On the Casimir effect from the zero-point energy: a tangential force and its properties

Abstract

We investigate the Casimir effect in the systems that consist of parallel but misaligned finite-size plates from the point of view of zero-point energy. We elaborate the zero-point energies of the radiation field in the perfect conductor systems would generate a tangential Casimir force, and explore the properties and consequences of this tangential force in various conductor systems. Thereafter, we generalize our discussion to dielectrics. After calculating the total zero-point energies of the surface modes in the multilayered systems, we show that the tangential force also exists in dielectrics. We obtain the finite-conductivity corrections to the tangential force for imperfectly conducting plates, and calculate the finite-temperature corrections to the force. The typical strength of the tangential force suggests it might be observable.

Research on the Current Situation of Korean Literature Teaching in Qingdao National University, Shandong Province, China

“…To our knowledge, however, all the experiments performed so far for the (sphere-related) parallel conducting plates, the most elementary Casimir objects, were devoted to the normal Casimir force which is perpendicular to the surfaces. Recently, we discussed that there may be a tangential Casimir force between parallel conducting plates in the misaligned system [15]. This tangential force has unusual properties and was generalized to dielectrics in the same place.…”

“…Therefore, it is of interest to extend the tangential Casimir force to magnetodielectrics. Note that from a technical point of view, in this generalization a major obstacle that we have no established concept for the total zero-point energy of the multilayered system has been removed [15].…”

“…Section III will focus on the theoretical predictions for real metals, which would be crucial for experimental verification of the tangential force. In the previous study, to consider the dissipation effect in real conductors, we calculated the tangential force for gold plates with its optical data [15]. However, the temperature dependence of the dielectric constant was not taken into account there, see, for example, Ref.…”

“…The study on the tangential force could lead us to consider, to a certain extent, a related effect that the Casimir torque of isotropic plates in the parallel configuration [15]. In section IV we shall discuss this torque in detail.…”

“…1, where the widths of the parallel rectangular plates, along the y-axis in the Cartesian coordinate system, are the same. We shall ignore the edge contributions in this system by assuming that their widths L 10 −3 m and min{d 2 , d 4 } 10 −6 m min{b, H − b}, which would be a moderate experimental setting in Casimir physics [15]. FIG.…”