Casimir forces beyond the proximity approximation

The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Pad\'e extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere-plate Casimir force at all separations.Comment: 4 pages, 1 figur

Casimir force between sharp-shaped conductors

Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest

Photon density of states for deformed surfaces

A new approach to the Helmholtz spectrum for arbitrarily shaped boundaries and a rather general class of boundary conditions is introduced. We derive the boundary induced change of the density of states in terms of the free Green's function from which we obtain both perturbative and non-perturbative results for the Casimir interaction between deformed surfaces. As an example, we compute the lateral electrodynamic Casimir force between two corrugated surfaces over a wide parameter range. Universal behavior, fixed only by the largest wavelength component of the surface shape, is identified at large surface separations. This complements known short distance expansions which are also reproduced.Comment: 8 pages, J Phys A Special Issue QFEXT0

Material Dependence of the Wire-Particle Casimir Interaction

We study the Casimir interaction between a metallic cylindrical wire and a metallic spherical particle by employing the scattering formalism. At large separations, we derive the asymptotic form of the interaction. In addition, we find the interaction between a metallic wire and an isotropic atom, both in the non-retarded and retarded limits. We identify the conditions under which the asymptotic Casimir interaction does not depend on the material properties of the metallic wire and the particle. Moreover, we compute the exact Casimir interaction between the particle and the wire numerically. We show that there is a complete agreement between the numerics and the asymptotic energies at large separations. For short separations, our numerical results show good agreement with the proximity force approximation

Universality versus material dependence of fluctuation forces between metallic wires

We calculate the Casimir interaction between two parallel wires and between a wire and a metall plate. The dielectric properties of the objects are described by the plasma, Drude and perfect metal models. We find that at asymptotically large separation interactions involving plasma wires and/or plates are independent of the material properties, but depend on the dc conductivity $\sigma$ for Drude wires. Counterintuitively, at intermediate separations the interaction involving Drude wires can become independent of $\sigma$. At smaller separations, we compute the interaction numerically and observe an approach to the proximity approximation

Casimir interaction between a plate and a cylinder

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate--sphere, where it is known at large separations. The force has an unexpectedly weak decay \sim L/(H^3 \ln(H/R)) at large plate--cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.Comment: 4 pages, 3 figure

Molecular phylogeny of brachiopods and phoronids based on nuclear-encoded small subunit ribosomal RNA gene sequences

Brachiopod and phoronid phylogeny is inferred from SSU rDNA sequences of 28 articulate and nine inarticulate brachiopods, three phoronids, two ectoprocts and various outgroups, using gene trees reconstructed by weighted parsimony, distance and maximum likelihood methods. Of these sequences, 33 from brachiopods, two from phoronids and one each from an ectoproct and a priapulan are newly determined. The brachiopod sequences belong to 31 different genera and thus survey about 10% of extant genus-level diversity. Sequences determined in different laboratories and those from closely related taxa agree well, but evidence is presented suggesting that one published phoronid sequence (GenBank accession UO12648) is a brachiopod-phoronid chimaera, and this sequence is excluded from the analyses. The chiton, Acanthopleura, is identified as the phenetically proximal outgroup; other selected outgroups were chosen to allow comparison with recent, non-molecular analyses of brachiopod phylogeny. The different outgroups and methods of phylogenetic reconstruction lead to similar results, with differences mainly in the resolution of weakly supported ancient and recent nodes, including the divergence of inarticulate brachiopod sub-phyla, the position of the rhynchonellids in relation to long- and short-looped articulate brachiopod clades and the relationships of some articulate brachiopod genera and species. Attention is drawn to the problem presented by nodes that are strongly supported by non-molecular evidence but receive only low bootstrap resampling support. Overall, the gene trees agree with morphology-based brachiopod taxonomy, but novel relationships are tentatively suggested for thecideidine and megathyrid brachiopods. Articulate brachiopods are found to be monophyletic in all reconstructions, but monophyly of inarticulate brachiopods and the possible inclusion of phoronids in the inarticulate brachiopod clade are less strongly established. Phoronids are clearly excluded from a sister-group relationship with articulate brachiopods, this proposed relationship being due to the rejected, chimaeric sequence (GenBank UO12648). Lineage relative rate tests show no heterogeneity of evolutionary rate among articulate brachiopod sequences, but indicate that inarticulate brachiopod plus phoronid sequences evolve somewhat more slowly. Both brachiopods and phoronids evolve slowly by comparison with other invertebrates. A number of palaeontologically dated times of earliest appearance are used to make upper and lower estimates of the global rate of brachiopod SSU rDNA evolution, and these estimates are used to infer the likely divergence times of other nodes in the gene tree. There is reasonable agreement between most inferred molecular and palaeontological ages. The estimated rates of SSU rDNA sequence evolution suggest that the last common ancestor of brachiopods, chitons and other protostome invertebrates (Lophotrochozoa and Ecdysozoa) lived deep in Precambrian time. Results of this first DNA-based, taxonomically representative analysis of brachiopod phylogeny are in broad agreement with current morphology-based classification and systematics and are largely consistent with the hypothesis that brachiopod shell ontogeny and morphology are a good guide to phylogeny

The boundary element approach to Van der Waals interactions

We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response. We achieve this by rewriting the interaction energy expression exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.Comment: 4 pages, 4 figures, RevTe