Casimir Force between a Small Dielectric Sphere and a Dielectric Wall

The possibility of repulsive Casimir forces between small metal spheres and a dielectric half-space is discussed. We treat a model in which the spheres have a dielectric function given by the Drude model, and the radius of the sphere is small compared to the corresponding plasma wavelength. The half-space is also described by the same model, but with a different plasma frequency. We find that in the retarded limit, the force is quasi-oscillatory. This leads to the prediction of stable equilibrium points at which the sphere could levitate in the Earth's gravitational field. This seems to lead to the possibility of an experimental test of the model. The effects of finite temperature on the force are also studied, and found to be rather small at room temperature. However, thermally activated transitions between equilibrium points could be significant at room temperature.Comment: 16 pages, 5 figure

A generalized Kramers-Kronig transform for Casimir effect computations

Recent advances in experimental techniques now permit to measure the Casimir force with unprecedented precision. In order to achieve a comparable precision in the theoretical prediction of the force, it is necessary to accurately determine the electric permittivity of the materials constituting the plates along the imaginary frequency axis. The latter quantity is not directly accessible to experiments, but it can be determined via dispersion relations from experimental optical data. In the experimentally important case of conductors, however, a serious drawback of the standard dispersion relations commonly used for this purpose, is their strong dependence on the chosen low-frequency extrapolation of the experimental optical data, which introduces a significant and not easily controllable uncertainty in the result. In this paper we show that a simple modification of the standard dispersion relations, involving suitable analytic window functions, resolves this difficulty, making it possible to reliably determine the electric permittivity at imaginary frequencies solely using experimental optical data in the frequency interval where they are available, without any need of uncontrolled data extrapolations.Comment: 10 pages, 6 encapsulated figures. A few typos corrected, some references added. The new version matches the one accepted for publication on Phys. Rev.

FeAs-based superconductivity: a case study of the effects of transition metal doping on BaFe2As2

The recently discovered FeAs-based superconductors are a new, promising set of materials for both technological as well as basic research. They offer transition temperatures as high as 55 K as well as essentially isotropic and extremely large upper, superconducting critical fields in excess of 40 T at 20 K. In addition they may well provide insight into exotic superconductivity that extends beyond just FeAs-based superconductivity, perhaps even shedding light on the still perplexing CuO-based high-Tc materials. Whereas superconductivity can be induced in the RFeAsO (R = rare earth) and AEFe2As2 (AE = Ba, Sr, Ca)) families by a number of means, transition metal doping of BaFe2As2, e.g. Ba(Fe1-xTMx)2As2, offers the easiest experimental access to a wide set of materials. In this review we present an overview and summary of the effect of TM doping (TM = Co, Ni, Cu, Pd, and Rh) on BaFe2As2. The resulting phase diagrams reveal the nature of the interaction between the structural, magnetic and superconducting phase transitions in these compounds and delineate a region of phase space that allows for the stabilization of superconductivity.Comment: edited and shortened version is accepted to AR:Condensed Matter Physic

Matter Bounce in Horava-Lifshitz Cosmology

Horava-Lifshitz gravity, a recent proposal for a UV-complete renormalizable gravity theory, may lead to a bouncing cosmology. In this note we argue that Horava-Lifshitz cosmology may yield a concrete realization of the matter bounce scenario, and thus give rise to an alternative to inflation for producing a scale-invariant spectrum of cosmological perturbations. In this scenario, quantum vacuum fluctuations exit the Hubble radius in the pre-bounce phase and the spectrum is transformed into a scale-invariant one on super-Hubble scales before the bounce because the long wavelength modes undergo squeezing of their wave-functions for a longer period of time than shorter wavelength modes. The scale-invariance of the spectrum of curvature fluctuations is preserved during and after the bounce. A distinctive prediction of this scenario is the amplitude and shape of the bispectrum.Comment: 6 pages, 1 figure, a couple of minor wording change

Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit

In earlier papers we have applied multiple scattering techniques to calculate Casimir forces due to scalar fields between different bodies described by delta function potentials. When the coupling to the potentials became weak, closed-form results were obtained. We simplify this weak-coupling technique and apply it to the case of tenuous dielectric bodies, in which case the method involves the summation of van der Waals (Casimir-Polder) interactions. Once again exact results for finite bodies can be obtained. We present closed formulas describing the interaction between spheres and between cylinders, and between an infinite plate and a retangular slab of finite size. For such a slab, we consider the torque acting on it, and find non-trivial equilibrium points can occur.Comment: 4 pages, 3 figure

