Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders

We analyze the Casimir force between two parallel infinite metal cylinders with nearby metal plates using two methods. Surprisingly, the attractive force between cylinders depends nonmonotonically on the separation from the plate(s), and the cylinder-plate force depends nonmonotonically on the separation of the cylinders. These multibody phenomenona do not follow from simple two-body force descriptions. We can explain the nonmonotonicity with the screening (enhancement) of the interactions by the fluctuating charges (currents) on the two cylinders and their images on the nearby plate(s).

Figure 1

(Color online) Casimir force per unit length between two cylinders (black) vs the ratio of sidewall separation to cylinder radius $h∕R$, at fixed $a∕R=2$, normalized by the total PFA force per unit length between two isolated cylinders [$F_{\mathrm{PFA}}=\frac{5}{2}(\hslash c{\pi }^3∕1920)\sqrt{R∕a^7}$ [18]]. The solid lines refer to the case with one sidewall, while dashed lines depict the results for two sidewalls, as indicated by the inset. Also shown are the individual TE (red) and TM (blue) forces.

Figure 2

(Color online) Casimir force per unit length between two cylinders of fixed radius $R$ vs the ratio of sidewall separation to cylinder radius $h∕R$ (for one plate), normalized by the total PFA force per unit length between two isolated cylinders. The force is plotted for different cylinder separations of $a∕R=0.2$, 0.6, 1.0, 2.0, 3.0, and 4.0.

Figure 3

(Color online) Casimir force per unit length between a plate and two cylinders of fixed radius $R$ vs the ratio of cylinder separation to cylinder radius $a∕R$, normalized by the total PFA force per unit length between a cylinder and a plate $F_{\mathrm{PFA}}=\frac{5}{2}(\hslash c{\pi }^3∕960)\sqrt{R∕2a^7}$ [19]. The force is plotted for different plate separations of $h∕R=0.28$, 0.6, 1.0, and 2.0. Note that the normalization is different from the cylinder-cylinder PFA in the previous figures.