Casimir effect for soft boundaries

Actor, Alfred; Bender, I.

doi:10.1103/physrevd.52.3581

Cited by 70 publications

(64 citation statements)

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“…Under this condition the force acting in both configurations is one and the same because the upper part of a sphere makes a negligible contribution to the force value. We put the coordinate origin on a surface of a disk under a sphere center, which is situated at a point z = a + R. Then the width of a gap is 104) and the principal radii of a gap curvature are simply calculated…”

Section: Sphere (Lens) Above a Disk: Additive Methods And Proximity Fmentioning

confidence: 99%

“…In addition, due to the missing curvature of the boundaries, most heat kernel coefficients are zero which makes it much easier to extract the finite part of the vacuum energy even if additional external factors are included. In a series of papers [102,103] generalizations of flat boundaries to rectangular regions (e.g., a half plane sticked to a plane), and in [104] to softened boundaries (e.g. a background potential growing to infinity at the position of the boundary) are considered.…”

Section: Flat Boundariesmentioning

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: Sphere (Lens) Above a Disk: Additive Methods And Proximity Fmentioning

confidence: 99%

Section: Flat Boundariesmentioning

confidence: 99%

New developments in the Casimir effect

2001

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“…The closest work that we know of in previous literature is that of Actor and Bender 14 , in which the perfectly reflecting wall is replaced by a harmonic-oscillator potential. That paper was written before the modern critiques of formal renormalization 15,16 and the modern emphasis on local quantities (such as energy density).…”

Section: Precursorsmentioning

confidence: 99%

Energy Density and Pressure in Power-Wall Models

Fulling

Milton

Wagner

2012

Int. J. Mod. Phys. Conf. Ser.

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A finite ultraviolet cutoff near a reflecting boundary yields a stress tensor that violates the basic energy-pressure relation. Therefore, a "soft" wall described by a power-law potential, which needs no ad hoc cutoff, is being investigated by the collaboration centered at Texas A&M University and the University of Oklahoma. Progress is reported here.Keywords: vacuum energy; stress tensor; boundary; soft wall. PACS numbers: 03.70.+k, 11.10.Gh Hard Walls: The Pressure Paradox Basic formalism and empty spaceWe model the electromagnetic vacuum-energy problem by a massless scalar field in three space dimensions, subjected to the Dirichlet boundary condition on the "conducting" boundaries. The vacuum energy can be calculated from a Green function, such as the "cylinder kernel", 1,2,3where the φ n are the normalized eigenfunctions with frequencies ω n . The classical formulas for the components of the vacuum expectation value of the stress-energy

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“…Consequently, we prefer to maintain the hard walls assumption. In the context of the Casimir energy of minimally coupled scalar fields, many authors used soft, hard and semihard BC's [2]. Different questions sometimes require more complicated BC's, like the quantum mechanical treatment of the boundary conditions presented by Ford and Svaiter [3], a device implemented to solve a long standing paradox concerning the renormalized energy of minimally and conformally coupled scalar fields.…”

Section: Introductionmentioning

confidence: 99%

Finite size effects in the anisotropic (λ/4!)(φ14+φ24)d model

Fosco

Svaiter

2001

Journal of Mathematical Physics

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We consider the λ 4! (ϕ 4 1 + ϕ 4 2 ) model on a d-dimensional Euclidean space, where all but one of the coordinates are unbounded. Translation invariance along the bounded coordinate, z, which lies in the interval [0, L], is broken because of the boundary conditions (BC's) chosen for the hyperplanes z = 0 and z = L. Two different possibilities for these BC's boundary conditions are considered: DD and NN, where D denotes Dirichlet and N Newmann, respectively. The renormalization procedure up to one-loop order is applied, obtaining two main results. The first is the fact that the renormalization program requires the introduction of counterterms which are surface interactions. The second one is that the tadpole graphs for DD and NN have the same z dependent part in modulus but with opposite signs. We investigate the relevance of this fact to the elimination of surface divergences.

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Casimir effect for soft boundaries

Cited by 70 publications

References 20 publications

New developments in the Casimir effect

New developments in the Casimir effect

Energy Density and Pressure in Power-Wall Models

Finite size effects in the anisotropic (λ/4!)(φ14+φ24)d model

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