2011
DOI: 10.1103/physrevd.84.065027
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First analytic correction to the proximity force approximation in the Casimir effect between two parallel cylinders

Abstract: 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 ou… Show more

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Cited by 31 publications
(10 citation statements)
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References 42 publications
(94 reference statements)
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“…[27] from the exact representation of the Casimir interaction energy using perturbation method with careful order counting. This method was then extended to the sphere-plate configuration [44][45][46][47], the cylinder-cylinder configuration [48], and the sphere-sphere configuration [49]. There is no doubt that this method can be extended to the sphere-cylinder configuration considered here, although some tedious work is required.…”
Section: Appendix: Small Separation Behaviormentioning
confidence: 94%
“…[27] from the exact representation of the Casimir interaction energy using perturbation method with careful order counting. This method was then extended to the sphere-plate configuration [44][45][46][47], the cylinder-cylinder configuration [48], and the sphere-sphere configuration [49]. There is no doubt that this method can be extended to the sphere-cylinder configuration considered here, although some tedious work is required.…”
Section: Appendix: Small Separation Behaviormentioning
confidence: 94%
“…5, we plot the dependence of the two term asymptotic expansion (49), normalized by the proximity force approximation, on the normalized distance ε and dimension D. It is observed that the correction to the proximity force approximation becomes larger when D is larger. In fact, from (49), we find that when D is large,…”
Section: The Classical Casimir Interactionmentioning
confidence: 99%
“…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%