Three-body treatment of Coulomb effects in the problem of long-range effective interactions

The problem of Coulomb scattering of a charged particle by a two-particle bound system, consisting of a charged and a neutral particle, is investigated in the integral-equation approach of rigorous three-body theory. The bound state of the two particles is provided by a short-range interaction chosen in the simplest form using anS-wave separable potential. The integral equation defining the effective potential of the interaction of the charged particle with the two-particle bound system is formulated. It is shown that the multiple Coulomb scattering of the involved charged particles generates a sequence of long-range terms in the effective potential. It turns out that the long-range effects of Coulomb scattering are partly cancelled. As a result the polarization potential does not contain the longest-ranged terms which decrease at large distances as ^–2 and ^–3.     

Small deviations from local equilibrium for a process which exhibits hydrodynamical behavior. I

The symmetric simple exclusion process where infinitely many particles move randomly on , jump with equal probability on nearest-neighbor sites, and interact by simple exclusion is considered. It is known that the only extremal invariant measures are Bernoulli, that each measure, in a suitable class, after a macroscopic time is locally described, at a zero-order approximation, by a Bernoulli measure with parameter depending on macroscopic space and time, and that the so-defined equilibrium profile satisfies the heat equation. Small deviations from local equilibrium in the hydrodynamical limit are investigated. It is proven, under suitable assumptions, that at first order the state is Gibbs with one- and two-body potentials whose strength depends only on macroscopic space and time and on the equilibrium profile. More precisely, the one-body potential is linear (on the microscopic positions of the particles) and proportional to the macroscopic space gradient of the equilibrium parameter at that time, so that Fourier law holds. The two-body potential varies on a macroscopic scale and does not depend on the microscopic positions of the particles; it is given by the value of the covariance of the Gaussian macroscopic density fluctuation field.     

Affine connection structure of the charged symplectic 2-form

It is shown that the charged symplectic form in Hamiltonian dynamics of classical charged particles in electromagnetic fields defines a generalized affine connection on an affine frame bundle associated with spacetime. Conversely, a generalized affine connection can be used to construct a symplectic 2-form if the associated linear connection is torsion-free and the antisymmetric part of theR ^4* translational connection is locally derivable from a potential. Hamiltonian dynamics for classical charged particles in combined gravitational and electromagnetic fields can therefore be reformulated as aP(4)=O(1, 3)R ^4* geometric theory with phase space the affine cotangent bundleAT ^* M of spacetime. The sourcefree Maxwell equations are reformulated as a pair of geometrical conditions on the ^4* curvature that are exactly analogous to the source-free Einstein equations.     

Coverage and Structure of Films of Spherical Particles Deposited after Diffusing in a Gravitational Field

We investigate the coverage and structure of a layer of particles deposited on a line after diffusion in a gravitational field. The dynamics of the depositing particles is controlled by the gravity number N _G(=d ⁴ g/6k _B T), where d is the diameter of the particles, is the density difference between the particles and the solution, g is the acceleration due to gravity, k _B is Boltzmann's constant, and T is the temperature. The position-dependent flux of particles in a gap formed by two preadsorbed particles is estimated by superposition of solutions of a steady-state convective diffusion equation for the flux in the presence of a single preadsorbed particle. The saturation coverages are found with a recursion relation and are in good agreement with those obtained from Brownian dynamics simulation. The jamming coverage increases rapidly with increasing particle size, particularly for large values of . An algorithm is presented to generate adsorbed configurations from which the structure of the deposit is determined.     

Effect of Microscopic Noise on Front Propagation

We study the effect of the noise due to microscopic fluctuations on the position of a one dimensional front propagating from a stable to an unstable region in the linearly marginal stability case. By simulating a very simple system for which the effective number N of particles can be as large as N=10¹⁵⁰, we measure the N dependence of the diffusion constant D_N of the front and the shift of its velocity v_N. Our results indicate that D_N(log N)^–3. They also confirm our recent claim that the shift of velocity scales like v_min–v_NK(log N)^–2 and indicate that the numerical value of K is very close to the analytical expression K_approx obtained in our previous work using a simple cut-off approximation.     

Quantum tunneling with dissipation and the Ising model over ℝ

We consider a quantum particle in a double-well potential, for simplicity in the two-level approximation, coupled to a phonon field. We show that static and dynamical ground state correlations of the particle and of the field are expressible through expectations in an Ising model over (rather than ). Its free measure is a spin flip process with flip rate , the difference in energy between the ground state and the first excited state. The Ising model has a ferromagnetic pair interaction whose form depends on the couplings to the phonon field and on the dispersion relation of the phonon field. In physical applications the interaction is long ranged and decays ast ^–2 for large distances. In this case we prove that for sufficiently strong coupling the particle becomes localized in one of the wells. The effective tunnel rate is zero. The transition to localization is associated with the generation of an infinite number of low momentum phonons. We apply the Ising technology to our problem and discuss the phase diagram in some detail.     

