Brownian Motion Of A Charged Test Particle Near A Dielectric Half-space Or A Perfectly Reflecting Plane

In classical physics, vacuum is regarded as nothing. However, with the devel-opment of quantum field theory and the vacuum state is not considered as nothingany longer but as a state which has rich structures. One of the most significantcharacteristics is that there exists creation and annihilation of virtual particles andinteractions between them in the quantum vacuum state. That also means that thevacuum state fluctuates all the time. Vacuum fluctuations can lead to many observ-able effects, such as the anomalous magnetic moment, the spontaneous radiation ofthe excited state atoms, and Lamb shift. The effects resulting from vacuum fluc-tuations associated with non-triviality of spacetime topology or with the presenceof boundaries exhibit many novel properties. The Casimir effect is the most well-known example. Recently, Yu and Ford have studied the electromagnetic vacuumfluctuations and the Brownian motion of a charged test particle near a reflectingboundary. They have calculated the mean squared fluctuations in both the positionand the velocity of the test particle. Later on, Yu, Chen, Zhang and Tan studied theBrownian motion near some special kind of boundaries. We will give a brief reviewof their results in the first chapter.In chapter two, we study the random motion of a charged test particle coupled toelectromagnetic vacuum fluctuations near a perfectly reflecting plane boundary witha nonzero classicalconstant velocity in a direction parallel to the plane. We calculatethe mean squared fluctuations in the velocity and position of the test particle takinginto account both fluctuating el.ectric and magnetic forces. The results show thatthe influence of fluctuating magnetic fields is, in general, of the higher order thanthat caused by fluctuating electric fields and is thus negligible. Our results also showthat the dispersions in the normal direction are weakened while those in the paralleldirections are strengthened as compared to the classical static case when the testparticle classically moves away from the boundary. However, if the classical motionreverses its direction, then the dispersions in the normal direction are reinforcedwhile those in the parallel directions get weakened.We study the Brownian motion of a charged test particle near a dielectric half-space in the third chapter. We calculate the mean squared fluctuations inthe velocity and position of the test particle driven by the fluctuating electric andelectromagneticforces. Our results show that, one needs x≈1008.1 for <Δv_z~2>to be within 2% of its limiting value when the dielectric is replaced by a perfectconductor.Finally, we will conclude with a summary of our work and an outlook for possiblefuture research.