The Repulsive Casimir Effect

Casimir effect results from fluctuations of the zero-point electromagnetic energy introduced by boundary condition. Since the fluctuations are universal statistical phenomena, Casimir effect plays an important role in different fields of sciences such as atomic and molecular physics, condensed matter physics, quantum field theory, chemistry, biology, astrophysics, cosmology and et al.In 1974, Boyer first proposed a setup of repulsive Casimir force between two parallel plates with nontrivial magnetic properties, one is a perfect conductor and the other is an infinite permeable material. Physicists have developed many methods to calculate the Casimir effect,but only few of them have been used to deal with the repulsive Casimir effect. Physicists have also studied some aspects of Casimir effect between anisotropic dielectric plates, but only obtained numerical results in retarded limit.In this paper, we investigate the influence of finite temperature on the sign of the Casimir force for conducting planes and obtain the analytical expression of the total Casimir force with different temperatures in between and outside the plates. We also employ the quantized surface mode technique and 4×4 matrix formula to calculate the zero-point energy between two anisotropic parallel plates with nontrivial magnetic properties,one is dielectric and the other is permeable. The analytical approximate expressions of Casimir force were obtained in the retarded limit. We can see the force between the anisotropic plates is the sum of the isotropic result F0 and a minor correctional termδF ( a). The torque deriving from the anisotropy of the zero-point energy between the plates makes them rotate towards the configuration in which their optical axes are aligned (or orthogonal) and the energy is smaller. Detailed calculations of the mechanical torque on these two parallel anisotropic plates was presented and the analytical approximate expressions of Casimir torque were obtained. From the point of experiment, with the development of the micro-nanotechnology and quantum demonstration, the repulsive Casimir effect, including the force and torque, might be measured in future.