On First-order Corrections to the LSW Theory I: Infinite Systems

We present a new method to efficiently identify the first-order correction to the classical model by Lifshitz, Slyozov and Wagner (LSW). The latter describes the evolution of second phase particles embedded in a matrix during the last stage of a phase transformation and is valid in the regime of vanishing volume fraction of particles. We consider a statistically homogeneous (and thus infinite) system, where the first-order correction is of order ^1/2. The key idea is to relate the full system of particles to systems where a finite number of particles has been removed. This method decouples screening and correlation effects and allows to efficiently evaluate conditional expected values of the particle growth rates.     

Indomethacin nanoparticles directly deposited on the fluidized particulate excipient by pulsed laser deposition

Nanoparticles of indomethacin (IM), a sparingly soluble drug in water, were prepared by pulsed laser deposition with Nd: YAG laser at 1064 nm. Variation of the deposition rate (DR) with various experimental conditions, such as species and pressure of the background gas, and laser fluence, was discussed. We obtained highest DR, 2.7 g/cm²min, under He at 100 Pa with the laser fluence of 25 J/cm². In the deposited solid product, no trace of drug decomposition was observed by HPLC. Deposition of IM nanoparticles was achieved on the fluidized excipient, potato starch particles of 20 m regime. By TEM observation and zeta potential distribution measurement, we confirmed that surface of excipient particles was fully covered by nanoparticles of IM. Thus, the present method enables us a new method of one-step preparation of drug-excipient nanocomposites to eliminate tedious problems associated with nanoparticles handling.     

Analyticity in Hubbard Models

The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when t is small, or t ²/U is small; here, is the inverse temperature, U the on-site repulsion, and t the hopping coefficient. For more general models with Hamiltonian H=V+T where V involves local terms only, the free energy is analytic when T is small, irrespective of V. There exists a unique Gibbs state showing exponential decay of spatial correlations. These properties are rigorously established in this paper.     

Delay times for symmetrized and antisymmetrized quantum tunneling configurations

The quartic confining potential has emerged as a key ingredient to obtain fast rotating vortices in BEC as well as observation of quantum phase transitions in optical lattices. We calculate the critical temperature T_c of bosons at which normal to BEC transition occurs for the quartic confining potential. Further more, we evaluate the effect of finite particle number on T_c and find that ΔT_c/T_c is larger in quartic potential as compared to quadratic potential for number of particles <10⁵. Interestingly, the situation is reversed if the number of particles is 10⁵.     

Invariant measures for the2D-defocusing nonlinear Schrödinger equation

Consider the2D defocusing cubic NLSiu _t+u–u|u|²=0 with Hamiltonian . It is shown that the Gibbs measure constructed from the Wick ordered Hamiltonian, i.e. replacing ||⁴ by ||⁴ :, is an invariant measure for the appropriately modified equationiu _t + u‒ [u|u ²–2(|u|² dx)u]=0. There is a well defined flow on thesupport of the measure. In fact, it is shown that for almost all data the solutionu, u(0)=, satisfiesu(t)–e ^it C _Hs (), for somes>0. First a result local in time is established and next measure invariance considerations are used to extend the local result to a global one (cf. [B2]).     

Die Verteilung der natürlichen Radioaktivität auf das Größenspektrum des natürlichen Aerosols

The apparatus described allows to measure the distribution of natural radioactivity on aerosol particles. Careful measures were taken that the aerosol concentration and its size spectrum were not altered before being examined. To increase the accuracy of the measurements the natural aerosol was charged with thoron decay products. The resulting electric charge-distribution by ion diffusion on dust particles is known, therefore the radii of these particles could be calculated by mobility measurements. By means of the law, governing attachment of emanation decay products on dust particles — as derived byLassen orWieser andStierstadt (afterBricard), it is possible to calculate the size spectrum of natural aerosol from the measured activity spectrum. Until now we have onlyion spectra for the range of size 6×10^?7 to 10^?5 cm. With the quoted apparatus however it is possible to measure thesize spectrum of natural aerosol. So we have a simple size-spectrometer, that covers a large range of particles. Among other things can be deduced from these measurements, that the natural radioactivity of air is attached to particles of radii from 10^?6 up to 10^?5cm, — the main part of the activity being carried by aerosols with radii between 4 and 6×10^?6cm. From the calculated aerosol spectrum (r from 6×10^?7 to 10^?5 cm) follows a mean particle radius ofr=2,5×10^?6cm at a particle concentration of 3×10⁴cm^?3.     

