Hossein Falinejad

Determining the interaction potential between fine particles and a conductive wall is an important problem. By having the interaction potential, the force exerted on the particles by the conductive wall can be calculated. Now, for example, in relation to a dilute fluid (such as air) inside a tank (with conductive walls), the results can be used to remove suspended particles from the fluid. In this thesis, a case of the Casimir-Polder force, the interaction between a neutral polarizable particle and a perfectly conducting wall, is investigated. By substituting the explicit from of electric field operator (in the presence of a perfect conductive wall) in the quadratic Stark formula and taking the expectation value in the thermal state, an integral expression for the interaction energy (in terms of particle polarizability and the distance between the particle and the wall) is obtained. In the complex frequency space, by changing the path of integration from the real to the imaginary axis, the integral expression of the interaction potential is reduced to a summation of some terms. As a result, to calculated the interaction potential, it is only necessary to know the polarizability of the particle at a series of certain frequencies. At low temperatures, for particles close to the wall and at high temperatures for particles far from the wall (compared to the wavelength of thermal photons), simple expressions are introduced for the interaction potential by replacing the frequency dependent polarizability with the static polarizability.