Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation

Bordag, M.

doi:10.1103/physrevd.75.065003

Cited by 60 publications

(25 citation statements)

References 18 publications

(61 reference statements)

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“…In the case that the objects have certain symmetries that allow a separable coordinate system to be employed, one can calculate these matrices explicitly. This has made possible the exact analytic and numerical analysis of the Casimir interaction between a sphere and a plate [18][19][20][21][22][23][24][25][26][27][28][29], between two spheres [30][31][32], between a cylinder and a plate [2,33,34], between two cylinders [35][36][37][38], between a sphere and a cylinder [39,40], as well as other geometries [41][42][43].…”

Section: Introductionmentioning

confidence: 99%

“…One of the main objectives of the current work is to derive the TGTG formula for the Casimir interaction energy. As in [33], we are also going to study the asymptotic behaviors of the Casimir interaction in the small separation regime. We would expect that the leading term of the Casimir interaction coincides with the proximity force approximation (PFA), which we are going to confirm.…”

Section: Introductionmentioning

confidence: 99%

“…Our work can be considered as a generalization of [33] where * LeePeng.Teo@nottingham.edu.my we consider a spherical plasma sheet instead of a cylindrical plasma sheet. One of the main objectives of the current work is to derive the TGTG formula for the Casimir interaction energy.…”

Section: Introductionmentioning

confidence: 99%

“…In [33], the Casimir interaction between a cylindrical plasma sheet and a planar plasma sheet has been considered. Our work can be considered as a generalization of [33] where * LeePeng.Teo@nottingham.edu.my we consider a spherical plasma sheet instead of a cylindrical plasma sheet.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we consider the Casimir interaction between a spherical plasma sheet and a planar plasma sheet. The plasma sheet model was considered in [33,[44][45][46][47][48][49] to model a graphene sheet, describing the π electrons in C 60 molecules. This model has its own appeal in describing a thin shell of materials that have the same attributes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Casimir interaction between spherical and planar plasma sheets

Teo

2014

Phys. Rev. A

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We consider the interaction between a spherical plasma sheet and a planar plasma sheet due to the vacuum fluctuations of electromagnetic fields. We use the mode summation approach to derive the Casimir interaction energy and study its asymptotic behaviors. In the small separation regime, we confirm the proximity force approximation and calculate the first correction beyond the proximity force approximation. This study has potential application to model Casimir interaction between objects made of materials that can be modeled by plasma sheets such as graphene sheets.Comment: 13 page

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Casimir interaction between spherical and planar plasma sheets

Teo

2014

Phys. Rev. A

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Different Approaches

Sernelius¹

2018

Fundamentals of Van Der Waals and Casimir Interactions

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Sphere-plate Casimir interaction in (D + 1) -dimensional spacetime

Teo

2014

Journal of Mathematical Physics

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In this paper, we derive the formula for the Casimir interaction energy between a sphere and a plate in (D + 1)-dimensional Minkowski spacetime. It is assumed that the scalar field satisfies the Dirichlet or Neumann boundary conditions on the sphere and the plate. As in the D = 3 case, the formula is of TGTG type. One of our main contributions is deriving the translation matrices which express the change of bases between plane waves and spherical waves for general D. Using orthogonality of Gegenbauer polynomials, it turns out that the final TGTG formula for the Casimir interaction energy can be simplified to one that is similar to the D = 3 case. To illustrate the application of the formula, both large separation and small separation asymptotic behaviors of the Casimir interaction energy are computed. The large separation leading term is proportional to L −D+1 if the sphere is imposed with Dirichlet boundary condition, and to L −D−1 if the sphere is imposed with Neumann boundary condition, where L is distance from the center of the sphere to the plane. For the small separation asymptotic behavior, it is shown that the leading term is equal to the one obtained using proximity force approximation. The next-to-leading order term is also computed using perturbation method. It is shown that when the space dimension D is larger than 5, the next-to-leading order has sign opposite to the leading order term. Moreover, the ratio of the next-to-leading order term to the leading order term is linear in D, indicating a larger correction at higher dimensions.

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Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation

Abstract: We calculate the first correction beyond proximity force approximation for a cylindrical graphene sheet in interaction with a flat graphene sheet or a dielectric half space.

Cited by 60 publications

References 18 publications

Casimir interaction between spherical and planar plasma sheets

Casimir interaction between spherical and planar plasma sheets

Different Approaches

Sphere-plate Casimir interaction in (D + 1) -dimensional spacetime

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