed phenomenon in the equilibrium spectrum is a novel manifestation of the Fano mechanism, that occurs at characteristic frequencies of the system different from the conventional classical Fano frequencies.