Zur Approximation auf dünnen Mengen im ℂ2

Ohne ZusammenfassungHerrn Professor Tietz zum 60. Geburtstag     

The london approximation and the calculation of dispersion interactions as a sum of atom-atom terms

A London approximation utilizing atomic valence state ionization potentials and static polarizabilities yields C₆ results in good agreement with accurate values for a number of systems. Generally there is considerable improvement over the results obtained using the London approximation in conjunction with molecular parameters and reasons for this are discussed.     

Nuclear matter distributions for 16,17,18O from a microscopic analysis of elastic proton scattering

An analysis of 65 MeV elastic proton scattering by ^16,17,18O has been made in terms of a reformulated optical model. Matter distributions for ¹⁷O and ¹⁸O have been obtained relative to ¹⁶O. The results for the rms matter radii are R₁₇?R₁₆ = 0.04±0.03 fm and R₁₈?R₁₆ = 0.35± 0.07 fm.     

Linear response theory for systems obeying the master equation

Linear response theory is developed for systems whose time dependence is described by a master equation. The fluctuation dissipation theorem expressing the linear response of the system in terms of fluctuation properties of the system in equilibrium is derived. The time-dependent Ising spin system in interaction with a heat bath, the Glauber model, is discussed as a particular case of the formalism.The work of one of the authors (D.B.) was supported in part by the National Science Foundation under Contract GP 10536.On leave of absence from the Institute of Physics, Belgrade, Yugoslavia.     

On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion

Differential equations governing the time evolution of distribution functions for Brownian motion in the full phase space were first derived independently by Klein and Kramers. From these so-called Fokker-Planck equations one may derive the reduced differential equations in coordinate space known as Smoluchowski equations. Many such derivations have previously been reported, but these either involved unnecessary assumptions or approximations, or were performed incompletely. We employ an iterative reduction scheme, free of assumptions, and calculate formally exact corrections to the Smoluchowski equations for many-particle systems with and without hydrodynamic interaction, and for a single particle in an external field. In the absence of hydrodynamic interaction, the lowest order corrections have been expressed explicitly in terms of the coordinate space distribution function. An additional application of the method is made to the reduction of the stress tensor used in evaluating the intrinsic viscosity of particles in solution. Most of the present work is based on classical Brownian motion theory, but brief consideration is given in an appendix to some recent developments regarding non-Markovian equations for Brownian motion.Supported by the National Science Foundation.     

The phonon spectra of the superionic conductor KBiF4 (a CaF2 Analogue)

Theoretical calculations of the phonon infrared and Raman response in simple superionic conductors such as AgI, CuI, and CaF₂ types are based on two fundamental assumptions. First, most of the response can be understood in terms of a breakdown of the selection rules due to disorder (lack of translational symmetry) and second, harmonic lattice dynamics can be used with a good degree of accuracy. This is tested here experimentally in the superionic conductor K_1?xBi_1+xF_4+2x which has the CaF₂ structure (x=0.0 is analogous to 2CaF₂). By varying x we increase the disorder (via F-ion interstitials and vacancies) and measure broad temperature independent reduced Raman and infrared responses. The broad response is dependent on x in a manner consistent with the first assumption and the lack of temperature dependence is consistent with the second assumption. In order to understand the transverse optic vibrational frequencies (ω_TO) we have found that plots of ω_TO²vs. μ^-1 (reduced mass) are very helpful. The linearity of such plots, for example, for tetrahedrally bonded AgI, CuI, CuBr, CuCl (formal charge Z=1) and the difference of such results for similar materials but with formal charges of 2, 3, and 4 is surprising and not as yet understood. Other conclusions are discussed at the end of the paper.