| The Casimir effect is a pure quantum effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy, and it is a direct manifestation of the boundary dependence of quantum vacuum. To making theory confide with experiments, it is necessary to correct the Casimir effect for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness and also the combined effect of these important factors.Since Casimir made the remarkable prediction that there is an attractive force between a pair of uncharged parallel conducting plates due to the vacuum fluctuations of the electromagnetic field, a considerable amount of effort, which varies from the investigation of new geometries and theories to the application of the Casimir effect to alternation technologies, has been put into the study of this important subject. Up to now, we only get the analytical result for two parallel perfectly conducting metal plates. In 1998, R.Golestanian calculated the Casimir effect using the path-integral method, and got the analytical result for two deformed plates. This result did not consider the finite temperature and finite conductivity of the boundary metal, but it provides a new method for the study of the Casimir effect.In this thesis, based on the path-integral method, the corrections to the Casimir energy due to the combined effect of the surface roughness and the finite temperature were calculated. Firstly, the analytical result for two parallel perfectly conducting metal plates at finite temperature is obtained. Secondly, for the specific case of sinusoidally corrugated plates, the lateral Casimir force at finite temperature is obtained, where the amplitude of the lateral Casimir force has a maximum at an optimal wavelength ofλ≈2H with the mean plate distance H. At present, we always use the torsion balance experiment to measure the weak forces. In the experiment, one can design the plates with the area S=10cm×10cm and the beam length 3cm, the room temperature T=300K, the mean separation H=10μm and a=2μm. Then the amplitude of the lateral Casimir force will be about 4×10-10 N. In this condition, the torque will be about 1.2×10-11 Nm. It could be measured since the present sensitivity of the torsion balance is about 10-15Nm, which represents the thermal noise level for a general torsion balance. |
