We consider detailed roughness and conductivity corrections to the Casimir force in the recent Casimir force measurement employing an atomic force microscope. The roughness of the test bodies — a metal plate and a sphere — was investigated with the AFM and the SEM respectively. It consists of separate crystals of different heights and a stochastic background. The amplitude of roughness relative...

Let g be a complex simple Lie algebra. Vogel derived a universal decomposition of S2g into (possibly virtual) Casimir eigenspaces, S2g = C⊕Y2 ⊕Y ′ 2 ⊕Y ′′ 2 which turns out to be a decomposition into irreducible modules. If we let 2t denote the Casimir eigenvalue of the adjoint representation (with respect to some invariant quadratic form), these modules respectively have Casimir eigenvalues 4t...

We analyze pull-in instability of electrostatically actuated microelectromechanical systems, and study changes in pull-in parameters due to the Casimir effect. When the size of the device is reduced, the magnitude of the Casimir force is comparable with that of the Coulomb force and it significantly alters pull-in parameters. We model the deformable conductor as an elastic membrane and consider...

The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically for the first time for an arbitrary physically possible frequency dispersion of dielectric permittivity ε(iω). A microscopic model of dielectrics is considered, divergences are absent in calculations because an average interatomic distance λ is a physical cut-off in the theory. Thi...

The Casimir stress on two concentric spherical shell in de Sitter background for massless scalar field is calculated. The scalar field satisfies Dirichlet boundary conditions on the spheres. The metric is written in conformally flat form to make maximum use of Minkowski space calculations. Then the Casimir stress is calculated for inside and outside of the shell with different backgrounds. This...

Limit transitions are constructed between the generators (Casimir operators) of the center of the universal covering algebra for the Lie algebras of the groups of motions of n-dimensional spaces of constant curvature. A method is proposed for obtaining the Casimir operators of a group of motions of an arbitrary n-dimensional space of constant curvature from the known Casimir operators of the gr...

The Casimir force is the attraction between uncharged metallic surfaces as a result of quantum mechanical vacuum fluctuations of the electromagnetic field. We demonstrate the Casimir effect in microelectromechanical systems using a micromachined torsional device. Attraction between a polysilicon plate and a spherical metallic surface results in a torque that rotates the plate about two thin tor...

The temperature dependence of the Casimir effect for the radiation field confined between two conducting plates is analysed. The Casimir energy is shown to decline exponentially with temperature while the Casimir entropy which is defined in the text is shown to approach a limit which depends only on the geometry of the constraining plates. The results are discussed in terms of the relation betw...

The last 10 years have seen the emergence of microand nanomechanical force sensors capable of measuring the Casimir interaction with great accuracy and precision. These measurements have proved fundamental to further develop the understanding of vacuum fluctuations in the presence of boundary conditions. These micromechanical sensors have also allowed to quantify the influence of materials prop...

We study the Casimir force on a single surface immersed in an inhomoge-neous medium. Specifically we study the vacuum fluctuations of a scalar field with a spatially varying squared mass, m 2 + λ∆(x − a) + V (x), where V is a smooth potential and ∆(x) is a unit-area function sharply peaked around x = 0. ∆(x − a) represents a semi-penetrable thin plate placed at x = a. In the limits {∆(x−a) → δ(...