No abstract available

[en] The chaotic dynamics of a particle in two-dimensional periodic potentials or in potentials with quasicrystalline symmetry is investigated. It is shown that under conditions of deterministic chaos the infinite motion of a particle in a periodic hexagonal potential has the character of Levy flights, i.e., diffusion motion alternating with periods of almost free motion. A connection is established between the random walk of the particle and diffusion in multifractals. In potentials with higher degree of symmetry (of the quasicrystalline type) the random walk is close to the ordinary diffusion process

No abstract available

[en] A model system for the Lorentz gas can be made [Eder, Chen, and Egelstaff, Proc. Phys. Soc. London 89, 833 (1966); McPherson and Egelstaff, Can. J. Phys. 58, 289 (1980)] by mixing small quantities of hydrogen with an argon host. For neutron-scattering experiments the large H-to-Ar cross section ratio (∼200) makes the argon relatively invisible. Dynamic-structure-factor [S(Q,ω) for H₂] measurements at room temperature have been made on this system using the IN4 spectrometer at the Institute Laue Langevin, Grenoble, France. Argon densities between 1.9 and 10.5 atoms/nm³ were used for 0.4< Q<5 A^-1. Additional measurements were made with a He gas host at densities of 4 and 10.5 atoms/nm³; helium is relatively invisible also compared to hydrogen. These experiments are described, and some examples of the results are presented to show the qualitative effects observed. The principle observation is a pronounced narrowing of S(Q,ω) as a function of ω as the argon density is increased. This effect is large at low Q and decreases with increasing Q, and also decreases substantially when helium is used in place of argon. In addition, the shape of S(Q,ω) is more complex than can be accommodated within a simple model, but slightly less complicated than a computer simulation so showing the significance of multiple-collision processes

[en] We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion equation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation

[en] The traditional hard-disk Lorentz gas describes the chaotic motion of a classical point particle through an array of impenetrable disks. Soft-disk modifications of the two-dimensional Lorentz gas, where the scattering particle can move into the disk interiors, are considered here. Conditions on the soft-disk potentials and disk separations that guarantee chaotic motion are obtained

[en] The authors prove scaling to nondegenerate Brownian motion for the path of a test particle in the stochastic Lorentz lattice gas on Z^d under a weak ergodicity assumption on the scatterer distribution. They prove that recurrence holds almost surely in d ≤ 2. Transience in d ≥ 3 remains open

[en] Closed equation for the collision integral in the Lorentz quantum model is derived. Divergent diagrams are separated out in the decomposition in density. The procedure of divergency removing is indicated and regularized expressions for the collisionintegral in the two-dimensional case are derived

[en] Formal arguments are given that the self-diffusion process, understood as the mutual diffusion process in a system which consists of two mechanically similar species of particles, and which is at total equilibrium if the species labels are ignored, is an inherently linear, but nonlocal, transport process. There are no nonlinear Burnett effects, and the nonlocal diffusion coeffieient is independent of the composition of the mixture. The present state knowledge, from theory and from computer experiments, concerning the various quantities which appear in the formal anlaysis is summarized for both fluid and Lorentz systmes

[en] The eigenfrequencies are identified for two electromagnetically coupled semi-infinite solids with plane-parallel surfaces (two half-spaces) separated by a third, polarizable body. The corresponding van der Waals-London and Casimir forces are calculated from the zero-point energy (vacuum fluctuations) of the normal modes. It is shown how the results can be extended to bodies of any shape; in particular, the force is given for a sphere interacting with a half-space. The calculations are performed using the well-known Drude-Lorentz (plasma) model of (non-magnetic) polarizable matter. The polarization degrees of freedom are explicitly introduced. It is shown that the polarization dynamical variables for the two bodies are coupled through the electromagnetic field, very similar with two infinite sets of coupled harmonic oscillators.