Lateral projection as a possible explanation of the nontrivial boundary dependence of the Casimir force

Zanette, S. I.; Caride, A. O.

doi:10.1103/physreva.63.014101

Cited by 16 publications

(21 citation statements)

References 26 publications

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“…In this case the functional dependence is given by . By this means perturbation theory with account of the lateral Casimir force can be made consistent with experimental data and might explain the observed nontrivial boundary dependence of the Casimir force [276]. The complete solution of the problem may be achieved with an experiment where both the vertical and the lateral Casimir forces are measured.…”

Section: Possible Explanation Of the Nontrivial Boundary Dependence Omentioning

confidence: 64%

“…In consequence of this, the assumption of a simple perturbation theory that the locations of the sphere above different points of a corrugated surface are equally probable can be violated. As indicated in [276], the diverse assumptions on the probability distribution describing location of the sphere above different points of the plate result in an essential change in force-distance relation. Thus the perturbation theory taking the lateral force into account may work for a case of corrugated plate.…”

Section: Possible Explanation Of the Nontrivial Boundary Dependence Omentioning

confidence: 99%

“…Integrating in ρ the final result is obtained [276] 27) where the vertical Casimir force F (0) dl for ideal metal was defined in Eq. (4.108).…”

Section: Possible Explanation Of the Nontrivial Boundary Dependence Omentioning

confidence: 99%

“…[276] the perturbative calculations for both vertical and lateral Casimir force acting in the configuration of a sphere situated above a corrugated plate is presented (note that the lateral force arises due to the absence of translational symmetry on a plate with corrugations). The study of [276] revealed that a lateral force acts upon the sphere (in contrast to the usual vertical Casimir force) in such a way that it tends to change the bottom position of the sphere in the direction of a nearest maximum point of the vertical Casimir force (which coincides with the maximum point of corrugations). In consequence of this, the assumption of a simple perturbation theory that the locations of the sphere above different points of a corrugated surface are equally probable can be violated.…”

Section: Possible Explanation Of the Nontrivial Boundary Dependence Omentioning

confidence: 99%

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New developments in the Casimir effect

2001

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We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

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Section: Possible Explanation Of the Nontrivial Boundary Dependence Omentioning

confidence: 64%

Section: Possible Explanation Of the Nontrivial Boundary Dependence Omentioning

confidence: 99%

“…Integrating in ρ the final result is obtained [276] 27) where the vertical Casimir force F (0) dl for ideal metal was defined in Eq. (4.108).…”

Section: Possible Explanation Of the Nontrivial Boundary Dependence Omentioning

confidence: 99%

Section: Possible Explanation Of the Nontrivial Boundary Dependence Omentioning

confidence: 99%

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New developments in the Casimir effect

2001

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“…It is suggested that lateral movement of the two surfaces may be able to account for the deviations [21].…”

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confidence: 99%

How Casimir forces are shaping up

Lamoreaux¹

2008

Physics

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We report measurements of the Casimir force between a gold sphere and a silicon surface with an array of nanoscale, rectangular corrugations using a micromechanical torsional oscillator. At distances between 150 and 500 nm, the measured force shows significant deviations from the pairwise additive formulism, demonstrating the strong dependence of the Casimir force on the shape of the interacting bodies. The observed deviation, however, is smaller than the calculated values for perfectly conducting surfaces, possibly due to the interplay between finite conductivity and geometry effects. DOI: 10.1103/PhysRevLett.101.030401 PACS numbers: 03.70.+k, 12.20.Fv, 12.20.Ds, 42.50.Lc The Casimir force is the interaction between neutral conductors that can be understood as resulting from the alteration of the zero point energy of the electromagnetic field in the presence of boundaries [1]. For two perfect metallic planar surfaces, the force is attractive and is given by F c 2 @cA=240z4 , where c is the speed of light, @ is the Planck's constant=2, z is the separation between the plates, and A is the area of the plates. There exists a close connection between the Casimir force between conductors and the van der Waals (vdW) force between molecules. For the former, the quantum fluctuations are often associated with the vacuum electromagnetic field, while the latter commonly refers to the interaction between fluctuating dipoles. In simple geometries such as two parallel planes, the Casimir force can be interpreted as an extension of the vdW force in the retarded limit. The interaction between molecules in the two plates is summed to yield the total force. However, such summation of the vdW force is not always valid for extended bodies because the vdW force is not pairwise additive. The interaction between two molecules is affected by the presence of a third molecule. One important characteristic of the Casimir force is its strong dependence on geometry [2]. The Casimir energy for a conducting spherical shell [3] or a rectangular box [4,5] has been calculated to have opposite sign to parallel plates. Whether such geometries exhibit repulsive Casimir forces remains a topic of current interest [6].In recent years, there have been a number of precision measurements of the Casimir force [7][8][9][10][11][12][13][14][15]. These experiments yield agreement with the theoretical calculations to accuracies of better than 1% when nonideal behavior of the metallic surfaces [16][17][18] are taken into account. The vast majority of force measurements were performed between a sphere and a flat plate, two flat plates, or two cylinders. For these simple geometries, the Casimir force is not expected to show significant deviations from the pairwise additive approximation (PAA) at small separations. There has only been one experiment that involved surfaces of other geometries, where the Casimir force is measured between a sphere and a plate with small sinusoidal corrugations [19]. While this measurement shows deviations from PAA, the interpret...

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Attractive and Repulsive Casimir–Lifshitz Forces, QED Torques, and Applications to Nanomachines

Capasso

Munday

2011

Casimir Physics

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Lateral projection as a possible explanation of the nontrivial boundary dependence of the Casimir force

Cited by 16 publications

References 26 publications

New developments in the Casimir effect

New developments in the Casimir effect

How Casimir forces are shaping up

Attractive and Repulsive Casimir–Lifshitz Forces, QED Torques, and Applications to Nanomachines

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