Coulomb Systems Research Articles

Generalized exponential functions in variational calculations of molecular systems

A generalization of exponential and Gaussian trial functions is proposed for variational calculations of few-body Coulomb systems. It is shown that the new functions allow us to express the matrix elements of the Hamiltonian in a closed form. In comparison with other methods they allow us, in the case of two-center Coulomb systems, to reduce the length of variational expansion by an order without loss of accuracy. The efficiency of the method is demonstrated in calculations of three-particle systems $ppe$, $dde$, $tte$, $\ensuremath{\mu}\ensuremath{\mu}e$ and four-particle systems ${\mathrm{H}}_{2}$ and $\text{He}{\mathrm{H}}^{+}$ of different isotopic composition.

Casimir's spheres near the Coulomb limit: energy density, pressures and radiative effects

We study the quantum mechanics of an infinitesimally thin spherical fluid shell of radius R, having continuous charge and mass densities e/a2 and m/a2 per unit area, with a R, and subject to a Debye-type cut-off on surface-parallel wave numbers. Attention is confined to the regime ? ? 4?e2R/mc2a2 1, where nonretarded (NR) Coulomb forces dominate, and the coupling to the quantized Maxwell field is only a weak perturbation. The unperturbed ground-state energy BNR is of order (e2/ma7)1/2R2. Half of BNR is kinetic energy, localized on the shell; the other half is Coulomb energy, with a density u appreciable only within distances of order a from the shell. The pressure P = 3BNR/8?R3 follows directly from the principle of virtual work: more detailed analysis shows that P/3 comes from Coulomb forces, and 2P/3 from the zero-point motion of the fluid. It seems likely that u and P behave in much the same way also for large ?. The purely Coulombic system has stable discrete-frequency excitations (plasmons); to leading order the perturbation displaces the frequencies and allows a plasmon to decay into a photon. The displacements and decay rates tally with what one infers from the exact classical multipole phase shifts, and from the already-known energy for arbitrary values of ?.

Microscopic Calculation of the Dielectric Susceptibility Tensor for Coulomb Fluids II

For a Coulomb system contained in a domain \Lambda, the dielectric susceptibility tensor \chi_{\Lambda} is defined as relating the average polarization in the system to a constant applied electric field, in the linear limit. According to the phenomenological laws of macroscopic electrostatics, \chi_{\Lambda} depends on the specific shape of the domain \Lambda. In this paper we derive, using the methods of equilibrium statistical mechanics in both canonical and grand-canonical ensembles, the shape dependence of \chi_{\Lambda} and the corresponding finite-size corrections to the thermodynamic limit, for a class of general \nu-dimensional (\nu\ge 2) Coulomb systems, of ellipsoidal shape, being in the conducting state. The microscopic derivation is based on a general principle: the total force acting on a system in thermal equilibrium is zero. The results are checked in the Debye-H\"uckel limit. The paper is a generalization of a previous one [L. \v{S}amaj, J. Stat. Phys. 100:949 (2000)], dealing with the special case of a one-component plasma in two dimensions. In that case, the validity of the presented formalism has already been verified at the exactly solvable (dimensionless) coupling \Gamma = 2.

Weighted Eigenvalue Problem Approach To The Critical Value Determination Of Screened Coulomb Potential Systems

AbstractIn this work, the radial time‐independent Schrödinger equation of a screened Coulomb potential system at the zero energy limit is first converted to a weighted eigenvalue problem of an ordinary differential operator. Then, by using an appropriate coordinate transformation, the differential equation is transformed into a form whose first and second order derivative related terms become same as the Extended Jacobi Polynomials' differential equation's corresponding terms. Only difference is the appearance of a multiplicative operator which can be considered as an effective potential. Work focuses on the point whether the solution is obtained easily depending on the structure of this potential. In this direction a screened Coulomb potential with a specific rational screening function is considered. The analytical solutions for the critical values of the screening parameter and the form of the wave function at the threshold of the continous spectrum are obtained. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Probing Two-Electron Dynamics of an Atom

Coherent short-pulse laser excitation has been used to control the approximate energy and relative proximity of two valence electrons within the same alkaline-earth atom, thereby providing insight into the dynamical evolution of a three-body Coulomb system. Our time-domain experiments enable direct experimental study of the electron dynamics at the classical limit of a two-electron atom. As an example, we look at the mechanism of autoionization for one two-electron configuration class and find that the doubly excited atom decays through a single violent electron-electron collision rather than a gradual exchange of energy between the electrons.

Three-dimensional oscillator and Coulomb systems reduced from Kähler spaces

We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kahler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid originate. Then we construct the superintegrable oscillator system on three-dimensional sphere and hyperboloid, coupled to a monopole, and find their four-dimensional origins. In the latter case the metric of configuration space is a non-Kahler one. Finally, we extend these results to the family of Kahler spaces with conic singularities.

