Identical Charged Particles Research Articles

Minimal Design Principles for Icosahedral Virus Capsids

The geometrical structures of single- and multiple-shell icosahedral virus capsids are reproduced as the targets that minimize the cost corresponding to relatively simple design functions. Capsid subunits are first identified as building blocks at a given coarse-grained scale and then represented in these functions as point particles located on an appropriate number of concentric spherical surfaces. Minimal design cost is assigned to optimal spherical packings of the particles. The cost functions are inspired by the packings favored for the Thomson problem, which minimize the electrostatic potential energy between identical charged particles. In some cases, icosahedral symmetry constraints are incorporated as external fields acting on the particles. The simplest cost functions can be obtained by separating particles in disjoint nonequivalent sets with distinct interactions, or by introducing interacting holes (the absence of particles). These functions can be adapted to reproduce any capsid structure found in real viruses. Structures absent in Nature require significantly more complex designs. Measures of information content and complexity are assigned to both the cost functions and the capsid geometries. In terms of these measures, icosahedral structures and the corresponding cost functions are the simplest solutions.

Normal modes of vibrations around Hubble flow in jellium

A macroscopic Coulomb system of identical charged particles with or without a compensating background charge can evolve maintaining spatial homogeneity and isotropy that mimic the cosmological evolution of a universe with repulsive gravity. Here we study dynamics of small perturbations on the background of the corresponding Hubble flow by analyzing its normal modes of vibrations. Arbitrary disturbance of the flow can be resolved into two electroacoustic, two vortical, and one entropic modes whose dynamics is investigated. Specifically, in the zero pressure or long-wavelength limits perturbations of density and velocity evolve in a manner that is independent of the form of the initial disturbance. The same conclusion applies to vortical perturbations of the velocity for arbitrary pressure while entropic perturbations are advected by the Hubble flow. Without the background charge the underlying Hubble flow describes a Coulomb explosion whose stability with respect to small disturbances is also demonstrated.

A pure non-neutral plasma under an external harmonic field: equilibrium thermodynamics and chaos

Motivated by the precedent study of Ordenes-Huanca and Velazquez (2016 J. Stat. Mech. 093303), we address the study of a simple model of a pure non-neutral plasma: a system of identical non-relativistic charged particles confined under an external harmonic field with frequency . We perform the equilibrium thermo-statistical analysis in the framework of continuum approximation. This study reveals the existence of two asymptotic limits: the known Brillouin steady state at zero temperature, and the gas of harmonic oscillators in the limit of high temperatures. The non-extensive character of this model is evidenced by the associated thermodynamic limit, , which coincides with the thermodynamic limit of a self-gravitating system of non-relativistic point particles in presence of Newtonian gravitation. Afterwards, the dynamics of this model is analyzed through numerical simulations. It is verified the agreement of thermo-statistical estimations and the temporal expectation values of the same macroscopic observables. The system chaoticity is addressed via numerical computation of Lyapunov exponents in the framework of the known tangent dynamics. The temperature dependence of Lyapunov exponent approaches to zero in the two asymptotic limits of this model, reaching its maximum during the transit between them. The chaos of the present model is very strong, since its rate is faster than the characteristic timescale of the microscopic dynamics . A qualitative analysis suggests that such a strong chaoticity cannot be explained in terms of collision events because of their respective characteristic timescales are quite different, and .

Orbits of two electrons released from rest in a uniform transverse magnetic field

Two identical charged particles released from rest repel each other radially. A uniform perpendicular magnetic field will then cause their trajectories to curve into a flower petal pattern. The orbit of each particle is approximately circular with a long period for a strong magnetic field, whereas it becomes a figure-eight for a weak magnetic field with each lobe completed in a cyclotron period. For example, such radially bound motions arise for two-dimensional electron gases. The level of treatment is appropriate for an undergraduate calculus-based electromagnetism course.

Pinned-to-sliding transition and structural crossovers for helically confined charges.

We explore the nonequilibrium dissipative dynamics of a system of identical charged particles trapped on a closed helix. The particles are subject to an external force accelerating them along the underlying structure. The effective interactions between the charges induce a coupling of the center of mass to the relative motion which in turn gives rise to a pinned-to-sliding transition with increasing magnitude of the external force. In the sliding regime we observe an Ohmic behavior signified by a constant mobility. Within the same regime a structural transition of the helical particle chain takes place with increasing the helix radius leading to a global change of the crystalline arrangement. The resulting crystal is characterized by the existence of multiple defects whose number increases with the helix radius.

Dynamics of nonlinear excitations of helically confined charges

We explore the long-time dynamics of a system of identical charged particles trapped on a closed helix. This system has recently been found to exhibit an unconventional deformation of the linear spectrum when tuning the helix radius. Here we show that the same geometrical parameter can affect significantly also the dynamical behavior of an initially broad excitation for long times. In particular, for small values of the radius, the excitation disperses into the whole crystal whereas within a specific narrow regime of larger radii the excitation self-focuses, assuming finally a localized form. Beyond this regime, the excitation defocuses and the dispersion gradually increases again. We analyze this geometrically controlled nonlinear behavior using an effective discrete nonlinear Schrödinger model, which allows us among others to identify a number of breatherlike excitations.

