Identical Charged Particles Research Articles

On exact singular wave functions of two identical particles

We discuss the occurrence and properties of exact singular anyonic wave functions describing stationary states of two identical charged particles moving on a plane and under the influence of a perpendicular uniform magnetic field.

Destruction of quantum coherence through emission of bremsstrahlung

The emergence of decoherence in quantum electrodynamics is investigated. On combining superoperator methods with functional techniques from field theory, the degrees of freedom of a thermal radiation field are eliminated and the influence phase functional is derived which governs the reduced dynamics of the matter variables. Employing a prototypical interference device, a decoherence functional is developed which provides a gauge invariant relativistic measure for the degree of decoherence. It is demonstrated that the decoherence functional describes the destruction of quantum coherence through the emission of bremsstrahlung which is caused by the relative motion of the interfering components of a superposition. Explicit analytical expressions for the vacuum and the thermal contribution to the decoherence functional and for the corresponding coherence lengths are determined. These expressions reveal that bremsstrahlung leads to a fundamental decoherence mechanism which dominates for short times and which is present even in the electromagnetic field vacuum at zero temperature. The influence of bremsstrahlung on the center of mass coordinate of a system of many identical charged particles is also studied and is shown to lead to a strong suppression of quantum coherence.

Methods of numerical analysis of 1-dimensional 2-body problem in Wheeler–Feynman electrodynamics

Numerical methods for solution of differential equations with deviating arguments describing 1-dimensional ultra-relativistic scattering of 2 identical charged particles in classical electrodynamics with half-retarded/halfadvanced interaction (Wheeler and Feynman, 1949) are developed. A bifurcation of solutions and violation of their reflectional symmetries in the region of velocities v>0.937c are found in numerical analysis.

METHODS OF NUMERICAL ANALYSIS OF ONE-DIMENSIONAL TWO-BODY PROBLEM IN WHEELER-FEYNMAN ELECTRODYNAMICS

Numerical methods for solutions of differential equations with deviating arguments describing one-dimensional ultra-relativistic scattering of two identical charged particles in Wheeler-Feynman electrodynamics with half-retarded/half-advanced interaction are developed. Utilization of the methods for the physical problem analysis leads to the discovery of a bifurcation of solutions and breaking of their reflectional symmetry for particles asymptotic velocity v>0.937c in their center-of-mass frame.

On the structure of solutions of 1-dimensional 2-body problem in Wheeler-Feynman electrodynamics

The problem of 1-dimensional ultra-relativistic scattering of 2 identical charged particles in classical electrodynamics with retarded and advanced interactions is investigated.

Order in very cold confined plasmas

The study of the structure and dynamic properties of classical systems of charged particles confined by external forces, and cooled to very low internal energies, is the subject of this talk. An infinite system of identical charged particles has been known for some time to form a body-centered cubic lattice and is a simple classical prototype for condensed matter. Recent technical developments in storage rings, ion traps, and laser cooling of ions, have made it possible to produce such systems in the laboratory, though somewhat modified because of their finite size. I would like to discuss what one may expect in such systems and also show some examples of experiments. If we approximate the potential of an ion trap with an isotropic harmonic force F = {minus}Kr then the Hamiltonian for this collection of ions is the same as that for J. J. Thomson`s ``plum pudding`` model of the atom, where electrons were thought of as discrete negative charges imbedded in a larger, positive, uniformly charged sphere. The harmonic force macroscopically is canceled by the average space-charge forces of the plasma-, and this fixes the overall radius of the distribution. What remains, are the residual two-body Coulomb interactions that keep the particles within the volume as nearly equidistant as possible in order to minimize the potential energy. The configurations obtained for the minimum energy of small ionic systems [2] in isotropic confinement are shown in figure 1. Indeed this is an `Exotic Atom` and fits well into the subject of this symposium honoring the 60th birthday of Professor Toshi Yamazaki.

Structure and rearrangements of small trapped-ion clusters.