Confined Coulomb Systems with Adsorbing Boundaries: The Two-Dimensional Two-Component Plasma

Using a solvable model, the two-dimensional two-component plasma, we study a Coulomb gas confined in a disk and in an annulus with boundaries that can adsorb some of the negative particles of the system. We obtain explicit analytic expressions for the grand potential, the pressure and the density profiles of the system. By studying the behavior of the disjoining pressure we find that without the adsorbing boundaries the system is naturally unstable, while with attractive boundaries the system is stable because of a positive contribution from the surface tension to the disjoining pressure. The results for the density profiles show the formation of a positive layer near the boundary that screens the adsorbed negative particles, a typical behavior in charged systems. We also compute the adsorbed charge on the boundary and show that it satisfies a certain number of relations, in particular an electro-neutrality sum rule.

Finite-size corrections for Coulomb systems in the Debye–Hückel regime

It has been argued that for a finite two-dimensional classical Coulomb system of characteristic size $R$, in its conducting phase, as $R\to \infty $ the total free energy (times the inverse temperature $\beta$) admits an expansion of the form: $\beta F=AR^{2}+BR+{1/6}\chi \ln R,$ where $\chi $ is the Euler characteristic of the manifold where the system lives. The first two terms represent the bulk free energy and the surface free energy respectively. The coefficients $A$ and $B$ are non-universal but the coefficient of $\ln R$ is universal: it does not depend on the detail of the microscopic constitution of the system (particle densities, temperature, etc...). By doing the usual Legendre transform this universal finite-size correction is also present in the grand potential. The explicit form of the expansion has been checked for some exactly solvable models for a special value of the coulombic coupling. In this paper we present a method to obtain these finite-size corrections at the Debye--H\"uckel regime. It is based on the sine-Gordon field theory to find an expression for the grand canonical partition function in terms of the spectrum of the Laplace operator. As examples we find explicitly the grand potential expansion for a Coulomb system confined in a disk and in an annulus with ideal conductor walls.

Computer Simulations of a Monolayer of Like-charged Particles Condensed on an Oppositely-charged Flat Area

A non-traditional approach to the computer simulation study of a class of quasi-two-dimensional Coulomb systems (charged particles confined to a layer near a charged planar surface) is presented. The essence of the approach lies in exploiting the fact that the charged confinement is of finite dimensions. The main consequence of such a finiteness is a non-zero potential gradient along the finite charged area that includes a non-zero tangential component of the electric field. A system of like-charged spherical particles confined by the planar surface that includes an oppositely charged squared area is considered as an example. We find that the like-charged particles, independent of their concentration, all become confined on the oppositely charged area, if the surface charge balances the total charge carried by the particles, and if the electrostatic coupling is sufficiently large. The local density of the particles above the charged area is not homogeneous; near the boundaries of the charged square a clear tendency of layer formation along the square sides is observed.

An efficient method for computation of long-ranged Coulomb forces in computer simulation of ionic fluids

Angular averaging of Ewald sums eliminating the nonphysical cubic symmetry of electrostatic field in the uniform ionic system under conditions of computer simulation with periodic boundaries is proposed. The resulting effective potential is central, has simple analytical form and its range is correspondent to the main box size. The approach provides a fast method for computation of electrostatic contribution to the energy of ionic fluids and other dense, uniform Coulomb systems in Monte Carlo or molecular dynamics computer simulation.

A Primer in Density Functional Theory

Density Functionals for Non-relativistic Coulomb Systems in the New Century.- Orbital-Dependent Functionals for the Exchange-Correlation Energy: A Third Generation of Density Functionals.- Relativistic Density Functional Theory.- Time-Dependent Density Functional Theory.- Density Functional Theories and Self-energy Approaches.- A Tutorial on Density Functional Theory.

Coulomb bicrystals of species with identical charge-to-mass ratios.

Structures of cold bicomponent Coulomb systems of particles with identical charge-to-mass ratios and common oscillation frequency in a spherical harmonic potential are studied by molecular dynamics simulations with up to 10(6) particles. For most initial conditions and cooling rates, the final state becomes a completely mixed core surrounded by a set of nearly degenerated double shells of separate species. For an equal amount of the two species, it is found that the ground state for larger systems consists of a simple cubic structured core surrounded by outer double-shell structures.

Quantum Fluctuations in a Four-Body Coulomb System and Breakdown of the Adiabatic Approximation

Accuracy of the Born–Oppenheimer adiabatic approximation to the ground state of a hydrogenlike molecule ( M + M + m - m - ) is examined in comparison with the exact results obtained by diffusion Monte Carlo simulations, fully incorporating quantum fluctuations. For the mass ratio m / M <0.1, the relative error in the ground-state energy is found to be less than 1%. We discuss the change in nature of the binding mechanism of this system with the increase of m / M from the usual chemical bonding at m / M ≪1 to the one in which nonadiabatic effects such as the retardation of electron response to proton motion play a crucial role.