Interference effects in the plasmon fields excited by a diatomic molecule

We study the fluctuations of the plasmon field associated to the wake potential generated by a dimer formed by two identical charged particles (such as two nuclei of the ionized hydrogen molecule) traveling through a semiinfinite dielectric medium. We use coherent states to describe bulk and surface plasmons as wave packets that raise fluctuations in the electronic density of the material. We analyze different configurations of interest, taking into account various trajectories and orientations of the dimer.

Fluctuation of electronic density in the plasmon fields excited by a diatomic molecule

We study the fluctuations of the electronic density due to plasmon field associated to the wake potential generated by a dimer formed by two identical charged particles (such as two nuclei of the ionized hydrogen molecule) traveling through a semi-infinite dielectric medium. We use coherent states to describe plasmons as wave packets that raise fluctuations in the electronic density of the material. We analyze different configurations of interest, regarding the geometry of the surface and the orientation of the dimer.

Fractionalization of interstitials in curved colloidal crystals

Understanding the effect of curvature and topological frustration in crystals yields insights into the fragility of the ordered state. For instance, a one-dimensional crystal of identical charged particles can accommodate an extra particle (interstitial) if all the particle positions are readjusted, yet in a planar hexagonal crystal interstitials remain trapped between lattice sites and diffuse by hopping. Using optical tweezers operated independently of three-dimensional imaging, we inserted interstitials in a lattice of similar colloidal particles sitting on flat or curved oil/glycerol interfaces, and imaged the ensuing dynamics. We find that, unlike in flat space, the curved crystals self-heal through a collective particle rearrangement that redistributes the increased density associated with the interstitial. This process can be interpreted in terms of the out-of-equilibrium interaction of topological defects with each other and with the underlying curvature. Our observations suggest the existence of particle fractionalization on curved surface crystals.

Theoretical description of Coulomb balls: Fluid phase

A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean-field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correlations is developed here by an extension of the hypernetted chain approximation, developed for bulk fluids, to the confined charges. The results reproduce all of the qualitative features observed in molecular dynamics simulations and experiments. These predictions are then tested quantitatively by comparison with benchmark Monte Carlo simulations. Quantitative accuracy of the theory is obtained by correcting the hypernetted chain approximation with a representation for the associated bridge functions.

Controlling the spatial distribution of superfluidity in radially ordered Coulomb clusters

When a few identical charged particles are trapped in a spherical electric field at low temperature, they form concentric shells resembling atoms. The behavior of these ``artificial atoms'' is easily controlled by varying the field strength. In particular, it is possible to transfer the system from a liquidlike to a crystal-like state. We analyze artificial atoms consisting of Bose particles and observe superfluid behavior, which even persists in the intermediate radially ordered crystal regime. Furthermore, we demonstrate that the superfluid density can be directed in a controlled way either to the core or to the boundary of the atom.

Theoretical and experimental study of elliptical Debye clusters

An elliptical Debye cluster is a system of n identical charged particles interacting through a screened Coulomb potential and confined in a two-dimensional anisotropic parabolic well. A model for this system has been developed with three parameters: n, the well anisotropy α2, and the Debye shielding parameter κ. From numerical solutions of the model, it is shown that the breathing mode persists as the anisotropy increases, and that the normalized, squared breathing frequency increases linearly with α2. Elliptical clusters with n=49 and 15 particles were studied experimentally. The anisotropic potential well was created using a rectangular aperture (17.5×30.2 mm) placed on a flat electrode. The well anisotropy was determined by measuring the center-of-mass (c.m.) oscillation frequencies along the major and minor axes of the resulting elliptical clusters using both driven and thermal oscillations. The two methods give results that are in good agreement. For n=49 particles, the square of the ratios of the c.m. frequencies was α2=2.9±0.1. From a measurement of the breathing frequency, the shielding parameter was found to be κ=2.1±0.2. For n=15 particles, α2=2.8±0.1 and κ=1.9±0.2, demonstrating that an analysis using the model gives consistent results.

Non-monotonic size effects on the structure and thermodynamics of Coulomb clusters in three-dimensional harmonic traps

Finite-size effects on the static and thermodynamical properties of small three-dimensional clusters of identical charged particles confined by an harmonic trap are investigated using global optimization and numerical simulations. The relative stabilities of clusters containing up to 100 particles are estimated from the second energy derivatives, as well as from the energy gap between the two lowest-energy structures at a given size. We also provide a lower bound for the number of permutationally independent minima, as a function of size, up to n=75. Molecular dynamics and exchange Monte Carlo simulations are performed to get insight into the finite temperature behaviour of these clusters. By focusing on specific sizes, we illustrate the interplay between the stable structures, the possible competition between different isomers, and the melting point. In particular, we find that the orientational melting phenomenon known in two-dimensional clusters has an equivalent form in some three-dimensional clusters. The vibrational spectra, computed for all sizes up to 100, shows an increasing number of low-frequency modes, but comparing to hydrodynamical theory reveals strong correlation effects. Finally, we investigate the effects of the trap anisotropy on the general shape of Coulomb clusters, and on the melting point of a selected case.

