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

Yukawa potentials are often used as effective potentials for systems such as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential; in this small screening limit, or Coulomb limit, the potential is long-ranged. As is well known in computer simulation, a simple truncation of the long-ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of space, has already been derived for the Yukawa potential [Molec. Phys. 88, 1357 (1996); J. Chem. Phys. 113, 10459 (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [J. Chem. Phys. 126, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. Special attention is paid to the Coulomb limit and its relation to the electroneutrality of systems.     

Resonances of Dirac Particle in the Yukawa Potential

We applied the complex scaling method to study the resonances of a Dirac particle in the Yukawa potential, and obtained the corresponding energies and widths. In the non-relativistic limit, our results are in excellent agreement with those by non-relativistic calculations with J-matrix approach. Furthermore, we found that the energies and widths of spin doublets are approximately degenerate, and preserve a good spin symmetry. The quality of spin symmetry is correlated with the parameters of the Yukawa potential.     

Characteristics of crystallization of complex plasmas in narrow channels

Molecular dynamics simulations are performed to analyze the dependence of the behavior of complex (dusty) plasmas in narrow three-dimensional channels on the confining potential. Dynamics of micrometer-sized particles is modeled by using Langevin thermostat and Yukawa (screened Coulomb) pair interaction potential. A detailed analysis shows that confinement strongly affects plasma crystallization characteristics and local ordering of dust grains. In particular, the formation of a new, quasi-crystalline phase induced by hard-wall confinement is revealed. Transitions between different lattice symmetries induced by changes in channel width are examined. Strong dependence of the transverse dust density profile on the shielding parameter (ratio between mean interparticle distance and screening length) can be used to manipulate the dust-grain flux in such a system.     

A derivation of the compressibility equation for liquid metals

The Kirkwood and Buff compressibility equation for multicomponent systems is applied to an assembly of ions and electrons, where the Coulomb potential is replaced by the Yukawa potential. It is then shown that the resulting formula gives the Watabe-Hasegawa-Chihara compressibility equation in the limit of infinitesimal damping constant of the Yukawa potential.     

Regge-Pole bei geschwindigkeitsabhängigen Potentialen unter Einschluß eines Yukawapotentials

The analytical behaviour of the scattering amplitude with respect to energy and angular momentum is considered for a group of soluble velocity-dependent potentials plus Yukawa potential. The Yukawa potential is brought in by means of a modified Born approximation. Convergent and semiconvergent expansions of the Jost functions are given for small and large energies.     

Mass of a lattice polaron from an extended Holstein model using the Yukawa potential

Renormalization of the mass of an electron is studied within the framework of the Extended Holstein model at strong coupling regime and nonadiabatic limit. In order to take into account an effect of screening of an electron-phonon interaction on a polaron it is assumed that the electron-phonon interaction potential has the Yukawa form and screening of the electron-phonon interaction is due to the presence of other electrons in a lattice. The forces are derived from the Yukawa type electron-phonon interaction potential. It is emphasized that the early considered screened force of (Kornilovitch (1998), Spencer et al. (2005), Hague et al. (2006), Hague and Kornilovitch (2009)) Refs. [7], [18], [19] and [22] is a particular case of the force deduced from the Yukawa potential and is approximately valid at large screening radiuses compared to the distances under consideration. The Extended Holstein polaron with the Yukawa type potential is found to be a more mobile than polaron studied in early works at the same screening regime.     

Durabiity of Neutron Star Crust

How long do neutron star mountains last? The durability of elastically deformed crust is important for neutron star physics including pulsar glitches, emission of gravitational waves from static mountains, and flares from star quakes. The durability is defined by the strength properties of the Yukawa crystals of ions, which make up the crust. In this paper we extend our previous results [Mon. Not. R. Astron. Soc. 407 , L54 (2010)] and accurately describe the dependence of the durability on crust composition (which can be reduced to the dependence on the screening length λ of the Yukawa potential). We perform several molecular dynamics simulations of crust breaking and describe their results with a phenomenological model based on the kinetic theory of strength. We provide an analytical expression for the durability of neutron star crust matter for different densities, temperatures, stresses, and compositions. This expression can also be applied to estimate durability of Yukawa crystals in other systems, such as dusty plasmas in the laboratory (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Modified coulomb law in a strongly magnetized vacuum

We study the electric potential of a charge placed in a strong magnetic field B>B(0) approximately 4.4x10(13) G, as modified by the vacuum polarization. In such a field the electron Larmour radius is much less than its Compton length. At the Larmour distances a scaling law occurs, with the potential determined by a magnetic-field-independent function. The scaling regime implies short-range interaction, expressed by the Yukawa law. The electromagnetic interaction regains its long-range character at distances larger than the Compton length, the potential decreasing across B faster than along. Correction to the nonrelativistic ground-state energy of a hydrogenlike atom is found. In the limit B = infinity, the modified potential becomes the Dirac delta function plus a regular background. With this potential the ground-state energy is finite--the best pronounced effect of the vacuum polarization.     

Structural and thermodynamic properties of a multicomponent freely jointed hard sphere multi-Yukawa chain fluid

The product-reactant Ornstein-Zernike approach, represented by the polymer mean-spherical approximation (PMSA), is utilized to describe the structure and thermodynamic properties of the fluid of Yukawa hard sphere chain molecules. An analytical solution of the PMSA for the most general case of the multicomponent freely jointed hard sphere multi-Yukawa chain fluid is presented. As in the case of the regular MSA for the hard sphere Yukawa fluid, the problem is reduced to the solution of a set of nonlinear algebraic equations in the general case, and to a single equation in the case of the factorizable Yukawa potential coefficients. Closed form analytical expressions are presented for the contact values of the monomer-monomer radial distribution function, structure factors, internal energy, Helmholtz free energy, chemical potentials and pressure in terms of the quantities, which follows directly from the PMSA solution. By way of illustration, several different versions of the hard sphere Yukawa chain model are considered, represented by one-Yukawa chains of length m, where m = 2, 4, 8, 16. To validate the accuracy of the present theory, Monte Carlo simulations were carried out and the results are compared systematically with the theoretical results for the structure and thermodynamic properties of the system at hand. In general it is found that the theory performs very well, thus providing an analytical route to the equilibrium properties of a well defined model for chain fluids.     