The physics of quark‐gluon plasma and relativistic charged particle systems

AbstractQED and QCD describe different systems, but show similar features. An interesting issue is the formation of bound states and their dissolution at high densities, what is described as metallization (plasma phase transition) in Coulomb systems or as hadron to quark‐gluon phase transition in nuclear matter. (© 2003 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Sum rules and exact relations for quantal Coulomb systems

AbstractA complex response function describing a reaction of a multi‐particle system to a weak alternating external field is the boundary value of a Nevanlinna class function (i.e. a holomorphic function with non‐negative imaginary part in the upper half‐plane). Attempts of direct calculations of response functions based on standard approximations of the kinetic theory for real Coulomb condensed systems often result in considerable discrepancies with experiments and computer simulations. At the same time a relatively simple approach using only the exact values of leading asymptotic terms of the response function permits to restrict essentially a subset of Nevanlinna class functions containing this response function, and in this way to obtain sufficient data to explain and predict experimental results. Mathematical details of this approach are demonstrated on an example with the response function being the (external) dynamic electrical conductivity of cold dense hydrogen‐like plasmas. In particular, the exact values of the leading terms of asymptotic expansions of the conductivity are calculated. (© 2003 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Negative specific heat, the thermodynamic limit, and ergodicity.

Thermodynamic stability, in particular, the positivity of the specific heat in the microcanonical ensemble, is not an automatic consequence of the thermodynamic limit. But it holds under special circumstances such as for the most important case of quantum-mechanical Coulomb systems. Therefore, it is surprising that there are experimental indications to the contrary. In this Letter we study a simple model for which the microcanonical specific heat is positive, if the system is ergodic. However, if the system is not ergodic, the energy shell in phase space has some ergodic components with a negative specific heat. This provides another possible general pathway for a negative specific heat in addition to the commonly accepted, the small number of particles.

Observation of self-organized filaments in a dielectric barrier discharge of Ar gas

Symmetric self-organized discharge filaments have been observed in the rf (500 kHz) dielectric barrier discharge of Ar gas between two parallel quartz plates with a MgO film. The arrangement of the filaments is confined around the center on the quartz plate plane. With increasing voltage, the number of filaments increases, and the area of filament arrangement also increases. The arrangement of the filaments does not move if the quartz plate with a MgO film is employed, while the whole arrangement rotates without a MgO film. According to the results of current–voltage measurements, Lorentz attractive force is much smaller than Coulomb repulsive force. This suggests that a confinement potential exists as in the case of two-dimensional Coulomb systems in a parabolic potential. However, some of the filament arrangements do not match to those for charged particles in the Coulomb systems, which suggests that the confinement potential does not have pure parabolic profile.

Spherical Boundary Conditions: A Finite and System Size Independent Geometry for Simulations of Electrolytic Liquids

The system size dependence of the thermodynamic properties of electrolytic systems in "Spherical Boundary Conditions" (SBC) have been examined in this work. Coulombic systems were simulated with different system sizes (N ) for a wide range of concentrations, different ionic charges and solvent permittivities. The effects of system size upon the mean internal energy ⟨U⟩ and mean ionic activity coefficient ⟨γ ±⟩ values were determined. Our results indicated that there was no dependence of the thermodynamic properties upon system size in the non-Euclidean geometry. Different methods of extrapolating the thermodynamic properties to infinite numbers were studied in detail. In contrast to the Euclidean geometry, the method of extrapolating ⟨U⟩ or ⟨γ ±⟩ versus N -1, N -2/3 and N -1/3 was not statistically justifiable nor advantageous. Therefore, SBC is well suited to simulating systems involving long-range electrostatic interactions because the results do not dependent upon system size.

Projectile-charge sign dependence of four-particle dynamics in helium double ionization.

Double ionization of helium by 6 MeV proton impact has been explored in a kinematically complete experiment using a "reaction microscope." For the first time, fully differential cross sections for positively charged projectiles have been obtained and compared with data from 2 keV electron impact. The significant differences observed in the angular distribution of the ejected electrons are attributed to the charge sign of the projectile, resulting in different dynamics of the four-particle Coulomb system, which is not considered in the first Born approximation.

QCD moment sum rules for Coulomb systems: The charm and bottom quark masses

In this work the charm and bottom quark masses are determined from QCD moment sum rules for the charmonium and upsilon systems. To illustrate the special character of these sum rules when applied to Coulomb systems, we first set up and study the behavior of the sum rules in quantum mechanics. In our analysis, we include both the results from nonrelativistic QCD and perturbation theory at next-next-to-leading order. The moments are evaluated at different values of ${q}^{2}$ which correspond to different relative influences among the theoretical contributions. In the numerical analysis, we obtain the masses by choosing central values for all input parameters. The error is estimated from a variation of these parameters. First, the analysis is performed in the pole mass scheme. Second, we employ the potential-subtracted mass in intermediate steps of the calculation to then infer the quark masses in the $\overline{\mathrm{MS}}$ scheme. Our final results for the pole and $\overline{\mathrm{MS}}$ masses are ${M}_{c}=1.75\ifmmode\pm\else\textpm\fi{}0.15\mathrm{GeV},{m}_{c}{(m}_{c})=1.19\ifmmode\pm\else\textpm\fi{}0.11\mathrm{GeV},{M}_{b}=4.98\ifmmode\pm\else\textpm\fi{}0.125\mathrm{GeV},$ and ${m}_{b}{(m}_{b})=4.24\ifmmode\pm\else\textpm\fi{}0.10\mathrm{GeV}.$