Continuum model for the breathing oscillation of a spherical complex plasma

A nonlinear equation of motion for the breathing oscillation of a spherical complex plasma is derived. A spherical complex plasma, or “dust ball,” is a three-dimensional arrangement of n identical charged particles interacting through a shielded Coulomb force (i.e., a Yukawa potential) with a Debye length λ and confined by a three-dimensional, isotropic, parabolic potential well for which the single-particle oscillation frequency is ω0. The dependence of the equilibrium radius R0 and small-amplitude breathing frequency ωbr on λ is computed. Exact analytical results are given for the continuum limit n→∞ (i.e., a spherical Yukawa fluid). The squared breathing frequency (ωbr∕ω0)2=3 for the unshielded Coulomb interaction (1∕λ→0), irrespective of n, and increases to (ωbr∕ω0)2=5 as 1∕λ→∞. The effects of a finite number of particles are modeled by assuming an inner cutoff for the Yukawa potential a distance a from any point in the complex plasma sphere. Three physical regimes are identified: a Coulomb regime where λ⪢R0 and corrections to the infinite-λ case are small, a nearest-neighbor regime, where R0⪢a>λ and nearest-neighbor interactions dominate, and a plasma regime where R0⪢λ≳a and continuum plasma theory is applicable. For 1∕λ→∞, (ωbr∕ω0)2∼a∕λ in the nearest-neighbor regime, while (ωbr∕ω0)2∼5 in the plasma regime.

Collisionality in an Ensemble of Identical Charged Particles in a Closed Magnetic Trap

A strict proof of the theorem of infinite collisionality in an ensemble of identical charged particles in a closed magnetic trap is presented.

Lowest energy states of three identical charged particles in a two-dimensional harmonic trap

A system of three identical charged particles in a two-dimensional harmonic well produced by an external potential and a transverse magnetic field is treated in the framework of the configuration space Faddeev approach. Energies of the three lowest states are calculated for the systems of different symmetry including spin one-half fermions, i.e., the three-electron quantum dot and spinless bosons. Calculations are performed for a wide range of the total angular-momentum values and results are fitted to a simple analytical formula which is exact in the limits of small and large frequency of the effective confining potential. This allows one to predict properties of the lowest states for almost arbitrary parameters of these systems.

Exact energy levels and magnetization of two identical planar charged particles in quantum dots

We discuss the effects of Coulomb repulsion in the dynamics of two identical planar charged particles without spin under the confining effect of a perpendicular magnetic field and a harmonic potential. The energy spectrum of stationary states is obtained exactly and the magnetization computed. We observe a behaviour found in other treatments of two electrons but over a more restricted range of existence with assumptions and methods different from ours.

Induced anyonicity and consequences

Abstract We discuss the induced anyonicity of a system of two identical planar charged particles without spin under the confining effect of a perpendicular magnetic field in a quantum dot. We show that this anyonic behaviour, inherent in quantum mechanics of bidimensional identical particles is due to the effects of Coulomb repulsion and that we observe characteristic aspects found exactly but existing in other treatments by different methods.

Attractive interactions in dispersions of identical charged colloidal particles: a Monte Carlo simulation

Using the Debye–Hückel pair potential, the collective interactions between identical charged particles were examined via Monte Carlo simulations. The results have shown that when the number of charges per particle and the particle volume fraction were sufficiently large, the pair long-range electrostatic repulsion generated an effective attractive interaction between identical charged particles because of many-body effects. Disordered liquid-like structures, ordered crystal-like structures, ordered structures dispersed in disordered ones, and disordered structures dispersed in ordered ones have been found. The structures are dependent on the volume fraction and charge of the particles, as well as on the electrolyte concentration.

Behaviour of three charged particles on a plane under perpendicular magnetic field

We consider the problem of three identical charged particles on a plane under a perpendicular magnetic field and interacting through Coulomb repulsion. This problem is treated within Taut's framework, in the limit of vanishing center of mass vector $\vec{R} \to \vec{0}$, which corresponds to the strong magnetic field limit, occuring for example in the Fractional Quantum Hall Effect. Using the solutions of the biconfluent Heun equation, we compute the eigenstates and show that there is two sets of solutions. The first one corresponds to a system of three independent anyons which have their angular momenta fixed by the value of the magnetic field and specified by a dimensionless parameter $C \simeq \frac{l_B}{l_0}$, the ratio of $l_B$, the magnetic length, over $l_0$, the Bohr radius. This anyonic character, consistent with quantum mechanics of identical particles in two dimensions, is induced by competing physical forces. The second one corresponds to the case of the Landau problem when $C \to 0$. Finally we compare these states with the quantum Hall states and find that the Laughlin wave functions are special cases of our solutions under certains conditions.