Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields

The equivalence of the covariant renormalization and the partial-wave renormaliz ation (PWR) approach is proven explicitly for the one-loop self-energy correction (SE) of a bound electron state in the presence of external perturbation potentials. No spurious correctio n terms to the noncovariant PWR scheme are generated for Coulomb-type screening potentia ls and for external magnetic fields. It is shown that in numerical calculations of the SE with Coulombic perturbation potential spurious terms result from an improper treatment of the unphysical high-energy contribution. A method for performing the PWR utilizing the relativistic B-spline approach for the construction of the Dirac spectrum in external magnetic fields is proposed. This method is applied for calculating QED corrections to the bound-electron $g$-factor in H-like ions. Within the level of accuracy of about 0.1% no spurious terms are generated in numerical calculations of the SE in magnetic fields.Comment: 22 pages, LaTeX, 1 figur

Friction Laws for Elastic Nano-Scale Contacts

The effect of surface curvature on the law relating frictional forces F with normal load L is investigated by molecular dynamics simulations as a function of surface symmetry, adhesion, and contamination. Curved, non-adhering, dry, commensurate surfaces show a linear dependency, F proportional to L, similar to dry flat commensurate or amorphous surfaces and macroscopic surfaces. In contrast, curved, non-adhering, dry, amorphous surfaces show F proportional to L^(2/3) similar to friction force microscopes. In our model, adhesive effects are most adequately described by the Hertz plus offset model, as the simulations are confined to small contact radii. Curved lubricated or contaminated surfaces show again different behavior; details depend on how much of the contaminant gets squeezed out of the contact. Also, it is seen that the friction force in the lubricated case is mainly due to atoms at the entrance of the tip.Comment: 7 pages, 5 figures, submitted to Europhys. Let

Fluid flow at the interface between elastic solids with randomly rough surfaces

I study fluid flow at the interface between elastic solids with randomly rough surfaces. I use the contact mechanics model of Persson to take into account the elastic interaction between the solid walls and the Bruggeman effective medium theory to account for the influence of the disorder on the fluid flow. I calculate the flow tensor which determines the pressure flow factor and, e.g., the leak-rate of static seals. I show how the perturbation treatment of Tripp can be extended to arbitrary order in the ratio between the root-mean-square roughness amplitude and the average interfacial surface separation. I introduce a matrix D(Zeta), determined by the surface roughness power spectrum, which can be used to describe the anisotropy of the surface at any magnification Zeta. I present results for the asymmetry factor Gamma(Zeta) (generalized Peklenik number) for grinded steel and sandblasted PMMA surfaces.Comment: 16 pages, 14 figure

Dynamical transitions and sliding friction in the two-dimensional Frenkel-Kontorova model

The nonlinear response of an adsorbed layer on a periodic substrate to an external force is studied via a two dimensional uniaxial Frenkel-Kontorova model. The nonequlibrium properties of the model are simulated by Brownian molecular dynamics. Dynamical phase transitions between pinned solid, sliding commensurate and incommensurate solids and hysteresis effects are found that are qualitatively similar to the results for a Lennard-Jones model, thus demonstrating the universal nature of these features.Comment: 11 pages, 12 figures, to appear in Phys. Rev.

Transverse thermal depinning and nonlinear sliding friction of an adsorbed monolayer

We study the response of an adsorbed monolayer under a driving force as a model of sliding friction phenomena between two crystalline surfaces with a boundary lubrication layer. Using Langevin-dynamics simulation, we determine the nonlinear response in the direction transverse to a high symmetry direction along which the layer is already sliding. We find that below a finite transition temperature, there exist a critical depinning force and hysteresis effects in the transverse response in the dynamical state when the adlayer is sliding smoothly along the longitudinal direction.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Elastic contact between self-affine surfaces: Comparison of numerical stress and contact correlation functions with analytic predictions

Contact between an elastic manifold and a rigid substrate with a self-affine fractal surface is reinvestigated with Green's function molecular dynamics. Stress and contact autocorrelation functions (ACFs) are found to decrease algebraically. A rationale is provided for the observed similarity in the exponents for stress and contact ACFs. Both exponents differ substantially from analytic predictions over the range of Hurst roughness exponents studied. The effect of increasing the range of interactions from a hard sphere repulsion to exponential decay is analyzed. Results for exponential interactions are accurately described by recent systematic corrections to Persson's contact mechanics theory. The relation between the area of simply connected contact patches and the normal force is also studied. Below a threshold size the contact area and force are consistent with Hertzian contact mechanics, while area and force are linearly related in larger contact patches.Comment: 12 pages, 9 figure

Enhancement of noncontact friction between closely spaced bodies by two-dimensional systems

. We consider the effect of an external bias voltage and the spatial variation of the surface potential, on the damping of cantilever vibrations. The electrostatic friction is due to energy losses in the sample created by the electromagnetic field from the oscillating charges induced on the surface of the tip by the bias voltage and spatial variation of the surface potential. A similar effect arises when the tip is oscillating in the electrostatic field created by charged defects in a dielectric substrate. The electrostatic friction is compared with the van der Waals friction originating from the fluctuating electromagnetic field due to quantum and thermal fluctuation of the current density inside the bodies. We show that the electrostatic and van der Waals friction can be greatly enhanced if on the surfaces of the sample and the tip there are two-dimension (2D) systems, e.g. a 2D-electron system or incommensurate layers of adsorbed ions exhibiting acoustic vibrations. We show that the damping of the cantilever vibrations due to the electrostatic friction may be of similar magnitude as the damping observed in recent experiments of Stipe \textit{et al} [B.C.Stipe, H.J.Mamin, T.D.Stowe, T.W.Kenny, and D.Rugar, Phys.Rev. Lett.% \textbf{87}, 0982001]. We also show that at short separation the van der Waals friction may be large enough to be measured experimentally.Comment: 11 pages, 2 figure

The effect of Coulombic friction on spatial displacement statistics

The phenomenon of Coulombic friction enters the stochastic description of dry friction between two solids and the statistic characterization of vibrating granular media. Here we analyze the corresponding Fokker-Planck equation including both velocity and spatial components, exhibiting a formal connection to a quantum mechanical harmonic oscillator in the presence of a delta potential. Numerical solutions for the resulting spatial displacement statistics show a crossover from exponential to Gaussian displacement statistics. We identify a transient intermediate regime that exhibits multiscaling properties arising from the contribution of Coulombic friction. The possible role of these effects during observations in diffusion experiments is shortly discussed.Comment: 11 pages, 9 figure

Self-energy correction to the bound-electron g factor in H-like ions

The one-loop self-energy correction to the 1s electron g factor is evaluated to all orders in Z\alpha with an accuracy, which is essentially better than that of previous calculations of this correction. As a result, the uncertainty of the theoretical prediction for the bound-electron g factor in H-like carbon is reduced by a factor of 3. This improves the total accuracy of the recent electron-mass determination [Beier et al. Phys. Rev. Lett. 88, 011603 (2002)]. The new value of the electron mass is found to be m_e = 0.000 548 579 909 3(3) u