Non-superposition effects in the Dirichlet–Casimir effect

Ttira, Claudio Ccapa; Fosco, C. D.; Losada, Edith L.

doi:10.1088/1751-8113/43/23/235402

Cited by 8 publications

(15 citation statements)

References 20 publications

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“…In a system of three atoms these effects were discussed in 1943 by Axilrod and Teller [18], and for N molecules they were discussed, in 1985, by Power and Thirunamachandran [19]. Recently, nonadditive effects were discussed for macroscopic bodies [20,21]. Here our purpose is to discuss the nonadditivity of the van der Waals interaction in systems involving an atom and complementary surfaces, such as the above-discussed atom-disk system and an atom interacting with an infinite conducting plate with a circular hole.…”

Section: Nonadditivity In the Van Der Waals Interactionmentioning

confidence: 99%

Finite-size effects and nonadditivity in the van der Waals interaction

Souza

Kort-Kamp²,

Sigaud³

et al. 2011

Phys. Rev. A

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We obtain analytically the exact nonretarded dispersive interaction energy between an atom and a perfectly conducting disk. We consider the atom in the symmetry axis of the disk and assume that the atom is predominantly polarizable in the direction of this axis. For this situation we discuss the finite-size effects on the corresponding interaction energy. We follow the recent procedure introduced by Eberlein and Zietal together with the old and powerful Sommerfeld's image method for nontrivial geometries. For the sake of clarity we present a detailed discussion of Sommerfeld's image method. Comparing our results for the atom-disk system with those recently obtained for an atom near a conducting plane with a circular aperture, we discuss the nonadditivity of the van der Waals interactions involving an atom and two complementary surfaces. We show that there is a given ratio z/a between the distance z from the atom to the center of the disk (aperture) and the radius of the disk a (aperture) for which nonadditivity effects vanish. Qualitative arguments suggest that this quite unexpected result will occur not only for a circular hole, but for any other symmetric hole.

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Section: Nonadditivity In the Van Der Waals Interactionmentioning

confidence: 99%

Finite-size effects and nonadditivity in the van der Waals interaction

Souza

Kort-Kamp²,

Sigaud³

et al. 2011

Phys. Rev. A

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“…Consequently, the applicability of the DE depends in this case on the analyticity of g (2) (n, 0) as a function of n. On the other hand, these problems with k || do not appear when Dirichlet conditions are fixed, since in that case the zero-momentum expansion of the function equivalent to g(k || ) has only the O(k 2 || ) term, apart from the constant one.…”

Section: Order 2 In ηmentioning

confidence: 99%

“…One of the main reasons for that is that those expectation values usually do not satisfy a superposition principle, when regarded as functionals of the boundary. Thus, it is not possible, in general, to calculate the total energy in the presence of a given boundary, by adding the contributions due to each one of the possible pairs of surface elements into which the boundary may be decomposed [2]. As a consequence, rather few 'universal' (i.e., applicable to an arbitrary surface) properties of the Casimir effect are known.…”

Section: Introductionmentioning

confidence: 99%

Casimir interaction between two smoothly deformed cylindrical surfaces

Fuksman

Fosco

2017

Phys. Rev. D

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We generalize the derivative expansion (DE) approach to the interaction between almost-flat smooth surfaces, to the case of surfaces which are optimally described in cylindrical coordinates. As in the original form of the DE, the obtained method does not depend on the nature of the interaction. We apply our results to the study of the static, zerotemperature Casimir effect between two cylindrical surfaces, obtaining approximate expressions which are reliable under the assumption that the distance between those surfaces is always much smaller than their local curvature radii. To obtain the zero-point energy, we apply known results about the thermal Casimir effect for a planar geometry. To that effect, we relate the time coordinate in the latter to the angular variable in the cylindrical case, as well as the temperature to the radius of the cylinders. We study the dependence of the applicability of the DE on the kind of interaction, considering the particular cases where Dirichlet or Neumann conditions are applied to a scalar field.

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“…g µν p µ p ν + m 2 c 2 becomes g µνq µqν + 2 /m 2 c 2 ). If we perform first the integral over the world line metric, the mass shell constraint is implemented (see [35] for a version implementing Dirichlet boundary conditions in field theory)…”

Section: The Relation To the Green Functionmentioning

confidence: 99%

Casimir forces from a loop integral formulation

Babington¹

2010

J. Phys. A: Math. Theor.

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Abstract. We reformulate the Casimir force between bodies in non-trivial background media. The force may be written in terms of loop variables, the loop being a curve around the scattering sites. A natural path ordering of exponentials takes place when a particular representation of the scattering centres is given. The basic object to be evaluated is a reduced (or abbreviated) classical pseudo-action that can be operator valued, and can be obtained from a classical path integral description.

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Non-superposition effects in the Dirichlet–Casimir effect

Cited by 8 publications

References 20 publications

Finite-size effects and nonadditivity in the van der Waals interaction

Finite-size effects and nonadditivity in the van der Waals interaction

Casimir interaction between two smoothly deformed cylindrical surfaces

Casimir forces from a loop integral formulation

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