Possibility of measuring the thermal Casimir interaction between a plate and a cylinder attached to a micromachined oscillator

Decca, R. S.; Fischbach, Ephraim; Krause, D. E.; López, D.; Mostepanenko, V. M.

doi:10.1103/physreva.82.052515

Cited by 16 publications

(10 citation statements)

References 74 publications

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“…Note that for Neumann BC (A = 0) the zero mode is present corresponding to n = 0, λ = 0. The normalization coefficient C σ in (2.7) is determined from the standard condition 10) where the integration over the radial coordinate goes over the region inside the cylinder. In (2.10), δ σσ ′ stands for the Kronecker delta in the case of discrete components of σ (quantum numbers n and l) and for the Dirac delta function for continuous ones (k).…”

Section: Interior Regionmentioning

confidence: 99%

Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime

Saharian

Manukyan

2014

Class. Quantum Grav.

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We evaluate the positive-frequency Wightman function, the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling for a cylindrical shell in background of dS spacetime. The field is prepared in the Bunch-Davies vacuum state and on the shell the corresponding operator obeys Robin boundary condition. In the region inside the shell and for non-Neumann boundary conditions, the Bunch-Davies vacuum is a physically realizable state for all values of the mass and curvature coupling parameter. For both interior and exterior regions, the VEVs are decomposed into boundary-free dS and shell-induced parts. We show that the shell-induced part of the vacuum energy-momentum tensor has a nonzero off-diagonal component corresponding to the energy flux along the radial direction. Unlike to the case of a shell in Minkowski bulk, for dS background the axial stresses are not equal to the energy density. In dependence of the mass and of the coefficient in the boundary condition, the vacuum energy density and the energy flux can be either positive or negative. The influence of the background gravitational field on the boundary-induced effects is crucial at distances from the shell larger than the dS curvature scale. In particular, the decay of the VEVs with the distance is power-law (monotonic or oscillatory with dependence of the mass) for both massless and massive fields. For Neumann boundary condition the decay is faster than that for non-Neumann conditions.

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Section: Interior Regionmentioning

confidence: 99%

Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime

Saharian

Manukyan

2014

Class. Quantum Grav.

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“…Depending on the relative size of length scales, different regimes can be reached: Arrow (1) corresponds to an increasing distance d which ultimately leads to a non-universal interaction. Arrow (2) indicates an overall increase of the geometry (i.e., d/R fixed) with constant conductivity leading to a universal interaction. ξ 1 or d R 2 /λ σ , we reproduce the universal (perfect metal) asymptotic energy of Eq.…”

Section: A Parallel Cylindersmentioning

confidence: 99%

“…From the perspective of the experimental Casimir force studies, nano-cylindrical shapes are an optimal candidate for precision Casimir force measurements, in comparison to spheres for two reasons: (i) their effective area of interaction is larger [1,2], and (ii) mechanical oscillation modes of quasi-one-dimensional structures can be probed with high precision [3].…”

Section: Introductionmentioning

confidence: 99%

Collective charge fluctuations and Casimir interactions for quasi-one-dimensional metals

et al. 2012

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We investigate the Casimir interaction between two parallel metallic cylinders and between a metallic cylinder and plate. The material properties of the metallic objects are implemented by the plasma, Drude and perfect metal model dielectric functions. We calculate the Casimir interaction numerically at all separation distances and analytically at large separations. The large-distance asymptotic interaction between one plasma cylinder parallel to another plasma cylinder or plate does not depend on the material properties, but for a Drude cylinder it depends on the dc conductivity σ. At intermediate separations, for plasma cylinders the asymptotic interaction depends on the plasma wave length λp while for Drude cylinders the Casimir interaction can become independent of the material properties. We confirm the analytical results by the numerics and show that at short separations, the numerical results approach the proximity force approximation.

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“…It can lead to favorable conditions to search for extragravitational forces in the micrometer range and for the observation of finite-temperature corrections. These latter subjects have been explored for the cylinder-plane configuration in [30][31][32][33]. In view of this, the cylindrical configuration is becoming increasingly important in the study of the Casimir effect.…”

Section: Introductionmentioning

confidence: 99%

First analytic correction to the proximity force approximation in the Casimir effect between two parallel cylinders

Teo

2011

Phys. Rev. D

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We consider the small separation asymptotic expansions of the Casimir interaction energy and the Casimir interaction force between two parallel cylinders. The leading order terms and the next-to-leading order terms are computed analytically. Four combinations of boundary conditions are considered, which are Dirichlet-Dirichlet, Neumann-Neumann, Dirichlet-Neumann, and Neumann-Dirichlet. For the case where one cylinder is inside another cylinder, the computations are shown in detail. In this case, we restrict our attention to the situation where the cylinders are strictly eccentric and the distance between the cylinders d is much smaller than the distance between the centers of the cylinders. The computations for the case where the two cylinders are exterior to each other can be done in the same way and we only present the results, which turn up to be similar to the results for the case where one cylinder is inside another except for some changes of signs. In all the scenarios we consider, the leading order terms are of order d À7=2 and they agree completely with the proximity force approximations. The results for the nextto-leading order terms are new. In the limiting case where the radius of the larger cylinder approaches infinity, the well-known results for the cylinder-plate configuration with Dirichlet-Dirichlet or Neumann-Neumann boundary conditions are recovered.

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Possibility of measuring the thermal Casimir interaction between a plate and a cylinder attached to a micromachined oscillator

Cited by 16 publications

References 74 publications

Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime

Scalar Casimir densities induced by a cylindrical shell in de Sitter spacetime

Collective charge fluctuations and Casimir interactions for quasi-one-dimensional metals

First analytic correction to the proximity force approximation in the Casimir effect between two parallel cylinders

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