Bohr-van Leeuwen theorem and the thermal Casimir effect for conductors

The problem of estimating the thermal corrections to Casimir and Casimir-Polder interactions in systems involving conducting plates has attracted considerable attention in the recent literature on dispersion forces. Alternative theoretical models, based on distinct low-frequency extrapolations of the plates reflection coefficient for transverse electric (TE) modes, provide widely different predictions for the magnitude of this correction. In this paper we examine the most widely used prescriptions for this reflection coefficient from the point of view of their consistency with the Bohr-van Leeuwen theorem of classical statistical physics, stating that at thermal equilibrium transverse electromagnetic fields decouple from matter in the classical limit. We find that the theorem is satisfied if and only if the TE reflection coefficient vanishes at zero frequency in the classical limit. This criterion appears to rule out some of the models that have been considered recently for describing the thermal correction to the Casimir pressure with non-magnetic metallic plates.Comment: 12 pages, no figures. Presentation has been significantly improved, more references included. The new version matches the one accepted for publication in Phys. Rev.

Application of the Lifshitz theory to poor conductors

The Lifshitz formula for the dispersive forces is generalized to the materials, which cannot be described with the local dielectric response. Principal nonlocality of poor conductors is related with the finite screening length of the penetrating field and the collisional relaxation; at low temperatures the role of collisions plays the Landau damping. The spatial dispersion makes the theory self consistent. Our predictions are compared with the recent experiment. It is demonstrated that at low temperatures the Casimir-Lifshitz entropy disappears as $T$ in the case of degenerate plasma and as $T^2$ for the nondegenerate one.Comment: Accepted for publication in PR

A theory of electromagnetic fluctuations for metallic surfaces and van der Waals interactions between metallic bodies

A new general expression is derived for the fluctuating electromagnetic field outside a metal surface, in terms of its surface impedance. It provides a generalization to real metals of Lifshitz theory of molecular interactions between dielectric solids. The theory is used to compute the radiative heat transfer between two parallel metal surfaces at different temperatures. It is shown that a measurement of this quantity may provide an experimental resolution of a long-standing controversy about the effect of thermal corrections on the Casimir force between real metal plates.Comment: 4 pages, 2 figures; typos corrected, minor changes to match the published version in Physical Review Letter

Gradient expansion, curvature perturbations and magnetized plasmas

The properties of magnetized plasmas are always investigated under the hypothesis that the relativistic inhomogeneities stemming from the fluid sources and from the geometry itself are sufficiently small to allow for a perturbative description prior to photon decoupling. The latter assumption is hereby relaxed and pre-decoupling plasmas are described within a suitable expansion where the inhomogeneities are treated to a given order in the spatial gradients. It is argued that the (general relativistic) gradient expansion shares the same features of the drift approximation, customarily employed in the description of cold plasmas, so that the two schemes are physically complementary in the large-scale limit and for the low-frequency branch of the spectrum of plasma modes. The two-fluid description, as well as the magnetohydrodynamical reduction, are derived and studied in the presence of the spatial gradients of the geometry. Various solutions of the coupled system of evolution equations in the anti-Newtonian regime and in the quasi-isotropic approximation are presented. The relation of this analysis to the so-called separate Universe paradigm is outlined. The evolution of the magnetized curvature perturbations in the nonlinear regime is addressed for the magnetized adiabatic mode in the plasma frame.Comment: 40 pages, no figure

Vacuum force on an atom in a magnetodielectric cavity

We demonstrate that, according to a recently suggested Lorentz-force approach to the Casimir effect, the vacuum force on an atom embedded in a material cavity differs substantially from the force on an atom of the cavity medium. The force on an embedded atom is of the familiar (van der Waals and Casimir-Polder) type, however, more strongly modified by the cavity medium than usually considered. The force on an atom of the cavity medium is of the medium-assisted force type with rather unusual properties, as demonstrated very recently [M. S. Tomas, Phys. Rev. A 71, 060101(R) (2005)]. This implies similar properties of the vacuum force between two atoms in a medium.Comment: RevTeX 4, 4 pages, 1 eps figure, corrected and slightly revise