Noncontact gears. I. Next-to-leading order contribution to the lateral Casimir force between corrugated parallel plates
Noncontact gears. I. Next-to-leading order contribution to the lateral Casimir force between corrugated parallel plates
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非接触式齿轮。
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
K. V. Shajesh
中科院分区：
文献类型：
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作者：
I. Cavero;K. Milton;Prachi Parashar;K. V. Shajesh
我们计算的横向Casimir力波纹平行板，描述的{δ}-功能的潜力，通过一个标量场相互作用，使用多重散射形式主义。从一开始就把无波纹平行板对Casimir能量的贡献作为背景。我们推导出领先的和下一个领先的顺序贡献的横向卡西米尔力的情况下，当的振幅是小的相比，λ波长。我们提出明确的结果，在有限积分的情况下的狄利克雷极限，弱耦合极限的精确结果，为领导和下一个领导的订单。由于次领先贡献的修正是显著的。在弱耦合的限制，我们计算的横向Casimir力正好在一个单一的积分，我们评估数值。弱极限情况下的精确结果使我们能够估计微扰结果中的误差。我们表明，在横向Casimir力的错误，在弱耦合限制，当下一个领先的顺序的贡献包括显着低时，的振幅是小的相比，λ波长。我们希望类似的结论适用于狄利克雷的情况。对电磁情况的类似计算应能充分减少理论误差，以便与实验比较。«少
We calculate the lateral Casimir force between corrugated parallel plates, described by {delta}-function potentials, interacting through a scalar field, using the multiple scattering formalism. The contributions to the Casimir energy due to uncorrugated parallel plates is treated as a background from the outset. We derive the leading- and next-to-leading-order contribution to the lateral Casimir force for the case when the corrugation amplitudes are small in comparison to corrugation wavelengths. We present explicit results in terms of finite integrals for the case of the Dirichlet limit, and exact results for the weak-coupling limit, for the leading- and next-to-leading-orders. The correction due to the next-to-leading contribution is significant. In the weak coupling limit we calculate the lateral Casimir force exactly in terms of a single integral which we evaluate numerically. Exact results for the case of the weak limit allows us to estimate the error in the perturbative results. We show that the error in the lateral Casimir force, in the weak coupling limit, when the next-to-leading order contribution is included is remarkably low when the corrugation amplitudes are small in comparison to corrugation wavelengths. We expect similar conclusions to hold for the Dirichlet case. The analogous calculation for the electromagnetic casemore » should reduce the theoretical error sufficiently for comparison with the experiments.« less