Quantum Vacuum Fluctuations With Special Boundaries And Brownian Motion

In classical physics, vacuum is regarded as having nothing. However, in quantum michanics and quantum field theory, although the average energy of vacuum is zero, there exist points where energy density can be positive at one time and negative at another because of the uncertainty principle. That is to say that vacuum fluctuates all the time. Due to the existence of vacuum fluctuations, there appear many new phenomena that are absent in classical physics, such as the Casimir effect which has been verfied in experiments. Recently, Yu and Ford have studied the electromagnetic vacuum fluctuations and the Brownian motion of a charged test particle near a reflecting boundary. They have calculated the mean squared fluctuations in both the posotion and the velocity of the test particle.In this paper we will explore vacuum fluctuations and the Brownian motion of a charged test particle between two parallel reflecting boundaries and in a cylindrical space-time. We will calculate the effects of vacuum fluctuations on the motion of a charged test particle and carry out detailed discussions of the results obtained. Our results show that the effects are stronger and easier to observe than that in the single-plate case. In the cylindrical spacetime, Our result for the L >> t case is in principle applicable to determining whether our spacetime has any compactified spatial dimensions.Finally, we will conclude with a summary of our work and an outlook for possible future research.