Far infrared absorption in ultrafine metallic particles: Calculations based on classical and quantum mechanical theories

Detailed calculations of far infrared absorption in ultrafine metallic particles are reported. Effective medium treatments of the composite of particles and their surrounding are carried out within the Maxwell Garnett and Bruggeman theories. Generalizations of these to encompass dipole-dipole interaction and oxide pellicles are discussed. The dielectric permeability of the particles is specified either by the Drude (D) model with a size limited mean free path, or by the quantum mechanical derivation of Gor'kov and Éliashberg (GE). Excepting narrow diameter (x) and frequency ( ) intervals the absorption coefficients can be approximated by =fCx , wheref is the filling factor (taken to be small),C is a constant which depends on the free electron parameters, and and are integers. Results for largerfs are included also. The magnitudes ofC, and differ in general for the Drude and Gor'kov-Éliashberg theories; they are also different forxx ^C , wherex _D ^C 5 nm andx _GE ^C is typically 20 nm. The quantityx ^c signifies a transition from a range where is dominated by the dielectric polarisation to one where the magnetic polarisation is largest. An interesting multiple peak structure is found from detailed calculations of _GE vs. for sufficiently small identical particles. Effects of log-normal size distributions are derived explicitely; any fine structure in the _GE vs.x functions is found to be completely washed out for practically attainable distribution widths.Work at Cornell University was supported by the National Science Foundation through the Materials Science CenterWork at Chalmers University of Technology was supported by the Swedish Natural Science Research Council     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

On the asymptotic behaviour of infinite gradient systems

We consider gradient systems of infinitely many particles in one-dimensional space interacting via a positive invariant pair potential with a hard core. The main assumption is that is strictly convex within the rangeR of (whereR is a fixed number ). Under some technical conditions we prove the following theorems: Let the initial distribution be given by a translation invariant point process onR ¹. Then there exists only one extreme equilibrium state with a given intensityI() satisfyingI()R ^–1, and all ergodic initial distributions with an intensityI()R ^–1 converge weakly ast to the extreme equilibrium state with the same intensity.     

NMR of23Na in small particles of ferroelectric NaNO2

Pulse and wide line NMR spectroscopy were applied to small ferroelectric NaNO₂ particles, produced from aqueous solution and embedded loosely in silicagel. Mean particle diameters as determined by SEM and TEM were between 0.2 and 5.0 µm. From the cw-experiments it followed, that the particles had the crystalline structure of the bulk. It is shown that the spectrum of critical fluctuations and the phase transition temperature in the particles proved to be independent of the size. If there is a dead layer at the particle surfaces its thickness does not exceed 1×10^–2µm.     

Spectral stochastic processes arising in quantum mechanical models with a non-L 2 ground state

A functional integral representation is given for a large class of quantum mechanical models with a non-L ² ground state. As a prototype, the particle in a periodic potential is discussed: a unique ground state is shown to exist as a state on the Weyl algebra, and a functional measure (spectral stochastic process) is constructed on trajectories taking values in the spectrum of the maximal Abelian subalgebra of the Weyl algebra isomorphic to the algebra of almost periodic functions. The thermodynamical limit of the finite-volume functional integrals for such models is discussed, and the superselection sectors associated to an observable subalgebra of the Weyl algebra are described in terms of boundary conditions and/or topological terms in the finite-volume measures.Supported by DFG, Nr. Al 374/1-2     

The Newtonian limit in a family of metric affine theories of gravitation

A brief review of a first order theory with a quadratic LagrangianL=R+₀R² is presented. It is shown that a test particle follows a geodesic of the metric connection. The theory behaves in the Newtonian limit as the Newtonian theory with a correction which is proportional to the matter density at the field point. This behavior can be produced by a Yukawa potential with an atomic scale characteristic range and a coupling constant proportional to 1/ ². This type of potential is not excluded by the present experimental data.     

Gravitomagnetic and Gravitoelectric Waves in General Relativity

Lower-order terms in expansions of the equations of General Relativity in powers of v/c (post-Newtonian approximations) have long been a source of analogies with em theory. A classic textbook example is the steadily spinning sphere generating a constant dipole gravitomagnetic field, with its associated vector potential B^* ₀ = × (analog of the magnetic field B of a spinning charged sphere). In the nonsteady case there are associated gravitoelectric fields E* = – _t – * also, where * is the gravitational Coulomb potential. The case of a rigid sphere spun up from rest by an external (nongravitational) torque at t = 0 is enlightening, as it demonstrates the generation of B* and E* wave fields propagating outward with the velocity of light c: for large t, B* B^* ₀. In a coordinate system for which the metric tensor is nearly equal to the Minkowski tensor, the three-vector potential obeys an equation isomorphic to the electrodynamic equation, that is, ² = –*j* with j* = –v, where is the mass density, v the three-velocity, and * = 16Gc^–2 = 3.7 × 10^–26 mksu, G being the gravitational constant. Significantly, one can construct a gauge invariant four-vector potential F* = (ic^–14*, ), obeying field equations isomorphic to Maxwell's in the Lorentz gauge F _, = 0. The traveling transient dipole field exerts torques on matter in its path, setting up shear strains that may be measurable for very large momentum transfers, for example, between massive astronomical bodies. A rough calculation suggests that such strains are in principle observable.     

Particle creation by a black hole as a consequence of the Casimir effect

Particle creation by a black hole is investigated in terms of temperature corrections to the Casimir effect. The reduction of the Hawking effect to more familiar effects observed in the laboratory enables us to reveal the mechanism of particle creation. The blackbody nature of the Hawking radiation is due to the interaction of virtual particles with the surface of a cavity formed by the Schwarzschild gravitational field potential barrier. These particles are squeezed out by the contraction of the potential barrier and appear to an observer atJ ⁺ as the real blackbody ones.