The potential-energy surfaces of clusters composed of identical charged particles confined by an isotropic harmonic potential are investigated with particular reference to rearrangement mechanisms. A number of intrashell and intershell rearrangements in systems with 4-60 ions are characterized. The intrashell processes, in which only the ions of one roughly concentric shell are permuted, generally exhibit much lower barriers than the intershell processes that involve the migration of an ion between shells. The former rearrangements may generally be described as concerted multiple diamond-square-diamond processes

Pion interferometry in jet events at the CERN Intersecting Storage Rings

We have observed an enhanced production of pairs and triplets of identical charged particles at small momentum differences in events with two central jets produced inpp collisions at the CERN Intersecting Storage Rings. The size and structure of this ‘Bose-Einstein’ enhancement, shown by the particles within a jet, resembles that observed in minimum-bias events. The correlation function can be well parametrized by the single variableQ — the absolute value of the four-momentum transfer — and is more peaked than a single Gaussian.

Intramembrane charge movement and calcium release in frog skeletal muscle.

Intramembrane charge movement and myoplasmic free calcium transients (delta[Ca2+]) were monitored in voltage-clamped segments of isolated frog muscle fibres cut at both ends and mounted in a double Vaseline-gap chamber. The fibres were stretched to sarcomere lengths of 3.5-4.6 micron to minimize mechanical movement and the related optical artifacts. The over-all calcium removal capability of each fibre was characterized by analysing the decay of delta[Ca2+] following pulses of several different amplitudes and durations. The rate of sarcoplasmic reticulum (s.r.) calcium release was then calculated for each delta[Ca2+] using the calcium removal properties determined for that fibre. The calculated calcium release wave form reached a relatively early peak and then declined appreciably during a 100-150 ms depolarizing pulse. The voltage dependence of the peak rate of calcium release was steeper and was centred at more positive membrane potentials than the steady-state voltage dependence of charge movement in the same fibres. A considerable fraction of the total intramembrane charge was moved at potentials at which delta[Ca2+] and calcium release were only a few per cent of maximum. This 'subthreshold' charge may correspond to charge moved in preliminary transitions that precede a final charge transition that activates release. A 'stepped on' pulse protocol was used to experimentally separate the subthreshold charge movement from the charge movement of the final transitions that may control calcium release. The stepped on pulse consisted of a set 50 ms pre-pulse to a potential just at or below the potential for detectable delta[Ca2+] followed immediately by a test pulse of varying amplitude and duration. For a wide range of test pulse amplitudes and durations in the stepped on protocol the peak rate of calcium release was linearly related to the charge movement during the test pulse. This result points to a tight control of activation of s.r. calcium release by intramembrane charge movement. The voltage dependence of both charge movement and of the rate of calcium release could be fitted simultaneously with a three-state, two-transition sequential model in which charge moves in both transitions but only the final transition activates s.r. calcium release. A model with three identical and independent charged gating particles per channel gave an equally good fit to the data. Both models closely fit the charge movement and release data except within about 10 mV of the voltage at which release became detectable, where release varied more steeply with membrane potential than predicted by either model.(ABSTRACT TRUNCATED AT 400 WORDS)

The threshold law for double ionisation in electron-atom collisions

The classical dynamics of three identical charged particles is considered in describing the threshold behaviour of the double ionisation cross section. The method due to Vinkalns and Gailitis (1967), previously extended to the general case of single ionisation, is applied now to triple escape. Analytical results for the ionisation function near threshold, for electron impact on the arbitrarily charged target, are in perfect agreement with the semiclassical calculations of Klar and Schlecht (1976). The threshold behaviour of the deviation of the mutual angles from the symmetric configuration is also derived.

A theoretical study for the dynamic interchromophoric interaction effects upon the susceptibility and hypersusceptibility of chromophore aggregates

The dynamic interchromophoric interaction effects upon the susceptibility and hypersusceptibility of the current–charge density of chromophore aggregates are formulated to infinite order and in closed form by means of a decoupling approximation, whereby the induced field operator contained in the dynamic perturbation Hamiltonian is replaced by its averaged form satisfying the generalized Maxwell’s equation for the current-charge source density. This decoupling approximation includes a basic condition that the total momentum and hence the total current of identical charged particles belonging to any chromophore remain as nearly constant in time throughout the dynamic perturbation interactions. The physical meaning of this condition is surveyed by making reference to the local conservation equation which can be derived for the chromophoric current and charge densities. Contributions of the aggregate’s susceptibility and hypersusceptibility to the mean rate of energy absorption caused by a single-frequency external field and to the mean rate difference generated by right and left circularly polarized light are studied in terms of the frequency reversal symmetries of the susceptibility and hypersusceptibility.

