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).