Calculation of thermal van der Waals interaction using Casimir-Polder potential

In this study, thermal Casimir-Polder potential is calculated for an atom in the presence of a dielectric sphere using the formula given in terms of the Green’s function. Then, the limiting cases of large and small sphere are investigated. In the limiting case of a large sphere, the formula of thermal potential for an excited atom in the presence of a dielectric half-space and then a perfectly conducting plate is obtained. The limiting case of the small sphere together with the proper replacement of its electric response by the polarizability of a second atom results in the thermal van der Waals interaction potential between the two atoms.