Kinetics of intramembrane charge movement and sodium current in frog node of Ranvier.

Intramembrane charge movement (Q) and sodium current (INa) were monitored in isolated voltage-clamped frog nodes of Ranvier, ON charge movements (QON) for pulses from the holding potential (-100 mV) to potentials V less than or equal to 0 mV followed single exponential time courses, whereas two exponentials were found for pulses to V greater than or equal to 20 mV. The voltage dependence of both QON and its time constant tauON indicated that the two ON components resolved at V greater than or equal to 20 mV were also present, though not resolvable, for pulses to V less than or equal to 0 mV. OFF charge movements (QOFF) monitored at various potentials were well described by single exponentials. When QOFF was monitored at -30 or -40 mV after a 200-microsecond pulse to +20 mV and QON was monitored at the same potential using pulses directly from -100 mV, tauON/tauOFF = 2.5 +/- 0.3. At a set OFF potential (-90 to -70 mV), tauOFF first increased with increasing duration tON of the preceding pulse to a given potential (0 to +30 mV) and then decreased with further increases in tON. The declining phase of tauOFF followed a time course similar to that of the decline in QOFF with tON. For the same pulse protocol, the OFF time constant tauNa for INA also first increased with tON but then remained constant over the tON interval during which tauOFF and QOFF were declining. After 200- or 300-microsecond pulses to +20, +20, or +50 mV, tauOFF/tauNa at -70 to -90 mV was 1.2 +/- 0.1. Similar tauOFF/tauNa ratios were predicted by channel models having three identical charged gating particles that can rapidly and reversibly form an immobile dimer or trimer after independently crossing the membrane from their OFF to their ON locations.

Quadrupole bremsstrahlung in the scattering of identical charged bosons and fermions

In a nonrelativistic formulation employing noncovariant perturbation theory in the Born approximation and including exchange effects, the differential cross section for bremsstrahlung is derived for scattering by identical charged particles of arbitrary spin. The problem is first treated in a general manner, giving the expression for the total direct amplitude for the complete process (photon emission in scattering) for the case where the scattering potential is arbitrary. The derivation by means of perturbation theory demonstrates the critical role played by the small momentum associated with the emitted photon. Graviton bremsstrahlung is discussed briefly and the corresponding quadrupole cross section is given by a simple comparison with the photon bremsstrahlung formula.

Lagrangian and Hamiltonian for the motion of charged particles up to the fourth-order terms

It is known that a special case of the Lagrangian of two identical charged particles up to fourth order terms has been found. The object of this paper is to derive the generalized Lagrangian by a scheme which is somewhat different from the one known. On the other hand one can then proceed to give the Hamiltonian form up to the same order.

Can the future influence the present?

One widely accepted model of classical electrodynamics assumes that a moving charged particle produces both retarded and advanced fields. This formulation first appeared at least 75 years ago. It was popularized in the 1940's by work of Wheeler and Feynman. But the most fundamental question associated with the model has remained unanswered: When (if ever) does the two-body problem have a unique solution? The present paper gives an answer in one special case. Imagine two identical charged particles alone in the universe moving symmetrically along the $x$ axis. One is at $x(t)$ and the other is at $\ensuremath{-}x(t)$. Their motion is then governed by a system of functional differential equations involving both retarded and advanced arguments. This system together with the Newtonian "initial" data $x(0)={x}_{0}>0$ and ${x}^{\ensuremath{'}}(0)=0$ has a unique solution for all time provided ${x}_{0}$ is sufficiently large. Perhaps the existence and uniqueness proof given for this special case will pave the way for more general results on this curious two-body problem.