Casimir Effect: a force from nothing
We Study the effect of finite conductivity and geometry of metal plates on Casimir effect based on path integral formalism. Arbitrary deformation is introduced through electromagnetic boundary condition. We calculate both normal and lateral force for specific geometry. We see a crossover in power laws. Strong deviation from PFA result for both normal and lateral force indicates the many body nature of the interaction. We also study the interaction between arbitrary dielectric hetero-structures within the framework of recently developed dielectric contrast perturbation theory. It is shown that periodically patterned dielectric or metallic structures lead to oscillatory lateral Casimir-Lifshitz forces, as well as modulation of normal force as they are displaced with respect to one another. This formalism is useful to calculate the fluctuations induced forces in nanomechanical devices.