A new model for calculating the binding energy of the lithium nucleus under the generalized Yukawa potential and Hellmann potential

In this paper, the Schrodinger equation for a 6-body system is studied. We solve this equation for the lithium nucleus by using a supersymmetry method with several specific potentials. These potentials are the Yukawa potential, the generalized Yukawa potential and the Hellmann potential. The results of our model for all calculations show that the ground state binding energy of the lithium nucleus with these potentials is very close to that obtained experimentally.     

Dynamical Background for L-G Phase Transition in QHD-I Model

Starting from the QHD-I model, the nucleon-nucleon interaction potential in hot/dense nuclear matter is studied. We find that the attractive and repulsive Yukawa potential between nucleons is modified by the variation of Debye mass directly and, especially, the nucleon system described by this Yukawa potential will be unbounded at some critical T and μ. The critical point we get accords with that of L-G phase transition given by the P - pB phase diagram.     

Cluster formation in binary charge-stabilized colloidal suspensions confined to a two-dimensional plane

Hypernetted chain (HNC) integral equation theory has been used to study the structural features of binary charged stabilized colloidal suspensions confined to a two-dimensional plane. The particles interact via purely repulsive Yukawa intermolecular potential, the inverse screening length scaled by the average distance between strongly interacting components of the mixture (dimensionless screening parameter) being 1, 3 and 5. Results of HNC theory for one-component systems are found to be in very good agreement with that of simulation, in the parameter range of our study. Binary Yukawa systems with dimensionless screening parameters 1 and 3 are found to exhibit diffuse clusters of the weakly interacting particles, marked by the emergence of a cluster peak in the corresponding partial structure factor curves. No cluster peak is found in the system with the screening parameter 5. For the entire range of mixture parameters, the strongly interacting particles remain homogeneously distributed.     

Pressure and Stress Tensor in a Yukawa Fluid

Systems of particles interacting through a screened Coulomb potential of the Debye–Yukawa form are considered. The pressure is obtained from the stress tensor of the field corresponding to the Yukawa interaction, by a suitable statistical average. This approach is especially appropriate for systems living in a curved space. In a curved space, a self contribution to the pressure appears, and it is essential to take it into account for retrieving a correct pressure when the Yukawa interaction tends to the Coulomb interaction.     

Vapour-liquid equilibrium of the charged Yukawa fluid from Gibbs ensemble Monte Carlo simulations and the mean spherical approximation

A Gibbs ensemble Monte Carlo (GEMC) study supplemented by theoretical calculations using the mean spherical approximation (MSA) is reported for the charged Yukawa system. In this system the particles interact via an attractive Yukawa potential and a Coulomb potential. When the Coulomb potential is weak compared to the Yukawa attraction the results obtained for the vapour-liquid equilibrium from the GEMC and the MSA are very similar. On increasing the charge, the system becomes similar to the primitive model of electrolytes, and at high charges similar phenomena, such as ion association, are observed. At these charges, the MSA yields poorer results. Using both methods, an increase of the charge results in an increase of the critical temperature but a decrease of the critical density.     

Dynamical Background for L-G Phase Transition in QHD-I Model

Starting from the QHD-I model, the nucleon-nucleon interaction potential in hot/dense nuclear matter is studied. We find that the attractive and repulsive Yukawa potential between nucleons is modified by the variation of Debye mass directly and, especially, the nucleon system described by this Yukawa potential will be unbounded at some critical T and μ. The critical point we get accords with that of L-G phase transition given by the P - ρs phase diagram.     

Molecular dynamics study of two-and three-dimensional classical fluids using double Yukawa potential

We have carried out a molecular dynamics simulation of two- and three-dimensional double Yukawa fluids near the triple point. We have compared some of the static and dynamic correlation functions with those of Lennard—Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. However, when repulsive and attractive parameters occurring in double Yukawa potential are varied, we found distinct differences in static and dynamic correlation functions. We have also compared the two-dimensional correlation functions with those of three-dimensional to study the effect of dimensionality, near the triple point region.     

Reentrant transitions in colloidal or dusty plasma bilayers

The phase diagram of crystalline bilayers of particles interacting via a Yukawa potential is calculated for arbitrary screening lengths and particle densities. Staggered rectangular, square, rhombic, and triangular structures are found to be stable including a first-order transition between two different rhombic structures. For varied screening length at fixed density, one of these rhombic phases exhibits both a single and even a double reentrant transition. Our predictions can be verified experimentally in strongly confined charged colloidal suspensions or dusty plasma bilayers.     

Asymmetric mixture of hard particles with Yukawa attraction between unlike ones: a cluster algorithm simulation study

The influence of a Yukawa attraction between unlike species on the structure of an asymmetric mixture of hard particles is investigated. A recently proposed cluster algorithm for the simulation of hard particle fluids is extended in order to treat the Yukawa tail. Starting with nonoverlapping hard core configurations generated by the cluster algorithm, the attractive tail is treated according to a standard Metropolis scheme. Preliminary results on the effect of the Yukawa attraction on the pair distribution of the larger particles and the potential of mean force at infinite dilution confirm important changes in comparison with pure hard sphere mixtures.